ansys high-frequency electromagnetic analysis guide

ANSYS High-FrequencyElectromagneticAnalysis GuideANSYS Release 9.0

002114November 2004

ANSYS, Inc. is aUL registeredISO 9001: 2000Company.

ANSYS High-FrequencyElectromagnetic Analysis Guide

ANSYS Release 9.0

ANSYS, Inc.Southpointe275 Technology DriveCanonsburg, PA [email protected]://www.ansys.com(T) 724-746-3304(F) 724-514-9494

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Table of Contents

1. Overview of High-Frequency Electromagnetic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1–12. Finite Element Analysis of High-Frequency Electromagnetic Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–13. Elements Available in High-Frequency Electromagnetic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–14. Performing a High-Frequency Harmonic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–1

4.1. Creating the Physics Environment ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–24.1.1. Specifying Element Types ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–24.1.2. Specifying the System of Units .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–34.1.3. Specifying Material Properties ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–3

4.2. Building the Model, Assigning Region Attributes, and Meshing ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–44.2.1. Defining Model Region Attributes ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–44.2.2. Meshing the Model .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–4

4.3. Applying Boundary Conditions and Excitations (Loads) .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–54.3.1. Applying Boundary Conditions ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–5

4.3.1.1. Perfect Electric Conductor (PEC) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–64.3.1.2. Perfect Magnetic Conductor (PMC) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–74.3.1.3. Surface Impedance ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–74.3.1.4. Perfectly Matched Layers (PML) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–94.3.1.5. Periodic Boundary Conditions ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–12

4.3.2. Applying Excitation Sources ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–154.3.2.1. Excitation Port .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–164.3.2.2. Current Source ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–214.3.2.3. Plane Wave Source ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–234.3.2.4. Surface Magnetic Field Source ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–234.3.2.5. Electric Field Source ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–244.3.2.6. Equivalent Source Surface ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–254.3.2.7. Lumped Circuits .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–26

4.4. Solving Harmonic High-Frequency Analyses ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–284.4.1. Defining the Analysis Type ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–284.4.2. Defining Analysis Options and Estimating Computer Resources ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–284.4.3. Setting the Analysis Frequencies ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–294.4.4. Defining a Scattering Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–294.4.5. Defining a Radiation Analysis for a Phased Array Antenna ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–294.4.6. Starting the Solution ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–294.4.7. Finishing the Solution ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–32

4.5. Postprocessing Harmonic High-Frequency Analyses ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–324.5.1. Reviewing Results .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–324.5.2. Commands to Help You in Postprocessing ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–334.5.3. Calculating Near Fields, Far Fields, and Far Field Parameters ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–34

4.5.3.1. Near Fields ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–344.5.3.2. Far Fields and Far Field Parameters ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–354.5.3.3. Symmetry ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–364.5.3.4. Radiation Solid Angle ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–37

4.5.4. Calculating Circuit Parameters for High-Frequency Devices ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–384.5.4.1. Scattering Parameters (S-Parameters) .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–384.5.4.2. Reflection Coefficients in a COAX Fed Device ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–394.5.4.3. Power and Frequency Selective Surface Parameters ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–394.5.4.4. Voltage, Current, and Impedance ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–394.5.4.5. Smith Chart and Network Parameter Conversion ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–41

5. Performing a Modal High-Frequency Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–15.1. Entering the SOLUTION Processor and Specifying the Modal Analysis Type ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–2

ANSYS High-Frequency Electromagnetic Analysis Guide . ANSYS Release 9.0 . 002114 . © SAS IP, Inc.

5.2. Setting Options for Modal Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–25.3. Specifying Modes to Expand ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–35.4. Applying Boundary Conditions ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–35.5. Solving a Modal High-Frequency Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–35.6. Calculating Propagating Constants ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–45.7. Reviewing Modal High-Frequency Results .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–4

6. Adaptive Remeshing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6–1

I. Basic Wave Radiation Examples

II. Basic Wave Propagation Examples

III. Basic Wave Resonance Examples

IV. Basic Wave Scattering Examples

V. Advanced Wave Radiation Examples

VI. Advanced Wave Propagation Examples

VII. Advanced Wave Resonance Examples

VIII. Advanced Wave Scattering Examples

Index ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index–1

List of Figures2.1. Computational Domain for a FEM Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–32.2. Open Microstrip Structure ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–42.3. Equivalent Circuit .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–52.4. Open Microstrip Structure Model .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–63.1. Mixed Elements ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–13.2. Object with a Large Aspect Ratio ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–24.1. Flow Chart for a Harmonic Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–14.2. Electric Field Distributions ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–54.3. Solid and Finite Element Models .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–54.4. PEC Boundary Condition ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–64.5. PMC Boundary Condition ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–74.6. Microstrip Structure with PML Regions ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–94.7. PML Region Attached to Interior Region ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–104.8. Attenuation Distribution ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–104.9. Buffer Elements in Interior Domain ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–114.10. Distance between Source/Objects and PML Region ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–124.11. Arbitrary Infinite Periodic Structure ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–124.12. Unit Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–134.13. Periodic Array Models .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–154.14. Exterior and Interior Ports .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–184.15. Soft Source Port .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–184.16. Hard Source Port .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–184.17. IMPD Option for Waveguide Port .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–184.18. HARD Option for Waveguide Port .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–19

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4.19. Interior Soft Source and Extraction Ports .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–194.20. Transmission Line Model .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–204.21. Model for Scattering Analysis of Periodic Structure ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–204.22. Current Excitation ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–224.23. Transmission Line Model with Current Excitation ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–224.24. Spherical Coordinates ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–234.25. Exterior Hard Surface Magnetic Field Excitation ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–244.26. Soft Interior Surface Magnetic Field Excitation ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–244.27. Equivalent Source Surface ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–254.28. Lumped Circuits .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–274.29. 2-Port Lumped Network ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–274.30. Equivalent Lumped Circuit Model .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–284.31. Spherical Coordinates ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–354.32. Solid Angle - Dipole Antenna ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–374.33. Solid Angle - Monopole Antenna above Ground Plane ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–384.34. Multi-port Network ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–384.35. Voltage Paths for Transmission Lines ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–404.36. Current Paths for Transmission Lines ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–404.37. Ten-Degree Symmetry Model of a Coaxial Waveguide ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–415.1. Flow Chart for a Modal Analysis .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5–21. Symmetry Model of a Coax Waveguide ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91. Magnetic Field in Coax ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172. Electric Field in Coax ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181. Teflon Filled Cavity ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211. Magnetic Field Vector Display of TE101 Mode ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262. Electric Field Vector Display of TE101 Mode ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271. 3×4 JRM Array and FEA Model of Unit Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392. S-Parameter of JRM Array with E-Plane Scan at 9.25 GHz ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423. Directive Gain of Unit Cell with E-Plane Scan at 9.25 GHz ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434. Directive Gain of a 25×25 JRM Array with E-Plane Scan at 9.25 GHz ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 441. 5×5 Lee-Jones Array and FEA Model of Unit Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452. Periodic Boundary Condition for Lee-Jones Array ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453. S-Parameter of Lee-Jones Array with E-Plane Scan at 9.5 GHz ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481. Line-fed Microstrip Patch Antenna Geometry and FEA Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502. S-Parameter of Line-Fed Microstrip Patch Antenna ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543. Contour of Electric Field Magnitude at 7.5 GHz ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551. Waveguide Radiator with No Flare ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572. Radiation Pattern of Waveguide Radiator Without Flare on E-Plane ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603. Electric Field Contour of Waveguide Radiator Without Flare ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 611. Contour of the Radiated Electric Field of a Half Wavelength Dipole ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 662. Far Electric Field of a Half Wavelength Dipole on E-Plane at r = 10 m ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 673. Radiation Pattern of a Half Wavelength Dipole on E-Plane ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 684. Directive Gain of a Half Wavelength Dipole on E-Plane ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 691. Top and Side views of Low-Pass Filter .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 732. S11 of microstrip low-pass filter .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 773. S21 of microstrip low-pass filter .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 781. Side View and FEA Model of Filter (Dimensions are in mm) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 792. |S11| of Three-Stub Waveguide Filter .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 823. Electric Field Contour of Three-Stub Waveguide Filter at 15 GHz ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 831. Three-layer Interconnect ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 862. S11 of the Multi-Layer Microstrip Interconnect ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 903. S21 of the Multi-Layer Microstrip Interconnect ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91


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4. Electric Field Contour of Multi-Layer Microstrip Interconnect at 6.5 GHz ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 921. Microstrip Meander Line (Top View) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 952. S11 of the Microstrip Meander Line ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 993. The Contour of Electric Field Magnitude ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1001. Waveguide with Ridge Discontinuity (Dimensions are in mm) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1012. |S21| of the Rectangular Waveguide with a Ridge Discontinuity ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1043. Electric Field Contour of the Waveguide with a Ridge at 15 GHz ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1051. Waveguide with Dielectric Post (Dimensions are in mm) ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1072. Initial Mesh Density .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1093. Mesh Density after First Mesh Refinement Iteration ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1104. Mesh Density after Second Mesh Refinement Iteration ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1115. Mesh Density after Third Mesh Refinement Iteration ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1126. |S11| of Rectangular Waveguide with a Dielectric Post from 8 GHz to 12 GHz ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1131. 3-D Parallel-plate Waveguide Model .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1152. 1-D Transmission Line Impedance Load ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1153. Lumped Circuit Loads ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1164. Shunt RCL Circuit .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1161. T-type Transmission Line Network ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1192. S11 on Smith Chart .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1203. Y11 on Smith Chart .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1214. S11 and S21 Magnitude vs. Frequency ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1225. Z11 and Z21 Magnitude vs. Frequency ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1231. Geometry and FEA Model of Dielectric Resonator ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1272. The Electric Field of TM01δ Mode in a DR with a Metallic Enclosure ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1293. The Electric Field of HEM Mode in a DR with a Metallic Enclosure ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1304. The Electric Field of TE01δ Mode in a DR with a Metallic Enclosure ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1311. Geometry and FEA Model of the Microstrip Line ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1332. Electric field of the Fundamental Mode in the Microstrip Line at 20 GHz ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1361. FEA Model for Scattering Analysis of a Lossy Dielectric-Coated Metallic Sphere ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1402. Scattering Electric Field Contour of the Lossy Dielectric-Coated Metallic Sphere ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1423. Normalized RCS of the Lossy Dielectric-Coated Metallic Sphere on E-plane and H-plane ... . . . . . . . . . . . . . . . . . . . . . . 1431. FEA Model for Scattering Analysis of a Dielectric Sphere ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1452. RCS of the Dielectric Sphere ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1473. Contour of the Scattering Electric Field from a Dielectric Sphere ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1481. Scattering Electric Field Contour from the Metallic Cube ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1522. Normalized RCS of the Metallic Cube on E-Plane and H-Plane ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1531. FEA Model for Scattering Analysis of a Dielectric-Coated Metallic Sphere ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1562. Scattering Electric Field Contour of The Dielectric-Coated Metallic Sphere ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1583. Normalized RCS of the Dielectric-Coated Metallic Sphere on E-Plane ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1591. Unit Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1611. Dielectric Grating ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1652. Reflection Coefficient of Dielectric Grating ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

List of Tables2.1. Physical and Model Features ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2–33.1. High-Frequency Elements ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3–14.1. Element DOFs ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–24.2. Material Guidelines ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–44.3. High-Frequency Boundary Conditions ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–64.4. Surface Impedance Boundary Conditions ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–7

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4.5. High-Frequency Excitation Sources ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–154.6. Port Types ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–174.7. HFPORT VALUE Arguments[] .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–204.8. Postprocessing Commands ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–334.9. Plotting Commands .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4–34


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Chapter 1: Overview of High-FrequencyElectromagnetic AnalysisThe ANSYS program supports high-frequency electromagnetic analysis. This type of analysis calculates thepropagation properties of electromagnetic fields and waves in a given structure. The ANSYS program supportsboth time-harmonic and modal high-frequency analysis.

Except in a few cases, most-high-frequency devices use electromagnetic waves to carry information. For thisreason, frequency plays a vital role in the design of such devices. High-frequency electromagnetic field analysissimulates the electromagnetic phenomena in a structure when the wavelength of the signal is of the same orderof magnitude or smaller than the dimensions of the model. The high-frequency band ranges from hundreds ofMHz to hundreds of GHz.

In general, you use high-frequency electromagnetic field analysis to solve interior problems or exterior problems.For interior problems, an electromagnetic field propagates or oscillates in a closed structure such as an acceler-ator chamber, a microwave filter, or a high-speed electronic package. The oscillating frequencies and scatteringmatrix parameter (S-parameter) are usually investigated. For exterior problems, an electromagnetic wave radiatesinto open space or it is scattered by an object in the open domain. Examples are phased antenna arrays andradar reflection from a metallic object. The radiation pattern, directive gain, or radar cross section (RCS) is usuallyinvestigated.


Chapter 2: Finite Element Analysis ofHigh-Frequency Electromagnetic FieldsIn practice, finite element analysis (FEA) is one of the most successful frequency domain computational methodsfor electromagnetic field simulation. It provides the capabilities you need to model any geometry and any ma-terials of composition. This material capability is particularly important in electromagnetic field engineeringsince most applications dealing with antennas, microwave circuits, scattering devices, motors, generators, etc.require simulation of nonmetal composite materials. Throughout the frequency spectrum, FEA enjoys widepopularity. It plays a major role in electromagnetic engineering applications such as:

• Microwave circuits and devices

• High-speed digital electronic circuits

• Antennas

• Electromagnetic Interference (EMI) / Electromagnetic Compatibility (EMC)

• Biomedical applications

The ANSYS high-frequency electromagnetic simulator (ANSYS Emag HF) uses tangential vector finite elementtechnology. It provides 3-D elements to perform harmonic analyses (see Chapter 4, “Performing a High-FrequencyHarmonic Analysis”) and 2-D and 3-D elements to perform modal analyses (see Chapter 5, “Performing a ModalHigh-Frequency Analysis”) analyses, with an exp (jωt) dependence assumed.

ANSYS Emag HF has a preprocessor, a solver, and a postprocessor. The preprocessor provides facilities for de-scribing the high-frequency structure to be simulated, the excitation to be applied, and the boundary conditionsor other constraints to be imposed. It includes the following:

Geometry Tool

• Solid Model using Built in Modeler and APDL

• CAD File Input via Connection Products

Meshing Tool

• Automatic Meshing

• Manual Meshing

• Adaptive Meshing

Tangential Vector Based Element Library

• 1st & 2nd Order Tetrahedral, Quadrilateral, and Wedge Elements

• 1st Order Pyramid Elements

• 1st & 2nd Order Quad and Triangle Elements

Material Model

• Lossy/Lossless Isotropic Material

• Lossy/Lossless Anisotropic Material

Boundary Conditions


• Perfect Electric Conductor (PEC)

• Standard Impedance Boundary Conditions (SIBC)

• Matched Waveguide Port

• Perfectly Matched Layers (PML)

• Periodic Boundary Conditions

Excitation Sources

• Waveguide Modal Source

• Volume, Surface, Line, and Point Current Density Source

• Plane Wave Source

• Surface and Line Electric Field Source

• Surface Magnetic Field Source

The solver generates the element descriptions, assembles the element matrices into global finite element matrices,imposes the appropriate boundary conditions, constraints, and excitation sources, and then solves the equations.It consists of the following:

Modal Analysis

• Lanczos Eigenvalue Solver

Harmonic Analysis

• Sparse Direct Solver

• Incomplete Cholesky Conjugate Gradient (ICCG) Solver

• Fast Frequency Sweep Solver

The postprocessor provides facilities to calculate parameters and visualize results. This includes the following:

• Electromagnetic Field Vectors and Contour Patterns

• Cut-off Frequency, Propagating Constant, and Resonant Frequency

• Quality Factor (Q-Factor)

• S-parameters and Touchstone File

• Voltage, Current, and Characteristic Impedance

• Conducting Current Density Distribution

• Near and Far Electromagnetic Field Extension

• Radar Cross Section (RCS)

• Antenna Parameters (Radiation Pattern, Directive Gain, Directivity, Radiation Power, Radiation Gain, Radi-ation Efficiency)

• Time-Averaged Power

• Joule Heat

ANSYS Emag HF is a frequency domain simulator that can analyze a large class of high-frequency devices andsystems. This includes uniform wave-guiding structures, cavity resonators, antennas, and antenna arrays. A high-

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Chapter 2: Finite Element Analysis of High-Frequency Electromagnetic Fields

frequency electromagnetic analysis can be coupled with another field analysis to simulate complicated physicalphenomena, such as RF heating.

To solve the full set of Maxwell's differential equations that govern high-frequency electromagnetic fields, thefinite element method discretizes the infinite continuous wave propagating space into a finite element model.Boundary conditions and excitations are applied to the solid model or finite element entities.

A typical electromagnetic configuration simulated by FEA is shown in Figure 2.1: “Computational Domain for aFEM Analysis”.

Figure 2.1 Computational Domain for a FEM Analysis

! "#$&%' ( *) *) ! + *), .- ( *)/ ")0! 12+ *)3

45! *) ! 6 / 7 2+98;: < = ! *)>! ! / - + ( $?

@60 &;) / $?

#+ - ) $?#.! ! ),A / ;) / B

C

D

E

F

GH H

HH

II

The high-frequency FEA procedure uses a weak integral form of the electric field vector Helmholtz equation asthe basis. For improved accuracy for scattering applications, the scattered field is investigated instead of thetotal electric field. Refer to High-Frequency Electromagnetic Field Simulation in the ANSYS, Inc. Theory Referencefor more information on the pure scattering field formulation.

The ANSYS high-frequency elements use the tangential vector finite element method. The vector electric fieldconsists of the linear combination of the vector basis functions. The associated coefficients are the degree offreedom (DOF) of the final matrix equation. The DOFs of the tangential vector method are the projections of thevector electric field on the edges and faces of the element. For example, for the first order tetrahedral element,its DOFs are the projection of the electric field along the edge of the element at the middle of the edge:

DOF = t ⋅ E at middle of edge

where t is the unit tangential vector of the edge.

Refer to the ANSYS, Inc. Theory Reference for details on this method.

As in any other type of ANSYS analysis, you must build a finite element model that correctly represents the system.The following table shows how physical features of an electromagnetic system correspond with model features.

Table 2.1 Physical and Model Features

Model FeaturesPhysical Features

Finite Element MeshElectromagnetic Structures and Space

Perfect Electric Conductor (PEC) Boundary ConditionLossless Metallic Surface


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Model FeaturesPhysical Features

Standard Impedance Boundary Condition (SIBC)Non-perfect Electric Conductor, Air-Dielectric Interface,Dielectric Coating on PEC

Perfect Magnetic Conductor (PMC) Boundary Condition orPEC

EM Field Symmetry

Absorbing Boundary ConditionEM Field at Infinity, Matching Load

Impressed Current DensityCurrent Source, Metallic Wire with Conducting Current, Excit-ation Gap

Modal FieldMatched Voltage Source

For an enclosed structure, you must mesh the entire structure. For propagation, radiation, and scattering problems,the electromagnetic field extends to infinity. You must trunicate the infinite space using absorbing boundaryconditions. Usually, the inside of an electric conductor is not meshed because a high-frequency electromagneticwave can only penetrate the surface a short distance.

If the ohmic loss does not play a significant role or is not a major concern in the design, a perfect electric conductor(PEC) is a very good approximation for metallic objects. The tangential electric field vanishes on the surface ofa PEC. It leads to a constraint condition DOF = 0 on the surface.

Often, meshing the skin of a non-perfect electric conductor or a dielectric coating on a PEC leads to extremelysmall elements inside of those layers. Instead of meshing those very small layers, apply a standard impedanceboundary condition on those surfaces to obtain a good approximation.

You can reduce the size of your model by taking symmetry of the electromagnetic field into account. If the tan-gential electric field is zero (that is, only the normal electric field exists on the symmetry plane), apply a PECboundary condition to the symmetry plane. If the tangential magnetic field is zero (that is, only the normalmagnetic field exists on the symmetry plane), apply a PMC boundary condition to the symmetry plane. In a ANSYShigh-frequency analysis, a PMC boundary condition is a natural boundary condition. You do not need to applya constraint condition to a PMC symmetry plane.

If an electromagnetic wave radiates into infinity, you must use an absorbing boundary condition to truncate thefinite computational domain. If an electromagnetic wave in a propagating system is absorbed by a matchingload, you must replace that matching load with an absorbing boundary condition.

The following example of an open microstrip structure with a capacitance gap shows you how to create amodel.

Figure 2.2 Open Microstrip Structure

The equivalent circuit including a matched source, s-parameter extractor, and matching load is shown in Fig-ure 2.3: “Equivalent Circuit”.



Figure 2.3 Equivalent Circuit

To create the model, you need to make use of the characteristics of electromagnetic fields and simplify themodel as follows:

• The thickness of the microstrip is assumed to be small compared to the other dimensions and is ignored.The ohmic loss of the microstrip is also assumed to be small and is ignored. These assumptions lead to aPEC microstrip with zero thickness.

• For the fundamental mode, the electric field is assumed to be symmetric about a vertical center line onthe cross section. Accordingly, the analysis can be done on a half model. A PMC boundary is applied tothe symmetry plane.

• Since the electromagnetic field decays rapidly in the transverse direction with the distance from a microstrip,PEC boundaries are added to enclose the open space at a proper separation distance. The distance fromthe microstrip to the top PEC boundary should be at least equal to two times the height of the substrate.The distance from the microstrip to the side PEC boundary should be at least two times the width of themicrostrip.

• The wave source is assumed to be a matched electric current source and the output of the two-port networkis terminated by a matching load (see Figure 2.3: “Equivalent Circuit”). Absorbing boundary conditionsare added to represent the matching loads.

• The real current source will be equivalent to the impressed current density. Considering the electric fielddistribution on the transverse cross section, the line current density pointing from the microstrip to theground will excite the fundamental mode in the microstrip. Since the line current density source launchesa bidirectional electromagnetic wave, an absorber must be located behind the line current density sourceto prevent a reflected wave.

These electromagnetic field characteristics and assumptions yield the following unmeshed model for the openmicrostrip structure.



Figure 2.4 Open Microstrip Structure Model

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6879 2&% 7 (&%

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Chapter 3: Elements Available inHigh-Frequency Electromagnetic AnalysisThree elements are available for high-frequency analysis: HF118, HF119, and HF120. HF118 is a 2-D element thatapplies only to modal analyses. You can use it to compute dispersion characteristics of high-frequency transmissionlines, including the cutoff frequencies and the propagating constants for multiple modes. HF119 and HF120 are3-D elements. You can perform harmonic analyses or modal analyses with them.

Table 3.1 High-Frequency Elements

DOFsNumber of Nodes and Shape2-D or 3-DElement

Projection of the electric field E (ANSYS degree offreedom "AX")

8-Node Quadrilateral with triangu-lar degeneracy

2-DHF118


10-Node Tetrahedral3-DHF119


20-Node Hexahedral with pyramidand prism degeneracy

3-DHF120

You can use one element shape (hexahedral, wedge, pyramid, or tetrahedral) or any combination of shapes inyour 3-D model. Figure 3.1: “Mixed Elements” (a) shows a mix of hexahedral and wedge elements and (b) showsa mix of hexahedral, pyramid, and tetrahedral elements. The pyramid elements are transitional elements betweenthe hexahedral and tetrahedral elements.

Figure 3.1 Mixed Elements

As an example, the following command input listing creates mixed hexahedral and wedge elements:

/prep7et,1,120 ! define hexahedral elementet,11,200,5 ! define 2-D 6-node triangle mesh elementet,12,200,7 ! define 2-D 8-node quadrilateral mesh elementrect,0,1,0,1 ! create area 1rect,1,2,0,1 ! create area 2aglue,all ! glue areas togetheresize,0.25 ! define the element sizeasel,s,loc,x,0,1 ! select area 1type,11 ! select triangle element typemshape,1 ! define the triangle element shapeamesh,all ! mesh area 1 with triangle mesh elementasel,s,loc,x,1,2 ! select area 2type,12 ! select quadrilateral mesh element type


mshape,0 ! define the element quadrilateral shapeamesh,all ! mesh area 2 with quadrilateral mesh elementallsesize,,4 ! define element operation type,1 ! select hexahedral elementasel,s,loc,z,0 ! select 2-D elementvext,all,,,0,0,1 ! create 3-D elements by extruding 2-D elementsfini

As an example, the following command input listing creates mixed hexahedral, pyramid, and tetrahedral elements:

/prep7ch=10.16e-3cw=22.86e-3cl=2.e-2h=2.e-3et,1,hf120,1 ! define hexahedral elementet,2,hf119,1 ! define tet elementblock,-cw/2,0,-ch/2,ch/2,0,cl/2 ! create volume 1block,-cw/2,0,-ch/2,ch/2,cl/2,cl ! create volume 2vglue,all ! glue volumes togetheresize,h ! define element sizetype,1 ! select hexahedral element typemshape,0,3d ! define hexahedral meshmshkey,1 ! use mapped meshvmesh,1 ! mesh first volumemshape,1,3d ! define tetrahedral elementmshkey,0 ! use free meshingvmesh,3 ! mesh second meshtchg,120,119,2 ! covert degen. hexahedral element into tetrahedral elementfini

Although a geometrically complex structure can be meshed with tetrahedral elements, it may require manyelements and that may lead to simulation failure because of computer resources. Even a regular shaped volumemay require many tetrahedral elements if it has a very large aspect ratio. Here, hexahedral or wedge elementswould be a better choice. Figure 3.2: “Object with a Large Aspect Ratio” illustrates this difference. It shows thatthe number of tetrahedral elements (a) is much larger than the number of hexahedral elements (b), if a similarmesh density is maintained on the transverse cross section.

Figure 3.2 Object with a Large Aspect Ratio

You can automatically refine a model meshed with HF119 elements. To decrease discretization error, theHFEREFINE macro refines elements that exceed a specified error limit. Moreover, based on the error indicatedby HFEREFINE, you can manually refine a model meshed with HF120 elements. For more information on thiscapability, see Chapter 6, “Adaptive Remeshing” in this guide and HFEREFINE in the ANSYS Commands Reference.


Chapter 3: Elements Available in High-Frequency Electromagnetic Analysis

See HF118, HF119, and HF120 in the ANSYS Elements Reference for more details on these elements. Refer to High-Frequency Electromagnetic Field Simulation in the ANSYS, Inc. Theory Reference for additional information onthe tangential vector finite element method and vector basis functions.

You cannot use other ANSYS Emag electromagnetic elements in a high-frequency analysis. They are not basedon a full-wave formulation. They do not account for displacement current.

Chapter 3: Elements Available in High-Frequency Electromagnetic Analysis


Chapter 4: Performing a High-FrequencyHarmonic AnalysisAs in any other type of ANSYS analysis, a harmonic high-frequency electromagnetic analysis consists of thesesteps:

• Create a physics environment.

• Build a model.

• Assign regional attributes to the model and mesh it.

• Apply boundary conditions and excitations (loads).

• Obtain a solution.

• Review the results.

The following flowchart illustrates these steps.

Figure 4.1 Flow Chart for a Harmonic Analysis


4.1. Creating the Physics Environment

To begin, specify a jobname and a title for your analysis. If you are using the ANSYS Graphical User Interface (GUI)and you wish to perform high-frequency electromagnetic analysis, one of the first things you should do uponentering the GUI is choose the following path: Main Menu> Preferences and select High Frequency underElectromagnetic. Doing this ensures that all of the GUI options you need for this type of analysis will be availableto you.

4.1.1. Specifying Element Types

Use either of the following to specify element type numbers and key options for HF119 and HF120:Command(s): ET,ITYPE,Ename,KEYOPT(1),KEYOPT(2),KEYOPT(3),KEYOPT(4),KEYOPT(5)GUI: Main Menu> Preprocessor> Element Type> Add/Edit/Delete

KEYOPT(1) defines the polynomial order of the elements. KEYOPT(1) = 0 or 1 defines a first order element witha 0.5 order polynomial vector basis function. KEYOPT(1) = 2 defines a second order element with a 1.5 orderpolynomial vector basis function. Greater accuracy is obtained using higher order elements (KEYOPT(1) = 2) atthe expense of additional degrees of freedom internally generated by the element. The second order elementsare not available for pure scattering or periodic boundary condition problems. The following table shows thenumber of DOFs per element.

Table 4.1 Element DOFs

Number of DOFs Per ElementElement Shape

2nd Order1st Order

124Quadrilateral

83Triangle

206Tetrahedral

5412Hexahedral

369Wedge

Not available8Pyramid

You cannot mix first and second order elements in a model. Both first and second order elements have midsidenodes to follow the curvature of a model. If you use MESH200 elements to generate 3-D high-frequency electro-magnetic elements (HF119 or HF120) choose one of theMESH200 options for midside nodes, KEYOPT(1) = 5 for3-D triangle elements or KEYOPT(1) = 7 for quadrilateral elements.

KEYOPT(4) allows you to specify element types for special high-frequency electromagnetic applications. KEYOPT(4)= 0 defines the normal element (default). KEYOPT(4) = 1 defines an electromagnetic wave absorbing elementreferred to as a perfectly matched layer (PML) element. KEYOPT(4) = 2 defines a special scattering element. Youneed to specify KEYOPT(4) = 2 for the region of the domain receiving the reflected wave when you are using asoft magnetic field excitation source that propagates in one direction (BF,,H option). For example, the followingcommand input listing defines first order normal and PML elements:

et,1,119,1,,,0 ! define normal tetrahedral elementet,1,119,1,,,1 ! define PML tetrahedral element

See Section 4.3.1.4: Perfectly Matched Layers (PML) for information on the PML element. See Section 4.3.2.4:Surface Magnetic Field Source for information on the scattering element and soft source magnetic field excitation.

The HF118 element applies only to modal analyses. Chapter 5, “Performing a Modal High-Frequency Analysis”describes this type of analysis in detail.


Chapter 4: Performing a High-Frequency Harmonic Analysis

4.1.2. Specifying the System of Units

HF Emag always uses the MKS system. In the MKS system of units, free-space permeability is set to 4 π x 10-7

henries/meter and free-space permittivity is set to 8.85 x 10-12 F/m.

See the EMUNIT command in the ANSYS Commands Reference for more details. The EMUNIT command defaultsto the MKS system of units. See Section 1.3: System of Units in the ANSYS Coupled-Field Analysis Guide for detailson MKS units.

4.1.3. Specifying Material Properties

Use either of the following to specify material properties:Command(s): MP,LAB,MAT,C0,C1,C2,C3,C4GUI: Main Menu> Preprocessor> Material Props> Material Models

High-frequency analysis requires three material properties: relative permeability diagonal tensor (MURX, MURY,MURZ), relative permittivity diagonal tensor (PERX, PERY, PERZ), and resistivity (inverse of conductivity) diagonaltensor (RSVX, RSVY, RSVZ). For isotropic materials, MURY and MURZ default to MURX; likewise, PERY and PERZdefault to PERX and RSVY and RSVZ default to RSVX. X, Y, and Z refer to the orthogonal coordinates in the elementcoordinate system specified by the ESYS command. The permeability and permittivity must be relative valueswith respect to their free-space definitions. Permeability of the material is equal to the product of the free-spacepermeability and the relative permeability constant (MURX, MURY, MURZ). Permittivity of the material is equalto the product of the free-space permittivity and the relative permittivity constant (PERX, PERY, PERZ).

For an isotropic lossy material, you can define the lossy characteristics of the material by the loss tangent (LSST).Loss tangent (tan δ) is defined by:

tan δ = σ/(2πfεoεr)

where:

f = frequency (Hz)σ = conductivity (S/m)εo = free-space permittivity (F/m)

εr = relative permittivity

If a complex permittivity is defined as:

εr = εr' - J.εr”

the loss tangent is defined by:

tan δ = εr”/ εr'

If a complex permittivity is defined as:

εr = εr' + jεr”

the loss tangent is defined by:

tan δ = - εr”/ εr'

The following table gives some guidelines for specifying material properties.

Section 4.1: Creating the Physics Environment


Table 4.2 Material Guidelines

GuidelineMaterial

Specify a relative permeability and a relative permittivity of 1.0.Air

Specify a relative permeability µr and a relative permittivity εr, which can be

either isotropic or anisotropic (i.e., a diagonal tensor in the predefined elementcoordinate system).

Lossless Dielectric

Specify a relative permeability µr, a relative permittivity εr, and a resistivity

(1/conductivity), which can be either isotropic or anisotropic (i.e., a diagonaltensor in the predefined element coordinate system).

Lossy Dielectric with aknown Conductivity

Specify a relative permeability µr, a relative permittivity εr, and a loss tangent.

If you specify both a resistivity and a loss tangent, only the loss tangent will beused.

Lossy Dielectric with aknown Loss Tangent

For example, the following command input listing defines two isotropic lossy materials:

mp,perx,1,2.5 ! the relative permittivity of material 1 is 2.5mp,murx,1,1.0 ! the relative permeability of material 1 is 1.0mp,rsvx,1,1.E-4 ! the resistivity of material is 1.E-4mp,perx,2,9.8 ! the relative permittivity of material 2 is 9.8mp,murx,1,2.0 ! the relative permeability of material 2 is 2.0mp,lsst,2,0.5 ! the loss tangent of material 2 is 0.5

If you want to calculate the specific adsorption rate (SAR) of a lossy material, you must specify the mass densityof the material (Lab = DENS).

See the MP command in the ANSYS Commands Reference for more details.

4.2. Building the Model, Assigning Region Attributes, and Meshing

Use the ANSYS preprocessor (PREP7) to create the model geometry. This model building process is common tomost analyses. See the ANSYS Modeling and Meshing Guide for details.

4.2.1. Defining Model Region Attributes

Attributes assigned to a model prior to meshing include element type and material number. You assign theseto the region using the VATT command for volumes to be meshed with 3-D elements (HF119 and HF120). Usedifferent material numbers to distinguish different material regions.

4.2.2. Meshing the Model

Use the ANSYS preprocessor (PREP7) to mesh the solid model geometry. This meshing is common to most analyses.See the ANSYS Modeling and Meshing Guide for details.

For a full-wave FEA formulation, the mesh must be fine enough to minimize numerical dispersion effects fromfinite discretization. In general, it should have at least 10 elements per propagating or resonant wavelength forthe material.

Note — If the propagating wavelength is 1 cm in free space, the wavelength is 0.5 cm in a dielectric withrelative permittivity εr = 4.

To obtain accurate S-parameters, the elements located at the ports should have as close to a 1:1 aspect ratio aspossible in the direction of the wave propagation.



You should also employ your knowledge of electromagnetic fields to determine an appropriate mesh density.For example, consider the following electromagnetic fields shown in Figure 4.2: “Electric Field Distributions” :

• (a) a TE10 mode on the transverse cross section of a rectangular waveguide

• (b) a fundamental mode on the transverse cross section of a microstrip structure

Since the electric field of a TE10 mode varies sinusoidally along the wide side of a rectangular waveguide and isuniform along the narrow side, there should be at least five elements along the wide side. Since the electromag-netic field concentrates under the metallic microstrip, to obtain the acceptable results, there should be at leastfour elements along the thickness of the substrate and at least five elements along the width of the microstrip.

Figure 4.2 Electric Field Distributions

4.3. Applying Boundary Conditions and Excitations (Loads)

You can apply most boundary conditions and excitations to a harmonic high-frequency analysis either on thesolid model entities or on the finite element model entities. Applying boundary conditions to the solid model isadvantageous in that they are independent of the underlying finite element mesh. Subsequent mesh refinementdoes not require reapplying the boundary conditions and excitation if adaptive meshing is used. For more in-formation, see Chapter 6, “Adaptive Remeshing” in this guide and HFEREFINE in the ANSYS Commands Reference.

Figure 4.3 Solid and Finite Element Models

4.3.1. Applying Boundary Conditions

Table 4.3: “High-Frequency Boundary Conditions” shows the available boundary conditions for a high-frequencyanalysis. See the detailed explanations of these boundary conditions below. For general information on applyingboundary conditions see Chapter 2, “Loading” in the ANSYS Basic Analysis Guide.

Section 4.3: Applying Boundary Conditions and Excitations (Loads)


Table 4.3 High-Frequency Boundary Conditions

Finite Element ModelEntities

Solid Model EntitiesBoundary Condition

NodesLines or AreasPerfect Electric Conductor (PEC)

None required [1]None required [1]Perfect Magnetic Conductor (PMC)

NodesAreasStandard Impedance Boundary Condition (SIBC)

ElementsNot ApplicablePerfectly Matched Layers (PML)

NodesAreasPeriodic Boundary Condition (PBC)

1. You do not need to specify a PMC boundary condition because it is a natural boundary condition.

4.3.1.1. Perfect Electric Conductor (PEC)

A perfect electric conductor (PEC) boundary (also called Electric Wall) is a surface on which the tangential com-

ponent of the vector electric field (rE

t) vanishes. Use boundary (DOF) constraints to define PEC boundary conditions

on the solid model or finite element model entities. You can remove a neighboring conductor from the modeland replace it with a PEC boundary condition, if the losses of the metallic conductor can be ignored. In manyapplications, a thin metallic object (for example, a metallic strip of a microstrip structure) simplifies to an infin-itesimally thin metallic sheet with a PEC boundary condition.

Figure 4.4 PEC Boundary Condition

µ,ε

!

µ,ε∞ → σ

To reduce your model size, you can also apply PEC boundary conditions to symmetry planes that have a zerotangential component of the vector electric field. You must know the electric field distribution before you cantake advantage of the symmetry.

To specify PEC boundary conditions, you can use the DL or DA command to set the AX DOFs to zero on thesurface of the model or you can use the D command to set the AX DOFs to zero on the nodes of the finite elementmodel. Alternatively, you can specify a PEC boundary condition from the GUI, which will impose AX = 0.

Command(s): D, DL, or DAGUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> Electric> Boundary> Electric Wall>On NodesMain Menu> Preprocessor> Loads> Define Loads> Apply> Electric> Boundary> Electric Wall> OnLinesMain Menu> Preprocessor> Loads> Define Loads> Apply> Electric> Boundary> Electric Wall> OnAreas



4.3.1.2. Perfect Magnetic Conductor (PMC)

A perfect magnetic conductor (PMC) boundary (also called Magnetic Wall) is a surface on which the tangential

component of the vector magnetic field (rH

t) vanishes. You can remove a highly permeable magnetic medium

from the model and replace it with a PMC, if the losses of the magnetic medium can be ignored.

Figure 4.5 PMC Boundary Condition

µ,ε

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µ,ε∞ → µ &

To reduce your model size, you can also apply PMC boundary conditions to symmetry planes that have a zerotangential component of the vector magnetic field. You must know the magnetic field distribution before youcan take advantage of the symmetry.

Note — You do not need to specify a PMC boundary condition because it is the natural boundary conditionin ANSYS Emag HF. Any exterior surface without a specified boundary condition assumes a PMCboundary condition.

4.3.1.3. Surface Impedance

Table 4.4: “Surface Impedance Boundary Conditions” shows surface impedance boundary conditions availablefor a high-frequency electromagnetic analysis. You can use surface impedance boundary conditions to approx-imate a radiation boundary and an electrically small lossy/dielectric layer where a very fine mesh would usuallybe required. See the detailed explanations of these impedance boundary conditions below.

Table 4.4 Surface Impedance Boundary Conditions

SF or SFA CommandLabel

Equation [1] [2]SIBC ApproximationsBoundary Condi-

tion

INFZ = o

o

µε

'(*))+,.-/0) 132 45

Far-Field RadiationBoundary

IMPDZ =

µε

637 89 8:<;>=?7 : @3ACBD

Air-dielectric Inter-face

IMPDZ = j tan (2 f

µε

π µετ )

EGFH

I3J K Hτ

Dielectric Coating onPEC



SF or SFA CommandLabel

Equation [1] [2]SIBC ApproximationsBoundary Condi-

tion

SHLDZ =

21+o rωµ µ

σ( )j

Non-perfect ElectricConductor

1. Enter the Z value calculated by this equation in the VALUE field of SF or SFA.

2. µo and εo are the free-space permeability and free-space permittivity, respectively.

µ and ε are the permeability and permittivity, respectively.

µr is the relative permeability.

τ is the thickness of the dielectric layer coating on the PEC.

f is the frequency.

σ is the conductivity of the non-perfect electric conductor.

ω = 2πf

You can apply surface impedance to the nodes of the finite element model or the areas of a solid model usingthe following commands and GUI menu paths with Lab = INF, IMPD, or SHLD:

Command(s): SF,Nlist,IMPD,VALUE,VALUE2 SFA,AREA,LKEY,IMPD,VALUE,VALUE2GUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> Electric> Boundary> Impedance>On NodesMain Menu> Preprocessor> Loads> Define Loads> Apply> Electric> Boundary> Impedance> OnAreas

For the impedance surface load label (Lab = IMPD), VALUE and VALUE2 are the real and imaginary componentsof the impedance, respectively.

When explicit values of impedance are not known or when a harmonic solution over a wide frequency range isrequired, it is more convenient to specify the surface impedance in terms of the conductivity (COND) and relativepermeability (MUR) of the non-perfect conductor. You can apply surface shielding properties using one of thefollowing commands or menu paths (Lab = SHLD):

Command(s): SF,Nlist, SHLD,COND,MUR SFA,AREA,LKEY,SHLD,COND,MURGUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> Electric> Boundary> Shield> OnNodesMain Menu> Preprocessor> Loads> Define Loads> Apply> Electric> Boundary> Shield> On Areas

Note — Be sure to specify conductivity in MKS units (Siemens/meter). The default for relative permeabilityis 1.0.

You can flag any exterior boundary and assign it as an infinite boundary using one of the following commandsor menu paths (Lab = INF):

Command(s): SF,Nlist,INF SFA,AREA,LKEY,INF SFL,LINE,INFGUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> Electric> Flag> Infinite Surface>On NodesMain Menu> Preprocessor> Loads> Define Loads> Apply> Electric> Flag> Infinite Surface> OnAreas



Main Menu> Preprocessor> Loads> Define Loads> Apply> Electric> Flag> Infinite Surface> OnLines

For modeling a far-field radiating boundary, you need to flag the exterior nodes or exterior areas where thepropagating wave is treated as a plane wave. When such an infinite far-field radiation boundary is close to theobjects and the scattering wave is not a plane wave or a spherical wave, numerical error will occur. Using perfectlymatched layers (PML) is a more accurate method for modeling the far-field radiation boundary (see the nextsection).

Applying boundary conditions to the solid model offers the advantage that they are independent of the under-lying finite element mesh. This allows you to make mesh modifications without having to reapply the loads.

4.3.1.4. Perfectly Matched Layers (PML)

The purpose of an absorbing boundary condition is to absorb the outgoing electromagnetic wave so that thereare no reflections back into the FEA computational domain. Perfectly matched layers (PML) are the layers ofelectromagnetic wave absorbing elements designed for the mesh truncation of an open FEA domain in a har-monic or modal analysis. It is an artificial anisotropic material that is transparent and heavily lossy to incomingelectromagnetic waves. PML can reduce the size of the computational domain significantly with very small nu-merical reflections. A PML region is backed by a PEC boundary condition.

If the electromagnetic wave needs to be absorbed in only one direction, as in the case of a traditional waveguideport or a planar transmission line port, you construct a 1-D PML region in the global Cartesian coordinate systemor a local Cartesian coordinate system as shown in the following figure.

Figure 4.6 Microstrip Structure with PML Regions

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A 3-D PML region consist of layers of elements extending from the interior volume towards the open domain asshown in the following figure. You construct a block about the origin of the global Cartesian coordinate systemor a local Cartesian coordinate system. You align the edges of the 3-D PML region with the axes of the Cartesiancoordinate system.



Figure 4.7 PML Region Attached to Interior Region

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6

7

To optimize the absorbing efficiency of the PML, you must properly construct the PML regions and appropriatelychoose the following PML parameters:

• Thickness of the PML Region

• Number of PML Elements

• Attenuation Parameters

• Number of Normal Elements between the PML Region and Objects or Discontinuities

Use the ET command to define PML elements. Set KEYOPT(4) = 1 for HF119 or HF120 and then mesh the PMLregion with this type of element.

More than one 1-D PML region may exist in a finite element model. The element coordinate system (ESYS com-mand) uniquely identifies each PML region. Use the LOCAL command to define a Cartesian coordinate system,and then assign this coordinate system to the elements in the PML region (VATT or ESYS command prior tomeshing or the EMODIF command after meshing).

The attenuation from the PML interface to the PML exterior surface is a parabolic distribution that minimizesnumerical reflections from the PML elements. The numerical reflections are caused by the discretization of acontinuous distribution of material from element to element. To obtain satisfactory numerical accuracy, youshould use at least four layers of PML elements. At lower operating frequencies (< 1 GHz), the PML thickness mayneed to be greater than a quarter wavelength.

Figure 4.8 Attenuation Distribution

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= OAH0S89:-RTD?(@"C ?UD0UVE*C V<@B"C WU/@C D?XYUZG[AB"C K(HS8$9:-\@A]^E*C V<@B"C WU@C D?

89:^Q5S AG[A?(@V

Since PML acts as an infinite open domain, any boundary conditions and material properties need to be carriedover into the PML region. Material properties such as permittivity, permeability, and conductivity in the PML regionmust be the same as the adjacent interior region. For example, in the model of a microstrip structure with PMLregions, you should carry over the dielectric and air properties to the adjacent PML layers (see Figure 4.6: “MicrostripStructure with PML Regions”).



A PEC boundary condition must back all exterior surfaces of the PML region, except for symmetric surfaces witha PMC boundary condition. To specify a PEC boundary condition on the outer surfaces of the PML region, usethe D command for a finite element model or the DL or DA command for a solid model. PEC or PMC boundaryconditions can be applied on the symmetric surfaces of a PML region. For a high frequency structure that has amatching load, rather than an open domain, the PML region plays the role of the matching load.

You should include some buffer elements (at least four) between the PML region and a discontinuity or objectin the interior domain. The PML will then absorb the outgoing wave effectively and minimize numerical reflections.

Figure 4.9 Buffer Elements in Interior Domain

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)+*-,

Since PML is an artificial anisotropic material, excitation sources are prohibited in the PML region.

The attenuation of the electromagnetic wave in a PML region may be controlled. You can specify the normalreflection coefficient (harmonic) for propagating waves or the attenuation factors (modal) for evanescent wavesby using one of the following:

Command(s): PMLOPT,ESYS,Lab,Xminus,Xplus,Yminus,Yplus,Zminus,ZplusGUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> Electric> Boundary> Shield> OnNodes

The direction designations are Xminus, Yminus, Zminus, Xplus, Yplus, and Zplus. The minus and plus refer to thenegative and positive directions along the Cartesian coordinate axes, respectively. If the propagating wave isonly absorbed in one direction, you define a 1-D PML region (Lab = ONE). You only need to specify the Xminusargument for a 1-D PML region. For a 3-D PML region, you can define a different normal reflection coefficientfor each direction (Xminus, Yminus, Zminus, Xplus, Yplus, and Zplus). The normal reflection coefficients defaultto 1.E-3 (-60 dB) for a harmonic analysis. The attenuation factors default to 4.0 for a modal analysis. Normal reflec-tion coefficients should be less than 1.0, and the attenuation factors should be greater than 1.0. If only a few PMLlayers are used (for example, four layers), specifying a very small normal reflection coefficient (such as -100 dB)may lead to significant numerical reflection. Increase the number of layers before specifying a very small reflectioncoefficient. Repeat the PMLOPT command for additional PML regions. Refer to the PMLOPT and PMLSIZEcommands in the ANSYS Commands Reference and Section 5.5.2.4: Perfectly Matched Layers in the ANSYS, Inc.Theory Reference for more information.

The number of PML layers dominates the absorbing efficiency of PML. However, an excessive number of PMLelements will significantly increase the computational requirements. The number of PML layers (n) for acceptablenumerical accuracy can be determined by one of the following:

Command(s): PMLSIZE,FREQB,FREQE,DMIN,DMAX,THICK,ANGLEGUI: Main Menu> Preprocessor> Meshing> Size Cntrls> PML

where



Figure 4.10 Distance between Source/Objects and PML Region

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If n is less than 5, the number of layers is set to 5 in order to reduce the numerical reflection. If n is greater than20, the number of layers is set to 20 to avoid having an excessive number of PML elements.

The PMLSIZE macro must be issued before you mesh your model. If the thickness of the PML region is known, itspecifies an element edge length. If the thickness of the PML region is unknown, it species the number of layers(n).

Refer to the PMLOPT and PMLSIZE commands in the ANSYS Commands Reference and Section 5.5.2.4: PerfectlyMatched Layers in the ANSYS, Inc. Theory Reference for more information.

4.3.1.5. Periodic Boundary Conditions

Periodic boundary conditions enable you to model time-harmonic electromagnetic scattering, radiation, andabsorption characteristics of doubly periodic array structures. A periodic array is assumed to extend infinitely asshown in the following figure. The direction normal to the periodic plane is selected as the Z direction of theglobal Cartesian coordinate system.

Figure 4.11 Arbitrary Infinite Periodic Structure

)*+)*-,

. / ,

/ +

For scattering problems, an arbitrarily polarized plane wave impinges on the periodic structure at some arbitraryoblique arrival angle with respect to the Z direction. The reflection, transmission, absorption, and polarizationcharacteristics of the periodic structure are simulated. For most scattering problems, the periodic structure willnot include internal excitation sources. For radiation problems, an electromagnetic current source or other excit-ation source will exist inside the periodic structure.

The infinite extension assumption allows you to investigate a single periodic unit cell as shown in the followingfigure. The electromagnetic fields on the cell sidewalls exhibit a dependency described by the theorem of Floquet.Refer to High-Frequency Electromagnetic Field Simulation in the ANSYS, Inc. Theory Reference for more informationon this theorem.



Figure 4.12 Unit Cell

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# $ %

The cell sidewalls are assigned as master and slave boundaries, and they are bound together by the periodicboundary conditions. The electromagnetic wave in the periodic volume radiates into infinity or is absorbed inthe z direction. You must use PML to truncate the open space because Floquet's electromagnetic wavepropagates in the periodic structure. You should also use PML or a matched impedance port to terminate a tra-ditional waveguide port, if it exists inside the periodic structure.

To impose periodic boundary conditions, the mesh pattern on the master boundary must be identical to themesh pattern on the slave boundary. You must mesh the master boundary using the AMESH command. Youthen use the AGEN or MSHCOPY command to generate the mesh on the slave boundary prior to meshing thecell volume. Matching the nodes on the master boundary to the nodes on the slave boundary imposes theperiodic boundary conditions. You use the CPCYC or CP command to generate the coupled nodes.

As an example, the following command input listing creates periodic boundary conditions for a unit cell of a in-finite rectangular waveguide periodic array:

/batch,list/title, S11 of JRM Array, E plane scan, 9.25 GHz/com, Problem: Compute S11 of JRM Array for E-Plane scan at 9.25 GHz/com, Numerical Model: Waveguide + Radiation Space + PML/com, Waveguide: 0.9"x0.4"x0.75"/com, Radiation Space: 1.0"x0.5"x0.75"/com, PML: 1.0"x0.5"x0.75"/com,/nopr/prep7freq=9.25e9lamda=3.e8/freqscal=25.4e-3a1=scal*0.9/2.b1=scal*0.4/2.a2=scal*1.0/2.b2=scal*0.5/2c1=scal*0.75c2=scal*0.5c3=scal*0.75c4=scal*1.5rmin=c3rmax=sqrt(2.)*c3dpml=c4-c3

h=lamda/5tiny=1.e-5ang=30angmax=60.

et,11,200,5et,1,119,1,,,0et,2,119,1,,,1 ! cycle elementmp,murx,1,1.mp,perx,1,1.

local,11wpcsys,,11block,-a1,a1,-b1,b1,0,-c1



!block,-a2,a2,-b2,b2,0,c2block,-a2,a2,-b2,b2,0,c3block,-a2,a2,-b2,b2,c3,c4vglue,alltype,11esize,hasel,s,loc,x,-a2asel,a,loc,y,-b2asel,r,loc,z,0,c3amesh,allPMLSIZE,9e9,9.5e9,rmin,rmax,dpml,angmaxasel,s,loc,x,-a2asel,a,loc,y,-b2asel,r,loc,z,c3,c4amesh,allallsasel,s,loc,x,-a2agen,2,all,,,2*a2asel,s,loc,y,-b2agen,2,all,,,0,2*b2allsnummrg,all

mat,1type,1 ! create normal elementvsel,s,loc,z,-c1,c3esize,hvmesh,alltype,2 ! create PML elementPMLSIZE,9e9,9.5e9,rmin,rmax,dpml,angmaxvsel,s,loc,z,c3,c4vmesh,allallsaclear,alletdel,11alls

nsel,s,loc,x,-a2nsel,a,loc,x,a2cpcyc,ax,,,2*a2,0,0,1nsel,s,loc,y,-b2nsel,a,loc,y,b2cpcyc,ax,,,0,2*b2,0,1allsfinish

The finite element models created are shown in the following figure.



Figure 4.13 Periodic Array Models

The SPSCAN macro can perform a harmonic analysis of the unit cell and extract the S-parameter at the port overa specified scanning angle range. You can then use the PLSYZ command to plot the S-parameter over thescanning angle range.

You can use the HFPA command to specify the scan angle for a harmonic analysis. In POST1, you can issue theHFARRAY command to define the antenna array. You can then use PRHFFAR or PLHFFAR to obtain the radiationpattern and the directive gain of the phased array antenna, based on the solution for the unit cell.

4.3.2. Applying Excitation Sources

Table 4.5: “High-Frequency Excitation Sources” shows all excitation sources available for a high-frequency ana-lysis. You can apply excitation sources on the listed solid model entities or finite element model entities. See thedetailed explanations of these excitation sources below. For general information on applying loads see Chapter 2,“Loading” in the ANSYS Basic Analysis Guide.

Table 4.5 High-Frequency Excitation Sources

Finite Element Model EntitiesSolid Model EntitiesExcitation Sources

NodesAreasExcitation Port

Nodes or ElementsVolumesCurrent Density Volume

Nodes or ElementsAreaCurrent Density Area

NodesLinesCurrent Density Line

NodesKeypointsCurrent Density Point

Not ApplicableNot ApplicablePlane Wave



Finite Element Model EntitiesSolid Model EntitiesExcitation Sources

NodesAreasSurface Magnetic Field

NodesLines or AreasElectric Field

4.3.2.1. Excitation Port

Excitation port refers to a plane where an excitation source is defined by the HFPORT command. Excitation portsinclude traditional waveguide ports, arbitrary transmission line ports associated with a specified current densitysource, and plane wave ports. The port plane can be an interior surface that is inside the computational domainor an exterior surface that truncates the computational domain. For traditional waveguides, you may launch amodal electromagnetic field for a coaxial waveguide, rectangular waveguide, circular waveguide or parallel platewaveguide. A waveguide port can be either interior or exterior with respect to the matching condition. For atransmission line port, there is no electromagnetic field to be specified on the port plane. You must use a currentdensity source to excite the propagating mode. The transmission line port needs to be bound to the excitationcurrent density source. A transmission line port must be inside the computational domain (see below for moredetails on exterior and interior ports). A plane wave port is an interior port that is only used for a scattering ana-lysis of a periodic structure.

Specifying the excitation port option is a two-step process. First you select the solid model area (or nodes) todefine the port location and assign a port number. The port number assigned must be between 1 and 50. Foran exterior port, you choose the areas or nodes and then use one of the following to assign a port number andapply a surface load:

Command(s): SF, SFAGUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> Electric> Excitation> Port> Exter-ior> On NodesMain Menu> Preprocessor> Loads> Define Loads> Apply> Electric> Excitation> Port> Exterior>On Areas

For an interior port, you would use one of the following to assign a port number and apply a body load:Command(s): BF, BFAGUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> Electric> Excitation> Port> Interior>On NodesMain Menu> Preprocessor> Loads> Define Loads> Apply> Electric> Excitation> Port> Interior>On Areas

Next, you need to identify the port type: coaxial waveguide, rectangular waveguide, circular waveguide, parallel-plate waveguide, transmission line, or plane wave. You also need to specify the attributes of the port (geometricproperties and excitation conditions). You may define geometric properties of a waveguide with respect to alocal coordinate system. For a waveguide port, the origin of the local coordinate system must be centered aboutthe face of the port without considering symmetry and the Z direction must correspond with the wavepropagation direction. A local coordinate system is not necessary for a transmission line port. For a plane waveport, the z direction of either the global Cartesian or a local coordinate system must be perpendicular to theperiodic plane (see Figure 4.11: “Arbitrary Infinite Periodic Structure”).

To define a local coordinate system, use one of the following:Command(s): LOCALGUI: Utility Menu> WorkPlane> Local Coordinate Systems> Create Local CS> At Specified Loc

To identify the port, use the command or menu path shown below.Command(s): HFPORT,Portnum,Porttype,Local,Opt1,Opt2,VAL1,VAL2,VAL3,VAL4,VAL5GUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> Electric> Excitation> Port> Exter-ior> On Nodes



Main Menu> Preprocessor> Loads> Define Loads> Apply> Electric> Excitation> Port> Exterior>On AreasMain Menu> Preprocessor> Loads> Define Loads> Apply> Electric> Excitation> Port> Interior>On NodesMain Menu> Preprocessor> Loads> Define Loads> Apply> Electric> Excitation> Port> Interior>On Areas

The Porttype argument defines the port type. The Opt1 argument defines the mode type for a waveguide portor the path name for a transmission line port.

Table 4.6 Port Types

Mode Type or Path Name (Opt1)Port Type (Porttype)

• Transverse Electromagnetic (TEM) ModeCoaxial Waveguide (COAX)

• Transverse Electric (TEmn) Mode [1]

• Transverse Magnetic (TMmn) Mode [1]

Rectangular Waveguide (RECT)

• Transverse Electric (TEmn) Mode [2]

• Transverse Magnetic (TMmn) Mode [2]

Circular Waveguide (CIRC)

• Transverse Electromagnetic (TEM)

• Transverse Electric (TEon) Mode [3]

• Transverse Magnetic (TMon) Mode [3]

Parallel Plate Waveguide (PARA)

Voltage Path Name (no default, maximum 8 characters)Transmission Line (TLINE)

Not UsedPlane Wave (PLAN)

1. The subscripts m and n mean the variation of the field along the wide side and narrow side of thewaveguide, respectively.

2. The subscripts m and n mean the variation of the field along the angular and radial directions of thewaveguide, respectively.

3. The subscript zero means no field variation and the subscript n means the variation of the field betweenthe plates.

The VAL1 - VAL5 arguments specify inputs such as geometric properties and excitation conditions. See the HFPORTcommand for additional information.

As shown in the following figure, a port may exist on the exterior surface or interior surface of a modeled domain.An exterior port allows you to launch an incident wave and the port absorbs the reflected wave for the launchedmode. An interior port allows you to launch a bidirectional incident wave. All reflected modes will pass throughthe interior port and will be absorbed by a PML absorbing boundary condition if the interior port is assigned asa matched port. The Opt2 argument controls the ability to launch a wave and to pass reflected waves.



Figure 4.14 Exterior and Interior Ports

You may consider a port to be a soft source or a hard source as shown in the following figures. At a soft sourceport, the electromagnetic field represents the summation of the incident field launched and the reflected wavepassing through the port. The soft source port is equivalent to a matched voltage source as shown in Fig-ure 4.15: “Soft Source Port”. At a hard source port, the electromagnetic field is fixed by the port type and mode.The reflected wave is reflected back into the computational domain again by the hard source port. The hardsource port is equivalent to an unmatched voltage source as shown in Figure 4.16: “Hard Source Port”. You usea hard source port only when you want to ignore the reflection of the electromagnetic field on the source planein order to simplify the model and reduce the size of the computational domain.

Figure 4.15 Soft Source Port

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Exterior Port Options

IMPD and HARD are the allowable options for the Opt2 argument when an exterior port is specified.

Opt2 = IMPD defines a port impedance boundary as shown in the following figure. For this option, if VAL3 andVAL5 are left blank (see HFPORT VALUE Arguments for definitions), the port is treated as a matched port for thespecified mode. If VAL3 or VAL5 is not blank, you may launch an incident wave and the port will absorb the samereflected mode. The port becomes a matched source port for the specified mode. When launching a fundamentalmode using the IMPD option, you should locate the port at least half of a wavelength away from any discontinuityor structure to ensure that other reflected higher order modes are damped out. You may extract S-parametersat this port for the single mode.

Figure 4.17 IMPD Option for Waveguide Port

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Opt2 = HARD defines a hard feeding source aperture. As shown in the following figure, this port launches anincident wave but it does not absorb any reflected waves. You should not extract S-parameters from this portbecause the electromagnetic field is fixed at the port.

Figure 4.18 HARD Option for Waveguide Port

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Interior Port Options

An interior port has the advantage that it supports launching of a wave and passing of all reflected waves. Hence,you can place an interior port very close to a structure or discontinuity with no loss in accuracy. SEXT, SOFT, andHARD are the allowable options for the Opt2 argument when a interior port is specified.

Note — An interior port can only be defined in the normal element region (KEYOPT(4) = 0), and not atthe interface between the normal region and the PML region or in the PML region.

Use Opt2 = SEXT strictly as a port to extract S-parameters. Locate it ahead of the 1-D PML region as shown inFigure 4.19: “Interior Soft Source and Extraction Ports”. This port will extract single mode S-parameters.

Opt2 = SOFT will launch the specified electromagnetic wave as a soft source on both sides of the port. In addition,all reflected modes will pass through the port. A PML region can be located behind the interior port to absorbthe reflected and incident waves as shown in the following figure. For waveguides (Porttype=COAX, RECT, CIRCor PARA), you can extract S-parameters of the specified single mode at this port.

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Opt2 = HARD will launch a waveguide mode on both sides of the port, but it will not allow any reflected wavesto pass through the port. You should not extract S-parameters at this port. A hard interior port is not recommended.

You can define a transmission line port (Porttype = TLINE; Opt2 = SEXT) to extract parameters for a planartransmission line. In addition to defining the transmission line port plane using the BF or BFA command, youneed to specify a voltage path from the central conductor to the ground on the port plane. Since a closed formsolution for the planar transmission line structure is not available, you should introduce a current density sourceto excite the propagating modes in the structure. They will propagate along the transmission line structure,while the excited evanescent modes damp out quickly away from the current density source. You must use PMLto terminate the computational domain. The parameter extraction plane of the transmission line port should bebetween the excitation current density source and the discontinuity for a input port. It should be between the



discontinuity and the PML region for output ports. A PML region should be behind the current density source.The model is shown in the following figure.

Figure 4.20 Transmission Line Model

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The plane wave source port (Porttype = PLAN, Opt2 = SOFT) launches a plane wave for a scattering analysis ofa periodic structure. Here, you need to define the coupled master and slave surfaces of the solid model or nodesof the finite element model. You must use PML to truncate the open space because Floquet's electromagneticwave propagates in the periodic structure. The plan wave port must be an interior soft port as illustrated in thefollowing figure. For information on how to define a plane wave, see Section 4.3.2.3: Plane Wave Source.

Figure 4.21 Model for Scattering Analysis of Periodic Structure9;: <=>@?A<B>C9EDFGHI9+JK8LNM

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The HFPORT arguments VAL1 - VAL5 define the other port inputs.

Table 4.7 HFPORT VALUE Arguments[1]

VAL5VAL4VAL3VAL2VAL1Port Type

Input PowerPhase AngleVoltage between Innerand Outer Conductors [2]

Outer RadiusInner RadiusCOAX

Input PowerPhase AngleEz for TM or Hz for TE [2]HeightWidthRECT

Input PowerPhase AngleEz for TM or Hz for TE [2]Not UsedRadiusCIRC



VAL5VAL4VAL3VAL2VAL1Port Type

Input PowerPhase AngleEy for TEM, Ez for TM, or Hz

for TE [2]

SeparationWidthPARA

Not UsedNot UsedRatio of model cross-sec-tional area to real cross-sectional area. For a half-symmetry model, enter0.5. Defaults to 1.0.

Susceptance ofReference Imped-ance

Resistance ofReference Imped-ance

TLINE

Angle θ in Spher-ical CoordinateSystem

Angle φ inSpherical Co-ordinate System

Ez [2]EyExPLAN

1. If time-averaged power is input, it overrides the applied voltage or field input. See the HFPORT commandfor more information on the VAL1 -VAL5 arguments.

2. VAL3 is a RMS value.

4.3.2.2. Current Source

You can use a current source to excite electromagnetic fields in a high-frequency structure. Current density isinput by defining up to three components of a vector quantity (JSX, JSY, and JSZ) and a phase angle. If the currentdensity vector is not aligned with the global Cartesian coordinate system, you may take advantage of either arotated nodal coordinate system (NROTAT command) or an element coordinate system (ESYS command). Ifcurrent density is specified at nodes (BF command) or transferred to nodes from a solid model entity (BFA, BFL,or BFK), you can use a rotated nodal coordinate system to align the current density vector. If current density isspecified on elements (BFE command) or transferred to elements from a solid model volume (BFV command),you can use an element coordinate system to align the current density vector. To view the current density vectors,use the /PBC,JS,,2 command option.

To define a current density volume source, use one of the following:Command(s): BF, BFV, BFEGUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> Magnetic> Excitation> CurrDensity> On NodesMain Menu> Preprocessor> Loads> Define Loads> Apply> Magnetic> Excitation> Curr Density>On VolumesMain Menu> Preprocessor> Loads> Define Loads> Apply> Magnetic> Excitation> Curr Density>On Elements

For a surface current source, you should specify the current density on at least three nodes on an element face.The surface current source must coincide with the element faces. You can define a current density surface sourceusing one of the following:

Command(s): BF, BFAGUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> Magnetic> Excitation> CurrDensity> On NodesMain Menu> Preprocessor> Loads> Define Loads> Apply> Magnetic> Excitation> Curr Density>On Areas

For a line current source, you should specify the current density at two nodes connected by an element edge.The line current source must coincide with the element edges. To define a current density line source, use oneof the following:

Command(s): BF, BFLGUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> Magnetic> Excitation> CurrDensity> On Nodes



Main Menu> Preprocessor> Loads> Define Loads> Apply> Magnetic> Excitation> Curr Density>On Lines

A point current source must be at the element nodes. You can define a current density point source using oneof the following:

Command(s): BF, BFKGUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> Magnetic> Excitation> CurrDensity> On NodesMain Menu> Preprocessor> Loads> Define Loads> Apply> Magnetic> Excitation> Curr Density>On Keypoints

In general, a current density source launches the electromagnetic wave in all directions. For a propagating orresonant system, you can use a current density source to excite the propagating modes or resonant modes ofthe structure. Only proper modes can exist in the structure. In order to reduce the parasitic modes, you shouldchoose the distribution of the current density based on the electric field distribution of the excited mode. Thefollowing figure shows an example for a planar transmission line. You can excite the fundamental propagatingmode by defining a line current density source pointing from the central conductor to the ground.

Figure 4.22 Current Excitation

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The following guidelines apply when a current density source is used to excite a high-frequency propagatingstructure:

• To avoid the parasitic modes around the excitation source, locate parameter extraction planes at least1/4 wavelength away from the excitation position.

• Use PML to terminate the computational domain along the wave propagating direction.

The following figure illustrates these guidelines.

Figure 4.23 Transmission Line Model with Current Excitation

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You can also define a radiation source using a current density distribution in terms of a conducting current dis-tribution on the radiator. For example, you can choose a sinusoidal current distribution to model a very thin half-wavelength dipole antenna.



4.3.2.3. Plane Wave Source

A incident plane wave source is available. You can define a plane wave by component values of an electric po-larization vector and the incident angles in a global Cartesian coordinate system:

E = E0jk xcos sin ysin sin zcoso ( )φ θ φ θ θ+ +

If a plane wave port is assigned, you can define a plane wave in a local Cartesian coordinate system.

Define a external plane wave (a free-space harmonic incident plane electromagnetic wave) using one of thefollowing:

Command(s): PLWAVEGUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> Electric> Excitation> Plane Wave>Define Wave

You need to specify the following plane wave attributes:

• Electric field amplitude in the X, Y, and Z directions.

• Angle between the X-axis and the projection of the incident plane wave vector on the X-Y plane (φ).

• Angle between the Z-axis and the incident plane wave vector.

Figure 4.24 Spherical Coordinates

θ

φ

Note — As shown in Figure 4.24: “Spherical Coordinates”, the wave vector points to the origin of theCartesian coordinate system.

When used together with an unbounded domain model (using PML as an absorber), the scattering effects of anincident field on a body can be simulated using the scattering analysis command HFSCAT.

You cannot use the PLWAVE command to define an incident plane wave for a scattering analysis of a periodicstructure. Here, a plane wave port must be specified using the HFPORT command. The scattering analysiscommand HFSCAT is not valid because a total field formulation is used for the scattering analysis of a periodicstructure.

4.3.2.4. Surface Magnetic Field Source

You can apply a fixed magnetic field (hard) excitation source on an exterior surface using one of the following:Command(s): BF, BFAGUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> Magnetic> Excitation> MagneticField> On NodesMain Menu> Preprocessor> Loads> Define Loads> Apply> Magnetic> Excitation> Magnetic Field>On Areas



You should impose a hard surface magnetic field excitation source on the exterior nodes of a computationaldomain as shown in Figure 4.25: “Exterior Hard Surface Magnetic Field Excitation”. Specify a soft excitation sourceif the surface magnetic field source is on the interior nodes of a computational domain as shown in Fig-ure 4.26: “Soft Interior Surface Magnetic Field Excitation”.

Figure 4.25 Exterior Hard Surface Magnetic Field Excitation

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For a surface magnetic field source, you should specify the magnetic field at three nodes on an element face, atleast. The surface magnetic field source must coincide with the element faces. The magnetic field is input bydefining up to three components of a vector quantity (HX, HY, HZ) and a phase angle. If the magnetic field vectordoes not align with the global Cartesian coordinate system, you may take advantage of a rotated nodal coordinatesystem (NROTAT command). The magnetic field specified at nodes (BF command) or transferred to nodes froma solid model entity (BFA, BFL, or BFK) may use a rotated nodal coordinate system to align the magnetic fieldvector. To view the magnetic field vectors, use the /PBC,H,,2 command option.

You can also apply a soft excitation source as shown in the following figure. It allows reflection waves to gothrough the source surface without any reflection. To do so, you define an interior surface magnetic field sourceusing the BF or BFA command. The HF119 or HF120 elements in the region that the reflection wave propagatesinto must be scattering elements (KEYOPT(4) = 2). However, you still define the elements in the PML region bya KEYOPT(4) = 1 setting.

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4.3.2.5. Electric Field Source

You can apply a fixed electric field source on an external surface using one of the following:Command(s): BF, BFL, BFAGUI: Main Menu> Preprocessor> Loads> Define Loads> Apply> Electric> Excitation> Electric Field>On NodesMain Menu> Preprocessor> Loads> Define Loads> Apply> Electric> Excitation> Electric Field> OnLinesMain Menu> Preprocessor> Loads> Define Loads> Apply> Electric> Excitation> Electric Field> OnAreas

For a line electric field source, you should specify the electric field at two nodes connected by an element edge.For a surface electric field source, you should at least specify the electric field at three nodes on an element face.The surface electric field source must coincide with the element faces. The line electric field source must coincidewith the element edges.



The electric field is input by defining up to three components of a vector quantity (EFX, EFY, and EFZ) and a phaseangle. If the electric field vector does not align with the global Cartesian coordinate system, you may take advant-age of a rotated nodal coordinate system (NROTAT command). The electric field specified at nodes (BF command)or transferred to nodes from a solid model entity (BFA, BFL, or BFK) may use a rotated nodal coordinate systemto align the electric field vector. To view the electric field vectors, use the /PBC,EF,,2 command option.

The electric field source is a fixed hard excitation source, which is equivalent to an unmatched voltage source.The AX DOF updates automatically after the excitation electric field is imposed on the element nodes.

Only the first order HF119 and HF120 elements are available for this excitation.

4.3.2.6. Equivalent Source Surface

The near and far fields beyond the FEA domain are of importance in high-frequency electromagnetics. Manydesign parameters (for example, radar cross-section, antenna pattern, directive gain, and radiation power) arebased on the far field values.

The surface equivalence principle enables you to calculate the electromagnetic fields beyond the FEA domain.It states that the electromagnetic field exterior to a given surface can be exactly represented by an equivalentelectric and magnetic current placed on that surface and allowed to radiate into the region external to that surface.Refer to the ANSYS, Inc. Theory Reference for more information on this principle.

For problems requiring near-field and far-field computations (for example, antenna parameters, radar crosssection, and electromagnetic field values) you must first define an equivalent source surface in the preprocessoras shown in the following figure. The surface must enclose the radiator or scatter, except for symmetry planes.The equivalent electric and magnetic current are computed and stored on the surface. This enables you to quicklycalculate near-field and far-field information in the postprocessor.

Figure 4.27 Equivalent Source Surface

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For radiation and scattering problems, you must use an absorbing boundary condition, either PML or far-fieldradiation boundary (INF). Since the ideal radiation or scattering plane wave leads to a very large spherical com-putational domain for an acceptable numerical accuracy, you should use PML to truncate the computationaldomain. The equivalent source surface should be between the radiator or scatter and the PML region. In principle,the equivalent source surface should be close to the radiator or scatter to obtain good near-field and far-fieldresults. However, because of the lower order element discretization of the computational domain and the nu-merical integration on the equivalent source surface, you should use half a wavelength or greater separationbetween the radiator or scatter and the equivalent source surface. You should also place some buffer elementsbetween the equivalent source surface and the PML region.



You define an equivalent source surface using a surface boundary condition with the Maxwell flag MXWF. Exercisecare when applying a MXWF surface load to define an equivalent source surface. Do not flag any surface on asymmetry plane (for example, the y-z and x-z planes in Figure 4.27: “Equivalent Source Surface”). The followingis one way to flag an equivalent source surface:

1. Select the elements interior to the equivalent source surface (ESEL).

2. Select all the nodes of these elements (NSLE,S).

3. Reselect just the exterior nodes to work with only the surface nodes (NSEL,R,EXT).

4. Apply the surface flag (SF,ALL,MXWF).

The following is another way you can flag an equivalent source surface:

1. Select the nodes interior to the equivalent source surface (NSEL).

2. Select the elements attached to the selected nodes, only if all of its nodes are in the selected nodal set(ESLN, S, 1, ALL).

3. Select the nodes on the "MXWF" surface.

4. Apply the surface flag (SF, ALL, MXWF).

Caution: Do not apply the surface flag using the SFA command. This option will transfer the surface flagto adjacent elements on either side of the equivalent source surface and may lead to erroneous results.

You do not need to define an equivalent source surface when performing a scattering analysis of a periodicstructure. The interior plane wave port surface serves as the equivalent source surface.

4.3.2.7. Lumped Circuits

You can simplify your model and reduce the number of DOFs if fringe effects at discontinuities can be ignoredor a passive device can be treated as a lumped circuit. As shown in the following figure, six types of lumped circuitsare available.



Figure 4.28 Lumped Circuits

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To utilize this simplification, you apply lumped circuit loads to the mid-nodes of element edges using the BFcommand with Lab = LUMP. HF Emag imposes the lumped circuit loads on the end nodes of the element edgesas well as the mid-nodes.

When applying lumped circuit loads to multiple edges, you must generate equivalent circuit loads whose sumis equal to the given lumped circuit load. For example, consider the 2-port lumped network shown in the followingfigure.

Figure 4.29 2-Port Lumped Network

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The following figure shows the equivalent circuit model and impedance values for a FEA mesh with the impedanceload shown in Figure 4.29: “2-Port Lumped Network”. The 2Z/3 loads are applied to the mid-nodes of the corres-ponding edges.

Figure 4.30 Equivalent Lumped Circuit Model

4.4. Solving Harmonic High-Frequency Analyses

The ANSYS program simulates electromagnetic wave propagation, radiation and scattering phenomena in a 3-D harmonic analysis.

To enter the SOLUTION processor, use either of the following:Command(s): /SOLUGUI: Main Menu> Solution

4.4.1. Defining the Analysis Type

To specify the analysis type, use either of the following:Command(s): ANTYPE,HARMICGUI: Main Menu> Solution> Analysis Type> New Analysis> Harmonic Analysis

You cannot restart a harmonic analysis. If you want to apply a different set of harmonic loads, do a new analysiseach time.

4.4.2. Defining Analysis Options and Estimating Computer Resources

For a full harmonic analysis, you can choose the sparse direct solver (SPARSE) (default), or the Incomplete CholeskyConjugate Gradient (ICCG) solver using one of the following:

Command(s): EQSLVGUI: Main Menu> Solution> Analysis Type> Analysis Options

For a relatively small-size problem (50,000 DOFs or less), the sparse solver is recommended. For larger problems,you can also use the ICCG solver. If you are using second order elements, the ICCG solver is not recommended.If the ICCG solver does not converge, you must switch to the sparse solver. In general, if a FEA model has 1 millionDOFs, it requires 2 GB RAM and 10-15 GB disk space for the SPARSE solver. For the number of DOFs per element,see Table 4.1: “Element DOFs” in this chapter.

If Ne is the total number of HF119 tetrahedral elements and M is defined by M=(Ne/5)1/3, the number of DOFsfor 1st order and 2nd order elements are 3M(M+1)(2M+1) and 6M(M+1)(4M+1)+8M3, respectively. If Ne is the

total number of HF120 hexahedral elements and M is defined by M=Ne1/3, the number of DOFs for 1st order and2nd order elements are 3M(M+1)2 and 6M(M+1)(3M+1)+6M3, respectively.



4.4.3. Setting the Analysis Frequencies

Set the frequency (in Hz), using the command or GUI path shown below:Command(s): HARFRQGUI: Main Menu> Preprocessor> Loads> Load Step Opts> Time/Frequenc> Freq and Substps

If you specify the frequency range on the HARFRQ command to perform a frequency sweep, you have to storeeach load step of data and manually process each result.

4.4.4. Defining a Scattering Analysis

To specify a pure vector scattering field analysis, use one of the following:Command(s): HFSCATGUI: Main Menu> Solution> Analysis Type> Analysis Options

Use the HFSCAT command to specify a scattering analysis and the type of electromagnetic field output:

• Use the scattering formulation and store the scattering field Esc(Lab = SCAT).

• Use the scattering formulation and store the total electromagnetic field Etotal = Einc + Esc (Lab = TOTAL)

• Turn off scattering formulation analysis (Lab = OFF)

If a Radar Cross Section (RCS) is required at postprocessing, you must specify Lab = SCAT. You must also flag thevirtual equivalent current source surface that encloses the scatter using the SF command (Lab = MXWF).

Note —

• Only first order HF119 or HF120 elements are available for a scattering analysis.

• The HFSCAT command is not applicable to a scattering analysis of a periodic structure.

4.4.5. Defining a Radiation Analysis for a Phased Array Antenna

For a radiation analysis of a phased array antenna, you must also define master/slave coupling pairs on theboundaries of a unit cell of the periodic structure (see the CP and CPCYC commands). You must also specify thescan angles. If a far-field computation is required at postprocessing, you must flag the virtual equivalent currentsource surface using the SF command (Lab = MXWF). The equivalent current source surface must not includethe master/slave surface of the unit cell.

Only first order HF119 or HF120 elements are available for a radiation analysis of a phased array antenna.

To specify a radiation scan angle for a phased array antenna analysis, use one of the following:Command(s): HFPAGUI: Main Menu> Solution> Analysis Type> Analysis Options

4.4.6. Starting the Solution

To initiate a single solution, use either of the following:Command(s): SOLVEGUI: Main Menu> Solution> Solve> Current LS

To solve the analysis over a range of frequencies, you can either execute the HFSWEEP macro or specify thefrequency range by the HARFRQ command. HFSWEEP saves you some steps in that it automatically solves theanalysis and executes ANSYS macros (such as SPARM, IMPD and REFLCOEF) which calculate S-parameters and

Section 4.4: Solving Harmonic High-Frequency Analyses


other coefficients automatically. If you specify the frequency range by HARFRQ to perform a frequency sweep,you need to store the data for each load step and manually process each result set to obtain S-parameters andcoefficient data. For detailed information on SPARM, IMPD, REFLCOEF and other macros, see Section 4.5.4:Calculating Circuit Parameters for High-Frequency Devices in this guide. Information on these macros can alsobe found in the ANSYS Commands Reference.

When using HFSWEEP, for a coaxial waveguide, you may elect to calculate multi-port S-parameters or reflectioncoefficient, voltage standing wave ratio, return loss, and impedance at a specified location from the driven port.For rectangular waveguides, you may calculate S-parameters for up to four ports. The ANSYS program calculatesthe data and stores it in the array parameter HFDATA. The program displays the results interactively in tabularform and on an output file, HFSWEEP.OUT. The data is also displayed on graphs stored in a file, HFSWEEP.GPRH.

You can view the graphs with the externally supplied DISPLAY program. It you want to export the data to a third-party package, you can do so through the HFSWEEP.OUT file or the HFDATA array parameter. To ensure thatall input data for executing the macro is defined properly, run a short sweep (one or two frequencies) beforeinitiating a lengthy frequency sweep.

To execute the HFSWEEP macro, use either of the following:Command(s): HFSWEEPGUI: Main Menu> Solution> Solve> Electromagnet> HF Emag> Freq Sweep

Note — Using the HFSWEEP macro may require you to define one or more paths through your model.You must define these paths in the postprocessor (with the PATH and PPATH commands) and savethem to an external file (PASAVE command) or to an array parameter (PAGET command) before issuingthe frequency sweep. See the ANSYS Basic Analysis Guide for information about paths or the descriptionsof the PATH, PPATH, and PAGET commands.

The SPSWP macro automatically performs harmonic analyses over a frequency range and executes the SPARMmacro to calculate S-parameters. It outputs a Touchstone file of S-parameters, filename.snp, where n is thenumber of ports. The SwpOpt argument specifies the solution method: Full, Variational Technology, or VariationalTechnologyusing a perfect absorber. The full method uses the direct or iterative solver to perform solutions atevery frequency between the beginning and ending frequencies (FREQB and FREQE arguments) as determinedby the frequency increment (FREQINC argument). For more information on this method, see the informationunder Scattering Parameters (S-Parameters). The separately licensed ANSYS Frequency Sweep VT performs afactorization solution of the linear equations at the mid-frequency of the specified range. It then performs goodapproximations of the results over the frequency range. Variational Technology can be much faster than the fullmethod. For more information on that method, see ANSYS Frequency Sweep VT in the ANSYS Advanced AnalysisTechniques Guide.

To execute the SPSWP macro, use either of the following:Command(s): SPSWPGUI: Main Menu> Solution> Solve> S-Par Freq Sweep

It is recommended that you perform an initial solution at a single frequency to ensure that all input argumentsare properly set before you run a frequency sweep. To run a single frequency, set FREQB to FREQE.

SPSWP performs a sequence of solutions whereby for each solution, one port is “excited” and the other portsare “matched”. Each solution represents one column of a S-parameter matrix (i.e., if Port 1 is excited for a three-port system, the resulting column represents the S11, S21 and S31 S-parameters). A full S-parameter matrix foran n port system at one frequency requires n solutions alternating “excited” and “matched” port boundaryconditions at each port. SPSWP will solve a column of the S-parameter matrix for each port that has a definedexcitation. If all ports have a defined excitation, then the full S-parameter matrix will be computed.



To use this function, you must flag the ports. Use the SF or SFA commands for exterior waveguide ports, anduse the BFA, BFL or BF commands for interior waveguide or transmission line ports. Number the ports sequentiallyfrom “1” with no gaps in the numbering.

To prepare the ports for SPSWP, you must define the port excitations. For waveguide ports, excitation is definedusing the HFPORT command. For transmission line ports, excitations are defined using BFA, BFL or BF andcurrent density sources. Transmission line excitation must be offset from the transmission line port plane definedby the HFPORT command. Each current density source must be bound to the associated transmission line port.For example, the following command input listing ties a current density source to port number 1.

…hfport,1,tline,,'volt_1',50.bf,js,jx,jy,jz, -1…

For transmission line ports, you also need to define a voltage path on the transmission line port plane with thePATH command. Save the path to the Jobname.PATH file using PASAVE,ALL.

For each solution, SPSWP computes S-parameters with the excitation on all ports nullified except for one. It restoresall excitation loads after the sequence of solutions is completed.

Postprocessing is limited to the solution with the last port excited and the other ports matched. The OutPutargument controls the results file output. The minimal size results file (OutPut = 0) only contains informationon elements attached to the flagged waveguide ports or to the defined paths for transmission line ports. It isrecommended if you have a large number of frequencies.

S-parameters results are written to a Touchstone format file jobname.snp, where n is the number of ports. Thefirst line is a general description of the output data and starts with an exclamation point (!). The second linecontains the following information:

• starts with a #

• frequency unit (GHz, MHz, KHz, Hz)

• parameter type: S = scattering parameters, Y = admittance parameters, and Z = impedance parameters

• data format: magnitude-angle (MA), dB-angle (DB), or real-imaginary (RI)

• normalizing impedance: R n, where n = ohms

Note — The following is an example of the first two lines.

! 2-port S-parameter file, 3 frequency points

# GHz S MA R 50. 50.

The output then lists the S-parameters in row format for each frequency. Up to four ports are listed in a row.Rows are repeated for each frequency until all port data is listed. The following examples demonstrate the format.Frequency appears as f and magnitude and phase appear as m and p, respectively.

Two port data appears in one row as follows:

f m(S11) p(S11) m(S21) p(S21) m(S12) p(S12) m(S22) p(S22)

Three port data appears in three rows as follows:

f m(S11) p(S11) m(S12) p(S12) m(S13) p(S13)m(S21) p(S21) m(S22) p(S22) m(S23) p(S23)m(S31) p(S31) m(S32) p(S32) m(S33) p(S33)

Section 4.4: Solving Harmonic High-Frequency Analyses


Six port data for one frequency appears in 12 rows as follows:

f m(S11) p(S11) m(S12) p(S12) m(S13) p(S13) m(S14) p(S14)m(S15) p(S15) m(S16) p(S16)m(S21) p(S21) m(S22) p(S22) m(S23) p(S23) m(S24) p(S24)m(S25) p(S25) m(S26) p(S26)...m(S61) p(S61) m(S62) p(S62) m(S63) p(S63) m(S64) p(S64)m(S65) p(S65) m(S66) p(S66)

The SPSCAN macro automatically performs harmonic analyses over a range of angles and executes the SPARMmacro to calculate S-parameters at the input port of a phased array antenna. It outputs a Touchstone-like file ofS-parameters, filename.snp. The Variational Technology solution method is not available in SPSCAN.

To execute the SPSCAN macro, use either of the following:Command(s): SPSACNGUI: Main Menu> Solution> Solve> S-Par Ang Sweep

4.4.7. Finishing the Solution

To leave the SOLUTION processor, use either of the following:Command(s): FINISHGUI: Main Menu> Finish

4.5. Postprocessing Harmonic High-Frequency Analyses

4.5.1. Reviewing Results

The ANSYS program writes results from a harmonic high-frequency electromagnetic analysis to the magneticsresults file, Jobname.RMG. Results include the data listed below, many of which vary harmonically at the oper-ating frequency (or frequencies) for which the measurable quantities can be computed as the real solution timescosine (ωt) minus the imaginary solution times sine (ωt). ω is the angular frequency. For more details, see theANSYS, Inc. Theory Reference.

Primary data: Nodal DOFs (AX)

Derived data:

• Nodal electric field (EX, EY, EZ, ESUM)

• Nodal magnetic field intensity (HX, HY, HZ, HSUM)

• Nodal conducting current density (JCX, JCY, JCZ, JSUM)

• Joule heat rate per unit volume (JHEAT)

• Element Poynting vector (PX, PY, PZ)

• Element dissipated power Pd (if it exists)

• Element stored time-average energy

• Element specific absorption rate (SAR) (if it exists)

• and so on



Additional data are available. See the ANSYS Elements Reference for details.

You can review analysis results in POST1, the general postprocessor. In general, the results are out-of-phase withthe input loads. The solution is calculated and stored in terms of real and imaginary components as detailedabove.

Use POST1 to review results over the entire model at specific frequencies. For viewing results over a range offrequencies, use the time-history postprocessor, POST26.

To choose a postprocessor, use one of the following:Command(s): /POST1 or /POST26GUI: Main Menu> General PostprocMain Menu> TimeHist Postpro

4.5.2. Commands to Help You in Postprocessing

You will find the following commands (listed below) helpful in postprocessing analysis results:

Table 4.8 Postprocessing Commands

Command(s)Task

SET,1,1,,0Select the real solution

SET,1,1,,1Select the imaginary solution

PRNSOL,EF (or H or JC)Print electric or magnetic field at corner nodes [1,3]

PRVECT,EFPrint electric field at corner nodes[1,3]

PRVECT,PPrint Poynting vector at element centroid[1,3]

PRVECT,HPrint magnetic field at corner nodes[1,3]

PRVECT,JCPrint conducting current at corner nodes[1,3]

PRESOL,EF (or H or JC)Print electric or magnetic field at element nodes[3]

PRESOL,JHEATPrint Joule heat density[2,4]

ETABLE,Lab,EF,XCreate element table item for centroid electric field[3], X component. (Issuesimilar commands for Y, Z, and SUM components.)

ETABLE,Lab,H,XCreate element table item for centroid magnetic field[3], X component. (Issuesimilar commands for Y, Z, and SUM components.)

ETABLE,Lab,JC,XCreate element table item for centroid conducting current[3], X component.(Issue similar commands for Y, Z, and SUM components.)

ETABLE,Lab,JHEATCreate element table item for Joule heat density[2,4]

PRETAB,Lab,...Print the indicated element table item(s)

1. Average of selected elements adjacent to nodes.

2. To obtain power loss, multiply by element volume.

3. Instantaneous value (real/imaginary, at ωt = 0 and ωt = -90) in case of a harmonic analysis.

4. RMS value: measurable values are the sum of real and imaginary parts.

See the ANSYS, Inc. Theory Reference for more information on the notation. The ETABLE command lets you viewless frequently-used items. The HF119 and HF120 descriptions in the ANSYS Elements Reference discuss theseitems.

Section 4.5: Postprocessing Harmonic High-Frequency Analyses


You can view most of these items graphically. To do so, substitute plotting commands or GUI paths (see the in-dividual commands for the appropriate GUI paths) for the commands whose names begin with "PL" (for example,use PLNSOL instead of PRNSOL, as illustrated below):

Table 4.9 Plotting Commands

Substitute this command...For this command...

PLNSOLPRNSOL

PLVECTPRVECT

PLESOLPRESOL

PLETABPRETAB

You also can plot element table items. See the ANSYS Basic Analysis Guide for more information.

The ANSYS Parametric Design Language (APDL) also contains commands that may be useful in postprocessing,and results processing purposes. For more information about the APDL, see the Guide to ANSYS User ProgrammableFeatures.

The following two sections discuss some typical POST1 operations for calculating the near and far-fields andparameters for high-frequency devices. For a complete description of all postprocessing functions, see the ANSYSBasic Analysis Guide.

4.5.3. Calculating Near Fields, Far Fields, and Far Field Parameters

Postprocessing commands are available for calculating the near or far electromagnetic fields beyond the FEAcomputational domain. The commands HFNEAR, PRHFFAR, and PLHFFAR use the surface equivalence principleto determine the fields. The surface equivalence principle states that equivalent currents can exactly representthe electromagnetic fields exterior to the surface. Refer to Surface Equivalence Principle in the ANSYS, Inc. TheoryReference for more information.

Use of near and far-field commands requires that an equivalent source surface be defined in the preprocessor.See Section 4.3.2.6: Equivalent Source Surface for details.

4.5.3.1. Near Fields

You can calculate either the near electric field (Lab = EF, default) or the near magnetic field (Lab = H) beyondthe FEA computational domain using one of the following:

Command(s): HFNEARGUI: Main Menu> General Postproc> List Results> Field Extension> Near FieldMain Menu> General Postproc> Path Operations> Map onto Path> HF Near Field

You can obtain the near electric field or near magnetic field at a point (X, Y, Z) in a coordinate system or along apath. When determining the field at a point, you specify a coordinate value in the global or a local coordinatesystem. You also specify a global coordinate system for the output vector. When determining the field along apath, you define a path using the PATH command and you set VAL to PATH. All previous path items are clearedbefore HFNEAR executes.

To use HFNEAR, you must first define an equivalent current source surface in the preprocessor. You must issuethe HFSYM command to account for symmetry planes in the modeled region.



4.5.3.2. Far Fields and Far Field Parameters

Far fields and far field parameters are essential for scattering analysis and antenna design. This section describessome useful POST1 operations for these analyses.

Far Electromagnetic Field

To plot far fields, use one of the following:Command(s): PLHFFARGUI: Main Menu> General Postproc> List Results> Field Extension> Far Field

To print far fields, use one of the following:Command(s): PRHFFARGUI: Main Menu> General Postproc> List Results> Field Extension> Far Field

You can display the magnitude or the Cartesian or spherical components of the far electromagnetic field.

Radar Cross Section (RCS) and Normalized Radar Cross Section (RCSN)

The bistatic scattering cross section (radar cross section), measures the scattering characteristics of a target foran incident plane wave. The radar cross section (RCS) depends on the dimensions and material properties of theobject and the wavelength and incident angle of the plane wave. It is also a function of the polarization of theincident wave. You can calculate the RCS for the pth component of the scattered field for a q-polarized incidentplane wave where p and q represent the φ and θ spherical components, respectively.

Figure 4.31 Spherical Coordinates

θ

φ

The RCS can be normalized by the wavelength in a 2-D analysis and the wavelength squared in a 3-D analysis.

To plot RCS or RCSN, use one of the following:Command(s): PLHFFARGUI: Main Menu> General Postproc> List Results> Field Extension> RCS (or RCS Normalized)

To print RCS or RCSN, use one of the following:Command(s): PRHFFARGUI: Main Menu> General Postproc> List Results> Field Extension> RCS (or RCS Normalized)

To plot RCS or RCSN, use one of the following:Command(s): PLHFFARGUI: Main Menu> General Postproc> List Results> Field Extension> RCS (or RCS Normalized)

Using PLHFFAR or PRHFFAR, you can calculate a 3-D RCS for radar echo area, φ-φ polarization, φ-θ polarization,θ-φ polarization, or θ-θ polarization. You can calculate a 2-D RCS using a 3-D computational model. You extrudea 2-D model a distance ∆z in the z direction to generate a 3-D numerical model. You can use PLHFFAR orPRHFFAR to calculate a 2-D RCS for a TE or TM incident plane wave.



Refer to High-Frequency Electromagnetic Field Simulation in the ANSYS, Inc. Theory Reference for more informationon RCS.

Antenna Parameters

You can obtain various antenna design parameters (for example, radiation pattern, radiation power, directivegain, directivity, power gain and radiation efficiency) based on the far field results. Refer to High-FrequencyElectromagnetic Field Simulation in the ANSYS, Inc. Theory Reference for definitions of these parameters.

To print antenna parameters, use one of the following:Command(s): PRHFFARGUI: Main Menu> General Postproc> List Results> Field Extension> Antenna> Pattern (or DirectGain, Rad Power, Power Gain, Efficiency)

To plot antenna parameters, use one of the following:Command(s): PLHFFARGUI: Main Menu> General Postproc> List Results> Field Extension> Antenna> Pattern (or DirectGain)

You can display Cartesian or polar components of the antenna radiation pattern and direct gain.

Before issuing PLHFFAR or PRHFFAR, you need to flag a virtual equivalent current source surface using Lab =MXWF on the SF command in the preprocessor before solution. See Section 4.3.2.6: Equivalent Source Surfacefor details. You must issue the HFSYM command if there is a symmetry plane in the modeled region. When cal-culating antenna parameters, use the HFANG command to define the spatial angles if the radiation space is notthe entire spherical domain.

Phased Array Antenna

Before calculating far field or antenna parameters, you need to define the characteristics of a phased array antennausing one of the following:

Command(s): HFARRAYGUI: Main Menu> General Postproc> List Results> Field Extension> Far FieldMain Menu> General Postproc> List Results> Field Extension> Antenna> Pattern (or Direct Gain)Main Menu> General Postproc> Plot Results> Field Extension> Far FieldMain Menu> General Postproc> Plot Results> Field Extension> Antenna> Pattern (or Direct Gain)

The total field of a phased array antenna is equal to the product of an array factor and the unit cell field.

Etotal = AF (Eunit cell)

Refer to High-Frequency Electromagnetic Field Simulation in the ANSYS, Inc. Theory Reference for the definitionof Array Factor.

4.5.3.3. Symmetry

You must account for symmetry planes in the modeled domain for postprocessing near or far electromagneticfields beyond the computational domain. To do so, use one of the following:

Command(s): HFSYMGUI: Main Menu> General Postproc> List Results> Field Extension> Near FieldMain Menu> General Postproc> Path Operations> Map onto Path> HF Near FieldMain Menu> General Postproc> Plot Results> Field Extension> Far Field (or RCS, RCS Normal-ized)



Main Menu> General Postproc> Plot Results> Field Extension> Antenna> Pattern (or DirectGain)

Main Menu> General Postproc> List Results> Field Extension> Far Field (or RCS, RCS Normalized)Main Menu> General Postproc> List Results> Field Extension> Antenna> Pattern (or DirectGain, Rad Power, Power Gain, Efficiency)

The HFSYM command accounts for PEC or PMC symmetry planes that coincide with the X-Y, Y-Z or Z-X planesof the global or a local Cartesian coordinate system. It applies the image principle on the symmetric part of thecomputational domain to represent the radiation effect of the partial equivalent current source beyond themodeled domain. HFSYM accounts for the radiation that would be present if the entire structure was modeled.If there is a PEC or PMC symmetry plane, you must issue the HFSYM command before issuing HFNEAR, PLHFFARor PRHFFAR. Although a PMC symmetry plane is a natural boundary condition in a finite element analysis, itmust be defined by the HFSYM command.

4.5.3.4. Radiation Solid Angle

You can specify the radiation space when calculating antenna parameters. To do so, use one of the following:Command(s): HFANGGUI: Main Menu> General Postproc> Plot Results> Field Extension> Antenna> Direct GainMain Menu> General Postproc> List Results> Field Extension> Antenna> Direct Gain (or RadPower, Power Gain, Efficiency)

The HFANG command defines the radiation space of an antenna in terms of the type of antenna. For example,the solid angle of a dipole antenna is determined by φε[ 0,360°] and θε[ 0,180°] and (Figure 4.32: “Solid Angle -Dipole Antenna”), while the solid angle of a monopole antenna above ground plane is associated with φε[ 0,360°]and θε[ 0,90°] (Figure 4.33: “Solid Angle - Monopole Antenna above Ground Plane”). If the electromagnetic waveis not radiated into the entire space, you must issue the HFANG command before issuing the PLHFFAR orPRHFFAR command.

Figure 4.32 Solid Angle - Dipole Antenna



Figure 4.33 Solid Angle - Monopole Antenna above Ground Plane

A phased array antenna is approximated by an infinite array of unit cells with periodic boundary conditions.When you calculate the antenna parameters of the entire array based on the solution of the unit cell , only halfa radiation space should be defined (that is, φε[ 0,360°] and θε[ 0,90°]).

4.5.4. Calculating Circuit Parameters for High-Frequency Devices

After you have solved a high-frequency problem, you often need to calculate some circuit parameters for theunderlying device. You can calculate the following parameters:

• Scattering matrix parameters (S-parameters) of the equivalent network

• Input power, reflected power, dissipated power, and transmitted power

• Voltage, current and characteristic impedance of the equivalent network

You can do this in POST1 by first reading in the solution for a given frequency and then performing certainpostprocessing tasks based on the corresponding definition of a parameter.

This section illustrates the basic steps you need to do to calculate parameters for high-frequency devices.

4.5.4.1. Scattering Parameters (S-Parameters)

You can calculate scattering parameters between a driven port (Port i) and a matched port (Port j) using one ofthe following:

Command(s): SPARMGUI: Main Menu> General Postproc> Elec&Mag Calc> S-Parameters

SPARM returns two S-parameters: Sii and Sji, where i represents the driven port and j is the matched port. For a

multi-port network, the S-parameters are defined as follows where a and b are the normalized incoming voltagewave and the normalized outgoing voltage wave, respectively.

Figure 4.34 Multi-port Network

Sba

Sb

aiii

i aji

j

i aj j

= == =0 0



The condition aj = 0 indicates a matched port. In your model, you should use an absorbing boundary condition,

such as PML, to truncate the computational domain. It represents the matched ports of the equivalent network.

If you are modeling a transmission line, you must define a voltage path from the central conductor to the groundon the transmission line port where the parameters will be extracted. You must also input the characteristic im-pedance of the transmission line prior to the solution. Usually, the characteristic impedance of the planar trans-mission line is assigned to be 50 Ohms. A current density source should be located away from the extractionport, which is located between the transmission line port and the PML region. PML must back the current densityexcitation source for wave absorption. The defined transmission line ports (see the HFPORT command) are onlyused for the extraction of parameters. You have to specify a current density excitation source for each port. Ifthe SPSWP macro is used, the current density sources need to be bound to an associated port using the BF, BFL,or BFA command with the current density (JS) load label.

For a multi-port device, you issue multiple commands to retrieve the required S-parameter matrix terms. TheSPARM macro will output the magnitude and phase angle of the S-parameters.

4.5.4.2. Reflection Coefficients in a COAX Fed Device

To calculate the voltage reflection coefficient (REFLC), standing wave ratio (VSWR), and return loss (RL) in a COAXfed device, use one of the following:

Command(s): REFLCOEFGUI: Main Menu> General Postproc> Elec&Mag Calc> Port> Refl Coeff

4.5.4.3. Power and Frequency Selective Surface Parameters

To calculate the input power, reflected power, return loss, and power reflection coefficient for a driven port, useone of the following:

Command(s): HFPOWERGUI: Main Menu> General Postproc> Elec & Mag Calc> Element Based> Power

If you define a matching output port, the HFPOWER macro can also calculate the transmitted power, insertionloss, and power transmission coefficient. For lossy materials and conducting surfaces, you can also use it to cal-culate the time-averaged dissipated power (from surface impedance or shielding boundary conditions). To cal-culate dissipated power in a region, you must select the elements that are associated with the lossy material orthe conducting surfaces.

For a periodic structure that is used as a frequency selective surface, you need to specify input and output ports.You can then calculate the reflection and transmission coefficients, power reflection and transmission coefficients,and return and insertion loss using one of the following:

Command(s): FSSPARMGUI: Main Menu> General Postproc> Elec & Mag Calc> Port> FSS Parameters

Refer to High-Frequency Electromagnetic Field Simulation in the ANSYS, Inc. Theory Reference for parameterdefinitions.

4.5.4.4. Voltage, Current, and Impedance

Voltage is defined as the line integral of the projection of electric field along the path.

V = - E dlbaa

b

⋅∫



To calculate it you need to define a path from the central conductor to the ground as shown in the followingfigure for a coaxial waveguide (a), a microstrip line (b), and a coplanar waveguide (c).

Figure 4.35 Voltage Paths for Transmission Lines

!

!

"#$ %

& '

()

''*

+,- .$ 0/12$ +3-45$ '6*$ %57$ +,- %' /1'2'$

You first define the path using the following commands or GUI paths:Command(s): PATH, PPATHGUI: Main Menu> General Postproc> Path Operations> Define Path> Path Status> Defined PathsMain Menu> General Postproc> Path Operations> Define Path> By Nodes (or By Location)

You then calculate the voltage using one of the following:Command(s): EMFGUI: Main Menu> General Postproc> Elec & Mag Calc> Path Based> EMF

The EMF command macro stores the results as the EMF parameter. All path items clear after EMF executes.

Current is defined as the line integral of the magnetic field H along a closed path containing the inner conductor:

I = H

c

Ñ∫ ⋅dl

To calculate it you need to define a closed current path contain the central conductor as shown in the followingfigure for a coaxial waveguide (a), a microstrip line (b), and a coplanar waveguide (c).

Figure 4.36 Current Paths for Transmission Lines89:;<=>8?:@AB;?<8CA<<9:;D#=;E

FG<?A:@F!<?A:@

HI;*<J K

LNM'OP5J B<?'Q;<J K5RJ :9 L,BO8?K'> =:=<S1=T9'UAJ @9

8CA<<9:V;D=';*E

8CA<<9:;D#=;*E

WGAV;9<8?:@AB;?<

X ::9<8?:@AB;?<

L,=O8?=YJ =>0S1=T9UAJ @9

After defining the current path using PATH or PPATH, you calculate the current using one of the following:Command(s): MMFGUI: Main Menu> General Postproc> Elec & Mag Calc> Path Based> MMF

A counter clockwise ordering of points on the PPATH command will yield the correct sign for MMF. The MMFcommand macro stores the results as the MMF parameter. All path items clear after MMF executes.

Characteristic impedance is defined as:



Z =VI

To calculate the impedance, you calculate both the EMF (voltage drop) and the MMF (current). The IMPD macrocalculates the complex impedance at the specified location. You must define the voltage and current paths beforeissuing IMPD. The impedance calculation can work with a symmetry sector of a model. For example, if youmodel only 10 degrees of a coax cable, you can supply a multiplier term on the MMF (current) calculation to ac-count for a full model.

Figure 4.37 Ten-Degree Symmetry Model of a Coaxial Waveguide

To invoke the IMPD macro, use one of the following:Command(s): IMPDGUI: Main Menu> General Postproc> Elec & Mag Calc> Path Based> Impedance

4.5.4.5. Smith Chart and Network Parameter Conversion

You can plot scattering, admittance, or impedance parameters on a Smith chart. A Touchstone file provides theinput parameters and their type. The PLSCH command can convert any input parameter type to a specifiedoutput parameter type.

To execute the PLSCH command, use one of the following:Command(s): PLSCHGUI: Main Menu> General Postproc> Plot Results> Smith Chart

You can also convert and list scattering, admittance, or impedance parameters input by a Touchstone file. ThePRSYZ command generates a new Touchstone file jobname_SYZ.snp for the network parameters.

To execute the PRSYZ command, use one of the following:Command(s): PLSCHGUI: Main Menu> General Postproc> Plot Results> SYZ conversion

You can also convert and plot scattering, admittance, or impedance parameters as a function of frequency.

To execute the PLSYZ command, use one of the following:Command(s): PLSCHGUI: Main Menu> General Postproc> Plot Results> SYZ parameters

For more information on Touchstone files, see Section 4.4.6: Starting the Solution. For an example problem, seePostprocessing Scattering, Admittance, and Impedance Parameters.



4–42

Chapter 5: Performing a Modal High-FrequencyAnalysisYou can use the ANSYS program to perform modal high-frequency analyses. Using a high-frequency modalanalysis in 3-D, you can perform tasks such as finding the resonant frequencies and modal shapes for the elec-tromagnetic field in a structure, as well as the quality factor if dielectric and surface losses are present. Fig-ure 5.1: “Flow Chart for a Modal Analysis” shows the flow of an ANSYS modal analysis.

For a 3 D modal analysis, the program uses the tetrahedral element HF119 or the hexahedral or triangular prismelement HF120 to calculate the resonant frequencies of multiple modes of a resonant cavity. The eigenvaluesolution does not consider any damping effects from lossy dielectric materials or surface losses. Input excitationis ignored, and the port is treated as an open circuit condition. Infinite surfaces (SF command, INF option (or GUIequivalent)) are treated as a Magnetic Wall boundary. Electric Wall conditions are accounted for properly. Specifiedlossy materials or surface impedance will be used in postprocessing to calculate a quality factor, but again willhave no bearing on the eigenvalue solution.

For a 2 D modal analysis, the ANSYS program uses the mixed nodal-edge element HF118 to determine the cutofffrequencies and propagating constants of multiple modes in a guided wave structure. Only a first order elementis available for determining the propagating constant for a fixed frequency.

For a modal high-frequency electromagnetic analysis you begin with the same steps as a harmonic high-frequencyanalysis as described in Section 4.1: Creating the Physics Environment and Section 4.2: Building the Model, As-signing Region Attributes, and Meshing. You then follow the procedures illustrated in the following figure anddescribed in the next few sections.


Figure 5.1 Flow Chart for a Modal Analysis

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5.1. Entering the SOLUTION Processor and Specifying the Modal AnalysisType

To enter the SOLUTION processor, use one of the following:Command(s): /SOLUGUI: Main Menu> Solution

To define the analysis as modal, use one of the following:Command(s): ANTYPE,MODALGUI: Main Menu> Solution> Analysis Type> New Analysis> Modal Analysis

5.2. Setting Options for Modal Analysis

To specify the type of high-frequency analysis, use one of the following:Command(s): HFEIGOPT,Lab,Val1GUI: Main Menu> Solution> Analysis Type> Analysis Options


Chapter 5: Performing a Modal High-Frequency Analysis

Use the HFEIGOPT command to specify one of the following modal analysis types:

• A 3-D eigenvalue analysis using HF119 or HF120.

• A 2-D modal analysis using HF118 to solve for cutoff frequencies.

• A 2-D modal analysis using HF118 to solve for propagating constants.

For a 2-D propagating constant analysis, only the first order HF118 element option (KEYOPT(1) = 1) is available.To obtain propagating constants over a frequency range, you have to execute a separate solution for each fre-quency and manually process each result. See the HFEIGOPT command for detals.

To specify solver options for your modal analysis, use one of the following:Command(s): MODOPTGUI: Main Menu> Solution> Analysis Type> Analysis Options

For a modal analysis, the Block Lanczos solver (MODOPT,LANB) or the subspace solver (MODOPT,SUBSP) shouldbe selected. The Block Lanczos solver, which is the default, is highly recommended.

Specifying a proper frequency range will make eigenvalue calculations more efficient and accurate. Input a lower-end frequency just below the anticipated frequency, using the FREQB argument on the MODOPT command. Inaddition, specify an upper-end frequency using the FREQC argument. Use the NMODE argument to request thenumber of modes to extract. Normalizing the mode shapes to unity (via the Nrmkey argument) is recommended.

5.3. Specifying Modes to Expand

To enable viewing of the modal solution and to perform other postprocessing options, you need to specify thenumber of modes to expand (i.e., calculate and write the element solution to the results file). This is required ifyou intend to postprocess the element data (plotting electric or magnetic fields, calculating the Quality factor,etc.). To specify the number of modes to expand, use one of the following:

Command(s): MXPANDGUI: Main Menu> Solution> Load Step Opts> ExpansionPass> Single Expand> Expand Modes

The MXPAND command is valid only within the first load step.

5.4. Applying Boundary Conditions

For a modal analysis, only the perfect electric conductor (PEC) boundary condition is required at appropriateboundaries. Specify this boundary condition using the methods described for a harmonic analysis in Section 4.3.1.1:Perfect Electric Conductor (PEC).

For a Quality factor computation, you may include effects from dielectric losses. To do so, specify a material res-istivity (RSVX) or loss tangent property (LSST) in the preprocessor. To include effects from surface losses, specifya surface impedance or shield properties using the SF or SFA command or their GUI paths. Specifiy these surfacequantities using the methods described for a harmonic analysis in Section 4.3.1: Applying Boundary Conditions.

5.5. Solving a Modal High-Frequency Analysis

To solve modal high-frequency analysis, use one of the following:Command(s): SOLVEGUI: Main Menu> Solution> Solve> Current LS

Once the solution process completes, use one of the following to leave the SOLUTION processor:Command(s): FINISH

Section 5.5: Solving a Modal High-Frequency Analysis


GUI: Main Menu> Finish

5.6. Calculating Propagating Constants

The first priority in transmission line design is to obtain the propagating constant at a fixed frequency (the dis-persion of a guided wave structure). The propagating constant will determine the characteristic impedance andphase wavelength of the transmission line. These parameters are the basic data for the design of RF and Microwavesystems and components.

The HFPCSWP macro calculates the propagating constants of a transmission line or waveguide over a frequencyrange. It displays them as a function of frequency in tabular or graphical output form. HFPCSWP writes out datato the file HFPCSWP.OUT and graphical displays to the file HFPCSWP.GRPH. You can use the DISPLAY programto display these graphis.

To invoke HFPCSWP, use one of the following:Command(s): HFPCSWPGUI: Main Menu> Solution> Solve> Electromagnet> HF Emag> 2D Freq Sweep

It is strongly recommended that you perform an initial solution at a single frequency to ensure that all input ar-guments are properly posed before you run a frequency sweep. To run a single frequency, set the begining andending frequencies to the same value. HFPCSWP can only be used with HF118 elements. See the HFPCSWPmacro for details.

5.7. Reviewing Modal High-Frequency Results

The eigenfrequencies are printed in the solution phase to the output file. In the postprocessor, reviewing thesolution of a high-frequency modal analysis involves only a few tasks. Begin by issuing the SET command or oneof its equivalent GUI paths to choose the mode to be read from the results file. (Issue the SET,LIST command orits GUI path to review the mode data sets on the results file.) Then, display the values of the electric field (E), themagnetic field (H), and the Pointing vector (P) as needed. Finally, calculate the Quality factor.

You can use the ANSYS macro QFACT to calculate the Quality factor of the resonance. It takes into accountdielectric losses (Qd) and surface losses (Qs):

1Q

=1

Q1

Qs d+

Use one of the following to execute QFACT:Command(s): QFACTGUI: Main Menu> General Postproc> Elec & Mag Calc> Cavity> Q-Factor


Chapter 5: Performing a Modal High-Frequency Analysis

Chapter 6: Adaptive RemeshingAmong the electromagnetic field boundary conditions, the normal electric flux should be continuous at theelement interfaces. However, discretization of the computational domain and numerical error lead to differencesat the element interfaces. Refining the mesh reduces these differences so that numerical accuracy is improved.For tetrahedral elements, you can use the HFEREFINE macro to automatically refine the mesh. It refines theelements with a difference value greater than the mean difference value. For a periodic structure, you cannotperform adaptive tetrahedral element meshing because identical mesh patterns are required on the master andslave surface.

To refine the elements, use one of the following:Command(s): HFEREFINEGUI: Main Menu> Preprocessor> Meshing> Modify Mesh> HF Refine

HFEREFINE removes all boundary conditions, excitation sources, and loads on the finite element model. Youmust reapply them. If you apply them to the solid model, they transfer automatically to the finite elementmodel.

The number of elements may increase very quickly with the number of refinements. Therefore, it is necessary tostart with a reasonable initial mesh and only perform a few refinements. You can adjust the HFEREFINE refinementfactor to reduce the number of elements refined. You can always start with a reasonable coarse mesh (for example,a mesh size of about 1/5 wavelength). See the HFEREFINE macro for details.

You can use APDL *do-loop to perform the refinement iterations. The following command input listing implementstwo refinements:

...et,1,HF119,1 ! define tetrahedral element..._n=3 ! two refinements are performed*do, i, 1, _n ! _i=1 skip refinement*if, _i, gt, 1, then/prep7hferefinefini*endif/solu...fini/post1...fini*enddo

See Example Harmonic Analysis of a Waveguide with a Dielectric Post (Command Method) for a problem usingadaptive meshing.

Automatic re-meshing is not available for the hexahedral element. However, HFEREFINE will list the elementswith the largest errors. You can then manually refine the local meshes by adjusting the mesh size on the associatedsolid model.


Part I. Basic Wave Radiation Examples

Harmonic Analysis for a Point Current RadiationSource (Command Method)Problem Description

This example demonstrates how to determine the near and far electric fields of a point current source usingANSYS commands.

In this example, you calculate the near and far electric fields of a point current source with a current density Jo

= 0.00125 A/m2. You use a PML region and reflective symmetry.

Target Results

The target results for this example problem are as follows:

Near-field at point (1,0,0): |E| = 1.862 V/m

Far-field at r = 10 m: |E| = 0.189 V/m

Radiation pattern: Normalized electric field = 0 dB

Commands This Example Uses

Below is the command input stream used to perform this analysis. All text preceded by an exclamation point (!)is a comment.

/batch,list/title, Near- and Far-field of Point Source with 4-Layer PML /nopr/prep7a1=0.3 $b1=0.3 $c1=0.3 ! normal element regiona2=0.4 $b2=0.4 $c2=0.4 ! PML exterior boundaryl1=c2-c1 ! thickness of PMLnx=12 $ny=12 $nz=12 ! division in normal element regionnpml=4 ! layers pf PMLfreq=300e6 ! working frequencycurr=1.25e-3 ! current density of point currentet,11,200,7 ! Temporary elementet,1,120,1 ! 1st-order BRICK elementet,2,120,1,,,1 ! PML elementmp,murx,1,1. ! air relative permeabilitymp,perx,1,1. ! air relative permittivitylocal,11 ! set up local coordinate systemwpcsys,,11rect,0,a1,0,b1 ! set up 2-D solid modelrect,0,a2,0,b2asba,2,1,,delete,keepaglue,1,3type,11 ! meshing 2-D modeleshape,0lesize,1,,,nxlesize,2,,,nylesize,3,,,nxlesize,4,,,nyamesh,1lesize,9,,,npmllesize,6,,,ny+npmllesize,7,,,nx+npmllesize,10,,,npmlamesh,3


esys,11 ! set up element coordinate systemtype,1 ! meshing normal element regionmat,1esize,,nzasel,s,area,,1vext,all,,,0,0,c1type,2 ! meshing PML regionesize,,nzasel,s,area,,3vext,all,,,0,0,c1esize,,npmlasel,s,loc,z,c1vext,all,,,0,0,l1allsel,all,allnummrg,all ! merge nodesasel,s,loc,z,0 ! delete 2-D elementaclear,allnsel,s,loc,x,0,0.51*a1 ! flag equivalence source surfacensel,r,loc,y,0,0.51*b1nsel,r,loc,z,0,0.51*c1esln,s,1,allnsel,s,loc,x,0.49*a1,0.51*a1nsel,a,loc,y,0.49*b1,0.51*b1nsel,a,loc,z,0.49*c1,0.51*c1sf,all,mxwfnsel,allesel,allnsel,s,loc,x,a2 ! set up PEC on PML exterior surfacensel,a,loc,y,b2nsel,a,loc,z,c2nsel,a,loc,z,0 ! set up PEC on z=0 symmetric planed,all,ax,0.nsel,allnsel,s,loc,x,0 ! set up point current source at (0,0,0) nsel,r,loc,y,0nsel,r,loc,z,0bf,all,js,0,0,curr ! J=Jznsel,allfinish/soluantype,harmic ! harmonic analysisharfrq,freq ! frequency for analysiseqslv,sparse ! sparse solversolvefinish/post1set,1,1hfsym,11,pmc,pmc,pec ! set up image symmetric planeprhffar,field,,0,360,6,90,90,,10. ! print out far-field at r=10/com,***** Target Results *****/com, ** Far-Field at R = 10 **/com, Magnitude = 0.189/com,hfnear,,11,1.,0.,0. ! print out near-field at (1,0,0)/com,***** Target Results *****/com, ** Near-Field at (1,0,0) **/com, Magnitude = 1.862/com,prhffar,patt,,0,360,6,90,90 ! print out antenna pattern/com,***** Target Results *****/com, ** Radiation Pattern **/com, Normalized Field = 0 (dB)/com,finish

ANSYS High-Frequency Electromagnetic Analysis Guide . ANSYS Release 9.0 . 002114 . © SAS IP, Inc.6

Harmonic Analysis for a Point Current Radiation Source (Command Method)

Part II. Basic Wave Propagation Examples

Harmonic Analysis of a Coaxial Waveguide(Command Method)Problem Description

This example describes how to do a simple harmonic high-frequency electromagnetic analysis of a coaxialwaveguide by issuing ANSYS commands, either manually during a session or in batch mode. You can also performthe analysis through the ANSYS GUI menus, using the procedures described in the next example.

This example calculates the scattering parameters (S-parameters), impedance, and reflection coefficients for acoax waveguide terminated in a matched port. Due to symmetry, the problem models only a 5° circumferentialangle.

Material Properties Used

µr = 1.0

εr = 1.0

Figure 1 Symmetry Model of a Coax Waveguide

Note — Nodes nbo, nbi, and nba are shown on the sketch for clarity. (These nodes are used in postpro-cessing.)

Geometric Properties Used

ri = .025 m

ro = .075 m


l = .375 m

Loading Used

Port voltage = 1.0

Ω = 0.8 GHz



/batch,list/prep7/show/title, Harmonic Response Analysis of a Coaxial Cable/comet,1,HF120,2 ! High-frequency solid brick element, 2nd ordermp,murx,1,1. ! Relative permeabilitymp,perx,1,1. ! Relative permittivitycylind,.025,.075,0,.375,0,5 ! Create wedge model/view,1,1,1,1/replotcsys,1lsel,s,loc,z,.375/2lesize,all,,,15 ! 15 elements along length of coaxlsel,s,loc,x,.05lesize,all,,,8 ! 8 elements along the radiuslsel,s,loc,y,2.5lesize,all,,,1 ! 1 element around the circumferencevmesh,1 ! Mesh the volumeasel,s,loc,x,.025asel,a,loc,x,.075da,all,ax,0 ! Set elec. wall boundary cond. (tangential E = 0)local,11,1csys,0asel,s,loc,z,0 ! Select area at port 1sfa,all,,port,1 ! Define as port 1hfport,1,coax,11,tem,hard,0.025,0.075,1,0 ! Specify port optionsasel,s,loc,z,.375 ! Select area at port 2sfa,all,,port,2 ! Define port 2hfport,2,coax,11,tem,impd,0.025,0.075,0,0 ! Specify port options (matching port)asel,allfinish/soluantype,harmic ! harmonic analysisharfrq,8e8solvefinish/post1sparm,1,2 ! Calculate S-parametersset,1,1plvect,h,,,h,vect,node ! Display H fieldplvect,ef,,,ef,vect,node ! Display E fieldcsys,1nbi=node(.025,0,.375) ! Retrieve node at inner radiusnbo=node(.075,0,.375) ! Retrieve node at outer radiusnba=node(.075,5,.375) ! Retrieve node at outer radius, angle 5 degreespath,vltg,2 ! Create path for voltageppath,1,nbi ! Define path points via nodesppath,2,nbopath,curr,2 ! Crete current path for currentppath,1,nbo ! Define path points via nodesppath,2,nbaimpd,'vltg','curr',1,72 ! Calculate impedance (current symm factor=72)reflcoef,1,1,0,.375,'vltg' ! Compute reflection coefficient and VSWRfinish


Harmonic Analysis of a Coaxial Waveguide (Command Method)

Harmonic Analysis of a Coaxial Waveguide (GUIMethod)Problem Description

This example shows how to use the ANSYS GUI to perform the same harmonic coaxial cable analysis done bythe command stream in the previous example.

Step 1: Start the Analysis

To begin the example analysis, do the following:

1. Activate the ANSYS GUI. When the GUI is fully active, choose Utility Menu> File> Change Title. A dialogbox appears.

2. Enter the title text, “Harmonic response analysis of a coaxial cable.”

3. Click OK.

4. Choose Main Menu> Preferences. The Preferences for GUI Filtering dialog box appears.

5. Select High Frequency, located under Electromagnetic.

6. Click OK.

Step 2: Define Element Types

1. Choose Main Menu> Preprocessor> Element Type> Add/Edit/Delete. The Element Types dialog boxappears.

2. Click Add. The Library of Element Types dialog box appears.

3. In the scrollable lists, choose (highlight) HF Electromagnet and 3D Brick 120 (HF120).

4. Check that the element type reference number is set to 1, then click OK.

5. Click Options. For "Element polynomial order K1,” choose "Second order elm." Then click OK.

6. Click Close in the Element Types dialog box.

Step 3: Define Material Properties

1. Choose Main Menu> Preprocessor> Material Props> Material Models. The Define Material ModelBehavior dialog box appears.

2. In the Material Models Available window, double-click on the following options: Electromagnetics, Rel-ative Permeability, Constant. A dialog box appears.

3. Enter 1 for MURX (Relative permeability), and click on OK. Material Model Number 1 appears in the Ma-terial Models Defined window on the left.

4. In the Material Models Available window, double-click on the following options: Relative Permittivity,Constant. A dialog box appears.

5. Enter 1 for PERX (Relative permittivity), and click on OK.

6. Click on menu path Material>Exit to remove the Define Material Model Behavior dialog box.


Step 4: Build the Model Geometry

1. Choose Main Menu> Preprocessor> Modeling> Create> Volumes> Cylinder> By Dimensions. TheCreate Cylinder by Dimensions dialog box appears.

2. Enter the following values:

THETA1 field: 0Z1 field: 0RAD1 field: .025

THETA2 field: 5Z2 field: .375RAD2 field: .075

3. Click OK. The ANSYS Graphics Window will show a wedge shape.

4. Choose Utility Menu> PlotCtrls> Pan, Zoom, Rotate. Click Iso. Click Close.

Step 5: Set Element Spacing and Mesh the Volume

1. Choose Utility Menu> WorkPlane> Change Active CS to> Global Cylindrical.

2. Choose Utility Menu> Select> Entities. The Select Entities dialog box appears.

3. Change the setting of the top button on the menu from Nodes to Lines.

4. Change the setting of the button below it to By Location.

5. Click the Z coordinates radio button on.

6. Check that the From Full radio button is on.

7. In the "Min, Max" field, enter .375/2.

8. Click OK.

9. Choose Main Menu> Preprocessor> Meshing> Size Cntrls> Lines> All Lines. The Element Sizes onAll Selected Lines dialog box appears.

10. Set the "No. of element divisions" field to 15.

11. Click OK.


13. The top button on the menu should be set to Lines and the next button should be set to By Location.

14. Click the X coordinates radio button on.

15. Check that the From Full radio button is on.

16. In the "Min, Max" field, enter .05.

17. Click OK.



20. Click OK.


22. The top button on the menu should be set to Lines and the next button should be set to By Location.

23. Click the Y coordinates radio button on.

24. In the "Min, Max" field, enter 2.5.

25. Click OK.


Harmonic Analysis of a Coaxial Waveguide (GUI Method)



28. Click OK.

29. Choose Main Menu> Preprocessor> Meshing> Mesh> Volumes> Mapped> 4 to 6 Sided. A pickingmenu appears.

30. Click Pick All.

31. Click SAVE_DB on the ANSYS Toolbar.

Step 6: Apply the Electric Wall Condition


2. Reset the top button to Areas and leave the next button set to By Location.

3. Click the X coordinates radio button on.


5. Click Apply.

6. Click the Also Sele button on.


8. Click OK.

9. Choose Main Menu> Preprocessor> Loads> Define Loads> Apply> Electric> Boundary> ElectricWall> On Areas. A picking menu appears.

10. Click Pick All.

11. Type local,11,1 in the ANSYS input window to define local coordinate system 11 (global cylindrical) andpress ENTER.

12. Choose Utility Menu> WorkPlane> Change Active CS to> Global Cartesian.

Step 7: Define the Waveguide Ports




4. In the "Min, Max" field, enter 0.

5. Click the From Full button on, then click OK.

6. Choose Main Menu> Preprocessor> Loads> Define Loads> Apply> Electric> Excitation> Port> Ex-terior> On Areas. A picking menu appears.

7. Click the Pick All button. The Define Waveguide Port on Areas dialog box appears.

8. Set the port number to 1 and click OK. The Define Waveguide PORT Options dialog box appears.

9. Verify the port type is set to Coaxial.

10. In the “Local CSYS number” field, enter 11.

11. Select “Hard Source” under the “Applied BC/Excitation” option menu.

12. In the "Inner radius or width" field, enter .025.

Section 1: Problem Description

13ANSYS High-Frequency Electromagnetic Analysis Guide . ANSYS Release 9.0 . 002114 . © SAS IP, Inc.

13. In the "Outer radius or height” field, enter .075.

14. In the "Field Amplitude" field, enter 1. Click OK.




18. In the "Min, Max" field, enter 0.375, then click OK.

19. Choose Main Menu> Preprocessor> Loads> Define Loads> Apply> Electric> Excitation> Port> Ex-terior> On Areas. A picking menu appears.

20. Click Pick All button. The Define Waveguide Port on Areas dialog box appears.

21. Set the port number to 2 and click OK. The Define Waveguide Port Options dialog box appears.

22. Verify the port type is set to Coaxial.

23. In the “Local CSYS number” field, enter 11. Set the “Applied BC/Excitation” type to “Impedance.” ClickOK.

24. Choose Utility Menu> Select> Everything.

Step 8: Solve the Harmonic Analysis

1. Choose Main Menu> Solution> Analysis Type> New Analysis. The New Analysis dialog box appears.

2. Choose Harmonic as the analysis type.

3. Click OK.

4. Choose Main Menu> Solution> Load Step Opts> Time/Frequenc> Freq and Substps. The HarmonicFrequency and Substep Options dialog box appears.

5. In the first "Harmonic frequency range" field, enter 8e8.

6. Click OK.

7. Choose Main Menu> Solution> Solve >Current LS. A pop-up window displays the solution optionsyou have defined. Review this information and click Close when you have finished reading it.

8. In the Solve Current Load Step dialog box, click OK to start the solution. A pop-up message notifies youwhen the solution is done. Click Close to close the message window.

9. Choose Main Menu> Finish.

Step 9: Calculate Scattering (S) Parameters

1. Choose Main Menu> General Postproc> Elec&Mag Calc> Port> S-Parameters. The Calculate S-Para-meters dialog box appears.

2. In the "Porti Source port number" field, enter 1.

3. In the "Portj Matched port number" field, enter .

4. Click OK. A pop-up window displays the scattering (s) parameters and their values. When you have readthis information, click Close.

Step 10: Display Vector Plots of the Magnetic and Electric Fields

1. Choose Main Menu> General Postproc> Read Results> By Load Step. The Read Results by Load StepNumber dialog box appears.



2. For both the "Load step number" and "Substep number" fields, enter 1.

3. Click OK.

4. Choose Utility Menu> Plot> Results> Vector Plot. The Vector Plot of Predefined Vectors dialog boxappears.

5. In the "Vector item to be plotted" scrollable lists, highlight Flux & Gradient and Mag Field H.

6. In the "Mode" field, click vector mode on.

7. In the "Vector location for results" field, click Elem Nodes on.

8. Click OK. The image in the Graphics Window becomes a vector plot of the magnetic field (H).

9. Again, choose Utility Menu> Plot> Results> Vector Plot. The Vector Plot of Predefined Vectors dialogbox appears.

10. In the "Vector item to be plotted" scrollable lists, highlight Flux & Gradient and Elec Field EF.

11. In the "Mode" field, click vector mode on.

12. In the "Vector location for results" field, click Elem Nodes on.

13. Click OK. The Graphics Window now displays a vector plot of the electric field (EF).


Step 11: Define Paths for EMF (Voltage Drop) and MMF (Current)

1. Choose Utility Menu> WorkPlane> Change Active CS to> Global Cylindrical.

2. Choose Utility Menu> Parameters> Scalar Parameters. The Scalar Parameters dialog box appears.

3. Enter the values shown below:

nbi = node (.025,0,.375)nbo = node (.075,0,.375)nba = node (.075,5,.375)

After typing each parameter value, click Accept. If you make a mistake typing a parameter value, backspaceand retype it. To erase an incorrect parameter after you have entered it, click on that parameter thenclick Delete.

4. Click Close.

5. Choose Main Menu> General Postproc> Path Operations> Define Path> By Nodes. The picking menuappears. At this point you may use the mouse to pick the nodes defining a path from the inner coax ra-dius to the outer coax radius identified as "nbi" and "nbo" in Figure 1: “Symmetry Model of a CoaxWaveguide”. Alternatively, since we have captured the node numbers at those locations as parameters,you can input the parameter values in the picker command line. We will detail this last procedure here(although the former procedure is simpler).

6. In the picker, enter NBI and press the ENTER key.

7. In the picker, enter NBO and press the ENTER key.

8. Click OK. Another dialog box appears.

9. In the "Define Path Name" field, enter VLTG.

10. Click OK. Close the PDEF window.

11. Choose Main Menu> General Postproc> Path Operations> Define Path> By Nodes. The picking menuappears.



12. In the picker, enter NBO and press the ENTER key.

13. In the picker, enter NBA and press the ENTER key.

14. Click OK. Another dialog box appears.

15. In the "Define Path Name" field, enter CURR.

16. Click OK. Close the PDEF window.

Step 12: Calculate Impedance

1. Choose Main Menu> General Postproc> Elec&Mag Calc> Path Based> Impedance. The CalculateImpedance dialog box appears.

2. Check that the "Voltage drop path name" is VLTG and the "Current calc path name" is CURR. (VLTG andCURR should be highlighted.)

3. Set the "Vsymm Voltage symmetry factor" field to 1.

4. Set the "Isymm Current symmetry factor" field to 72.

5. Click OK. A pop-up window displays impedance results. Click Close to close the results pop-up.

Step 13: Calculate Reflection Coefficients, Voltage Standing Wave Ratio, andInsert Loss, and Finish the Analysis

1. Choose Main Menu> General Postproc> Elec&Mag Calc> Port> Refl Coeff. The Calculate ReflectionCoefficients dialog box appears.

2. Set the "Input port number" field to 1.

3. Set the "Input port voltage" field to 1.

4. Set the "Voltage phase angle" field to 0.

5. Set the "Propagation distance" field to .375.

6. Set the "Propagation path name" field to VLTG.

7. Click OK. A pop-up window appears, showing you the reflection coefficient results.

8. Click Close to close the pop-up window.


10. Click on QUIT on the ANSYS Toolbar. Choose an exit option and click OK.

Calculated results: (see commands SPARM, IMPD, and REFLCOEF for parameter definitions): S11 = 0.0, S12 =1.007, ZRe = 65.14 Ω, Zim = -0.16 Ω, REFLC = 6.87e-4, VSWR = 1.001, RL = 63.26.



Figure 1 Magnetic Field in Coax



Figure 2 Electric Field in Coax



Part III. Basic Wave Resonance Examples

Modal Analysis of a Cavity (Command Method)Problem Description

This example describes how to do a modal high-frequency analysis of a cavity using ANSYS commands. You canalso perform the analysis through the ANSYS GUI menus, using the procedures described in the next example.

This example analysis calculates the TE101 mode eigenfrequency and quality factor in a Teflon filled cavity withcopper walls. The example assumes that the dielectric and surface losses are small and do not affect the eigen-frequency solution.

Material Properties Used

µr = 1.0

εr = 2.05

ρ = 1.0361x105

Figure 1 Teflon Filled Cavity

Geometric Properties Used

d = 1.0 m, w = 0.4 m, h = 0.3 m

Shielding Surface Properties Used

τ = .58x108 S/m


µr = 1.0



/batch,list/prep7/show/title, Eigenvalue analysis of a dielectric-filled cavity/com, Calculate the TE101 mode eigenfrequency and Quality/com, factor in a Teflon-filled cavity with copper walls/com,_length=1.0_width=0.4_height=0.3epsr=2.05rvsigma=1.0361e5cond=0.58e8et,1,hf120,2 ! HF solid brick element, 2nd ordermp,murx,1,1. ! Relative permeability - teflonmp,perx,1,epsr ! Relative permittivity - teflonmp,rsvx,1,rvsigma ! Resistivity - teflon_h=0.08block,0,_length,0,_width,0,_height ! Create cavity/view,1,1,1,1/replotesize,_hmshape,0,3d ! Hex elementsmshkey,1 ! Mapped meshvmesh,1 ! Mesh volumeda,all,ax,0 ! Set electric wall boundary cond. (tangential E=0)sfa,all,,shld,cond,1.0 ! specify surface shielding propertiesfinish/soluantype,modal ! Modal analysismodopt,lanb,1,2.2e8,4.0e8,,on ! Block Lanczos solver (the default)mxpand,,,,yes ! Expand modesolvefinish/post1set,last/view,,.75,.5,.6/vup,1,zplvect,h,,,,vect,node,on ! display H fieldplvect,ef,,,,vect,node,on ! display E fieldqfactfinish


Modal Analysis of a Cavity (Command Method)

Modal Analysis of a Cavity (GUI Method)Problem Description

Calculated Quality Factor = 3006.1

This example describes how to use the ANSYS GUI doing the same modal high-frequency analysis done usingANSYS commands in the previous example.

Step 1: Start the Analysis

To begin the example analysis, do the following:

1. Activate the ANSYS GUI. When the GUI is fully active, choose Utility Menu> File> Change Title. A dialogbox appears.

2. Enter the title text, Eigenvalue analysis of a dielectric filled cavity.

3. Click OK.

4. Choose Main Menu> Preferences. The Preferences for GUI Filtering dialog box appears.

5. Select High Frequency under Electromagnetic and click OK.

Step 2: Define Element Types

1. Choose Main Menu> Preprocessor> Element Type> Add/Edit/Delete. The Element Types dialog boxappears.

2. Click Add. The Library of Element Types dialog box appears.

3. In the scrollable lists, choose (highlight) HF Electromagnet and 3D Brick 120 (HF120).

4. Check that the element type reference number is set to 1, then click OK.

5. Click Options. For "Element polynomial order K1," choose "Second order elm." Then click OK.

6. Click Close in Element Types dialog box.

Step 3: Define Material Properties

1. Choose Main Menu> Preprocessor> Material Props> Material Models. The Define Material ModelBehavior dialog box appears.

2. In the Material Models Available window, double-click on the following options: Electromagnetics, Rel-ative Permeability, Constant. A dialog box appears.

3. Enter 1 for MURX (Relative permeability). Click on OK. Material Model Number 1 appears in the MaterialModels Defined window on the left.

4. In the Material Models Available window, double-click on the following options: Resistivity, Constant. Adialog box appears.

5. Enter 1.0361e5 for RSVX (Electrical resistivity). Click on OK.

6. In the Material Models Available window, double-click on the icons next to the following options: RelativePermittivity, Constant. A dialog box appears.

7. Enter 2.05 for PERX (Relative permittivity). Click on OK.

8. Choose menu path Material>Exit to remove the Define Material Model Behavior dialog box.


Step 4: Create the Cavity

1. Choose Main Menu> Preprocessor> Modeling> Create> Volumes> Block> By Dimensions. TheCreate Block By Dimensions dialog box appears.

2. Enter the values shown below in the appropriate fields. (Use the Tab key to move between fields.)

Z1 field: 0Y1 field: 0X1 field: 0

Z2 field: .3Y2 field: .4X2 field: 1

3. Click OK. The Graphics Window displays the new block.

4. Choose Utility Menu> PlotCtrls> Pan, Zoom, Rotate. Click Iso. Click Close.

Step 5: Mesh the Cavity

1. Choose Main Menu> Preprocessor> Meshing> MeshTool. The MeshTool appears.

2. Under the Size Controls section of the MeshTool, click the Set button beside "Globl." The Global ElementSizes dialog box appears.

3. In the "SIZE Element edge length" field, enter .08.

4. Click OK to return to the MeshTool.

5. Click Hex and Map.

6. Click the MESH button. A picking menu appears.

7. Click Pick All.

8. When meshing is complete, click Close in the MeshTool.


Step 6: Apply the Electric Wall Condition and Specify Surface Shielding Prop-erties

1. Choose Main Menu> Preprocessor> Loads> Define Loads> Apply> Electric> Boundary> ElectricWall> On Areas. The Apply Electric Wall picking menu appears.

2. Click Pick All. The Graphics Window displays the electric wall boundary condition

3. Choose Main Menu> Preprocessor> Loads> Define Loads> Apply> Electric> Boundary> Shield>On Areas. The Apply SHLD on Areas picking menu appears.

4. Click Pick All. The Apply SHLD on Areas dialog box appears.

5. Set COND = .58e8 and MUR = 1.0

6. Click OK.


Step 7: Solve the Analysis

1. Choose Main Menu> Solution> Analysis Type> New Analysis. The New Analysis dialog box appears.

2. Make sure that the Modal radio button is selected.

3. Click OK.


Modal Analysis of a Cavity (GUI Method)

4. Choose Main Menu> Solution> Analysis Type> Analysis Options. The Modal Analysis dialog box ap-pears.

5. Make sure that Block Lanczos is selected.

6. Specify the number of modes to extract (1).

7. Set the Expand mode shapes button to Yes.

8. Specify the number of modes to expand (1).

9. Set the Calculate elem results button to Yes.

10. Click OK. The Block Lanczos Method dialog box appears.

11. In the "FREQB Start Freq" field, enter 2.2e8.

12. In the "FREQE End Frequency" field, enter 4.0e8.

13. Set the Nrmkey Normalize mode shapes button to To Unity.

14. Click OK.

15. Choose Main Menu> Solution> Solve> Current LS. A pop-up window displays the analysis optionsyou specified. Review the window contents and then click Close.

16. In the Solve Current Load Step dialog box, click OK. A pop-up message notifies you when solution iscomplete. Click Close to close it.


Step 8: Display Vector Plots of the Magnetic and Electric Fields

1. Choose Main Menu> General Postproc> Read Results> Last Set.

2. Choose Utility Menu> PlotCtrls> View Settings> Viewing Direction. The Viewing Direction dialogbox appears.

3. Enter the values shown below in the appropriate fields:

XV field: .75

YV field: .5

ZV field: .6

4. Set the Coord axis orientation field to Z-axis Up.

5. Click OK.

6. Choose Utility Menu> Plot> Results> Vector Plot. The Vector Plot of Predefined Vectors dialog boxappears.

7. In the "Vector item to be plotted" scrollable lists, highlight “Flux & gradient” on the left and “Mag fieldH” on the right.

8. For "Mode," click vector mode on.

9. For "Vector location for results," click Elem Nodes on.

10. Turn “Edge element edges” on (Displayed).

11. Click OK. The image in the Graphics Window becomes a vector plot of the magnetic field intensity (H).

12. Again, choose Utility Menu> Plot> Results> Vector Plot. The Vector Plot of Predefined Vectors dialogbox appears.



13. In the "Vector item to be plotted" scrollable lists, highlight “Flux & gradient“ on the left and “Elec fieldEF” on the right.

14. For "Mode," click vector mode on.

15. For "Vector location for results," click Elem Nodes on.

16. Verify that “Edge element edges” is set to Displayed.

17. Click OK. The Graphics Window now displays a vector plot of the electric field (EF).

Step 9: Calculate the Quality Factor and Finish the Analysis

1. Choose Main Menu> General Postproc> Elec&Mag Calc> Cavity> Q-Factor. A dialog box appears.Click OK. The ANSYS program displays the results of the quality factor calculation in a pop-up window.

2. Review the results, then click Close to close the pop-up window.


4. Click Quit on the ANSYS Toolbar. Choose an exit option and click OK.

Figure 1 Magnetic Field Vector Display of TE101 Mode


Modal Analysis of a Cavity (GUI Method)

Figure 2 Electric Field Vector Display of TE101 Mode



Modal Analysis for a Circular Waveguide(Command Method)Problem Description

This example demonstrates how to determine the dispersion characteristics of a waveguide using ANSYS com-mands.

In this example, you calculate the propagating constants and cutoff frequencies for a circular waveguide with aradius of 1 meter.

Target Results


10.19310.30910.309Propagating constant (γ)

114.82 MHz87.911 MHz87.911 MHzFrequency (f)



/batch, list/title, Cutoff Freq. & Prop. Const. for Circular Waveguide /com, radius = 1 m/prep7a=1.et,1,118,1 ! 1st order elementtype,1emunit,mksmp,murx,1,1.mp,perx,1,1.cyl4,,,amshkey,0mshape,1 ! tri elementesize,0.1*aamesh,1!! set up PEC boundary condition!dl,all,,ax,0.finish! Solve propagating constants! Target result: Gamma = 10.309, 10.309, 10.193 /soluantype,modalhfeig,gamma,500.e6modopt,lanb,3,1.e6,1.e9,,onmxpand,,,,yessolvefini! Solve cutoff frequency! Target result: Freq. = 87.911 MHz, 87.911 MHz, 114.82 MHz/soluantype,modalhfeig,cutoffmodopt,lanb,3,,1.e12,,onmxpand,,,,yes


solvefinish


Modal Analysis for a Circular Waveguide (Command Method)

Part IV. Basic Wave Scattering Examples

Harmonic Analysis for Plane Wave Scatteringfrom a Metallic Plate (Command Method)Problem Description

This example demonstrates how to determine the radar cross section (RCS) of a metallic plate using ANSYScommands.

In this example, you calculate the RCS of a PEC plate (1λo x 1λo). You use a PML region and reflective symmetry.

Target Results


Method of Moment (MoM) Results:

RCS (dB)Angle θ (Degrees)

H-plane (φ = 90°)E-plane (φ = 0°)

10.510.50

9.99.910

9.08.520

7.56.230

5.03.040

1.90.050

-1.8-2.060

-6.2-2.170

-12.5-2.0580



/batch,list/title, RCS from a Metallic Plate /com, Problem: RCS from a Metallic Plate with 1 wavelength x 1 wavelength/com, Incident Wave: +y polarization with PHI = 90 (degree)/com, THETA = 0 (degree)/com, Field Symmetry: 1/4 Structure, x-z plane & y-z plane/nopr/prep7freq=300e6 $lambda=3.e8/freqa=0.5*lambda $b=0.5*lambda ! 1/4 metallic platea1=0.8*lambda $b1=0.8*lambda $c1=0.3*lambda ! PML interior boundarya2=1.2*lambda $b2=1.2*lambda $c2=0.7*lambda ! PML exterior boundaryl1=c2-c1 $la=a/a1 $lb=b/b1nx=8 $ny=8 $nz=3npml=4 ! number of PML layerset,11,200,7 ! temporary elementet,1,120,1 ! 1st order Brick elementet,2,120,1,,,1 ! PML elementmp,murx,1,1. ! relative permeabilitymp,perx,1,1. ! relative permittivity


rect,0,a1,0,b1 ! build up geometric modelrect,0,a2,0,b2asba,2,1,,delete,keepaglue,1,3type,11 ! 2-D meshinglesize,1,,,nxlesize,2,,,nylesize,3,,,nxlesize,4,,,nyamesh,1lesize,9,,,npmllesize,6,,,ny+npmllesize,7,,,nx+npmllesize,10,,,npmlamesh,3type,1 ! create normal elementmat,1esize,,nzasel,s,area,,1vext,all,,,0,0,-c1asel,s,area,,1vext,all,,,0,0,c1type,2 ! create PML elementesize,,nzasel,s,area,,3vext,all,,,0,0,-c1asel,s,area,,3vext,all,,,0,0,c1esize,,npmlasel,s,loc,z,-c1vext,all,,,0,0,-l1asel,s,loc,z,c1vext,all,,,0,0,l1asel,s,loc,z,0 ! delete temporary elementaclear,allallsel,all,allnummrg,allnsel,s,loc,x,0,a+1.01*a1/nx ! flag equivalence source surfacensel,r,loc,y,0,b+1.01*b1/nynsel,r,loc,z,-1.01*c1/nz,1.01*c1/nzesln,s,1,allnsel,s,loc,x,0.99*(a+a1/nx),1.01*(a+a1/nx)nsel,a,loc,y,0.99*(b+b1/ny),1.01*(b+b1/ny)nsel,a,loc,z,-1.01*c1/nz,-0.99*c1/nznsel,a,loc,z,0.99*c1/nz,1.01*c1/nzsf,all,mxwfnsel,allesel,allnsel,s,loc,x,a2 ! set PEC on exterior surface of PMLnsel,a,loc,y,b2nsel,a,loc,z,-c2nsel,a,loc,z,c2nsel,a,loc,y,0 ! set PEC on field symmetric planed,all,ax,0.nsel,allnsel,s,loc,z,-0.001,0.001 ! set PEC on metallic platensel,r,loc,x,-0.001,1.001*ansel,r,loc,y,-0.001,1.001*bd,all,ax,0.nsel,allplwave,0,1,0,90,0 ! incident plane wavefinish/soluantype,harmic ! harmonic analysisharfrq,freq ! working frequencyeqslv,sparse ! SPARSE solverhfscat,scat ! define a scattering solution solvefinish/post1set,1,1hfsym,,pmc,pec ! define image symmetric plane


Harmonic Analysis for Plane Wave Scattering from a Metallic Plate (Command Method)

prhffar,rcs,,90,90,,0,90,18 ! RCS on H-planeprhffar,rcs,,0,0,,0,90,18 ! RCS on E-planefinish



Part V. Advanced Wave Radiation Examples

Harmonic Analysis for a JRM Array Antenna(Command Method)Problem Description

This example demonstrates how to determine the S-parameter and antenna parameters of a 25×25 JRM arrayantenna using ANSYS commands.

The JRM array consists of 0.9" × 0.4" rectangular waveguides in a 1.0" × 0.5" rectangular lattice, as shown on theleft in the following figure. Only one radiation unit is modeled. The FEA model consists of a waveguide of 0.9" ×0.4" × 0.75" and an air box of 1.0" × 0.5" × 0.75" as shown on the right. The air box is covered by Perfectly MatchedLayers (PML) of absorbing material, 0.75" thick. An E-plane (φ=90°) scan is performed at 9.25 GHz.

Figure 1 3×4 JRM Array and FEA Model of Unit Cell



/batch,list/title, S11 and antenna directive gains of JRM Array, E plane scan, 9.25 GHz /com, Problem: Compute S11 of JRM Array for E-Plane scan at 9.25 GHz /com, Numerical Model: Waveguide + Radiation Space + PML/com, Waveguide: 0.9"x0.4"x0.75"/com, Radiation Space: 1.0"x0.5"x0.75"/com, PML: 1.0"x0.5"x0.75"/com, Refined meshes near the aperture /com, /nopr/prep7! --- Geometric and operating conditions ---freq=9.25e9lamda=3.e8/freqscal=25.4e-3_px=1.*scal_py=0.5*scal


a1=scal*0.9/2.b1=scal*0.4/2.a2=scal*1.0/2.b2=scal*0.5/2c1=0c2=c1+scal*0.5c3=c2+scal*0.25c4=c3+scal*0.25c5=c4+scal*0.5c6=c5+scal*0.75! --- Mesh definition ---h1=lamda/10h2=0.5*h1tiny=1.e-5ang=43! --- Define elements and materialet,11,200,5et,1,119,1,,,0et,2,119,1,,,1 mp,murx,1,1.mp,perx,1,1.! --- Numerical model ---local,11wpcsys,,11block,-a1,a1,-b1,b1,c1,c2block,-a1,a1,-b1,b1,c2,c3block,-a2,a2,-b2,b2,c3,c4block,-a2,a2,-b2,b2,c4,c5block,-a2,a2,-b2,b2,c5,c6vglue,alltype,11esize,h2asel,s,loc,x,-a2asel,a,loc,y,-b2asel,r,loc,z,c3,c4amesh,allesize,h1asel,s,loc,x,-a2asel,a,loc,y,-b2asel,r,loc,z,c4,c5amesh,allasel,s,loc,x,-a2asel,a,loc,y,-b2asel,r,loc,z,c5,c6amesh,allallsasel,s,loc,x,-a2agen,2,all,,,2*a2asel,s,loc,y,-b2agen,2,all,,,0,2*b2allsnummrg,allmat,1type,1 vsel,s,loc,z,c1,c2esize,h1vmesh,allvsel,s,loc,z,c2,c4esize,h2vmesh,allvsel,s,loc,z,c4,c5esize,h1vmesh,all! --- PML element ---type,2 vsel,s,loc,z,c5,c6vmesh,allallsaclear,alletdel,11allsnsel,s,loc,z,c3


Harmonic Analysis for a JRM Array Antenna (Command Method)

nsel,r,loc,x,-a1+tiny,a1-tinynsel,r,loc,y,-b1+tiny,b1-tinycm,ndapt,node! --- Define master/slave coupling ---nsel,s,loc,x,-a2nsel,a,loc,x,a2cpcyc,ax,,,2*a2,0,0,1nsel,s,loc,y,-b2nsel,a,loc,y,b2cpcyc,ax,,,0,2*b2,0,1alls! --- Set PEC on waveguide & PML wall ---nsel,s,loc,x,-a1nsel,a,loc,x,a1nsel,a,loc,y,-b1nsel,a,loc,y,b1nsel,r,loc,z,c1,c3d,all,ax,0nsel,s,loc,z,c3nsel,u,,,ndaptd,all,ax,0nsel,s,loc,z,c6d,all,ax,0nsel,all! --- Flag equivalent source surface with MXWF ---nsel,s,loc,z,c3,c4esln,s,1,allnsel,s,loc,z,c4sf,all,mxwfalls! --- Define waveguide port ---hfport,1,rect,11,TE10,impd,2*a1,2*b1,1. nsel,s,loc,z,c1sf,all,PORT,1allssavefini/solu! --- Perform angle scanning for S-parameter calculation ---spscan,freq,,90,90,,10,80,3.3,1! use PLSPmacro command to plot out S-parameter in GUIfini/solu! --- Perform an analysis at 43 degreeantype,harmic hfpa,scan,,90,angharfrq,freqeqslv,sparsesolvefini/post1hfang,angle,0,360,0,90 ! define the radiation space (semi-space)/thra,0,360 ! define the range of theta angle (undocumented)plhffar,dgain,polar,90,90,,-70,85,155 ! plot the directive gain of unit cellhfarray,25,25,_px,_py ! define a 25×25 arrayplhffar,dgain,polar,90,90,,-70,85,155 ! plot the directive gain of 25×25 arrayfini

The Target Results

Figure 2: “S-Parameter of JRM Array with E-Plane Scan at 9.25 GHz” depicts the S-parameter at the waveguideport over a range of angles, from 10° to 80°. Figure 3: “Directive Gain of Unit Cell with E-Plane Scan at 9.25 GHz”shows the directive gain of single radiation element at scan angle 43°. The directive gain of a 25×25 JRM arrayat scan angle 43° is shown in Figure 4: “Directive Gain of a 25×25 JRM Array with E-Plane Scan at 9.25 GHz”.



Figure 2 S-Parameter of JRM Array with E-Plane Scan at 9.25 GHz



Figure 3 Directive Gain of Unit Cell with E-Plane Scan at 9.25 GHz



Figure 4 Directive Gain of a 25×25 JRM Array with E-Plane Scan at 9.25 GHz



Harmonic Analysis for a Lee-Jones ArrayAntenna (Command Method)Problem Description

This example demonstrates how to determine the S-parameter of a Lee-Jones array antenna with a triangularlattice using ANSYS commands.

The Lee-Jones array consists of 1.122" × 0.497" rectangular waveguides in a 1.25" × 0.625" triangular lattice, asshown on the left in Figure 1: “5×5 Lee-Jones Array and FEA Model of Unit Cell”. Only one radiation unit is modeled.The FEA model shown on the right consists of a waveguide of 1.122" × 0.497" × 1.0" and an air box of 1.25" ×0.625" × 1.0". The air box is covered by Perfectly Matched Layers (PML) of absorbing material, 0.5" thick. An H-plane (φ=0°) scan is performed at 9.5 GHz. The periodic boundary conditions are shown in Figure 2: “PeriodicBoundary Condition for Lee-Jones Array”.

Figure 1 5×5 Lee-Jones Array and FEA Model of Unit Cell

Figure 2 Periodic Boundary Condition for Lee-Jones Array

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/batch,list/title, S11 of Lee-Jones Array with the triangular lattice/com, Numerical Model: Waveguide + Radiation Space + PML/com, Waveguide: 1.122"x0.497"1.0"/com, Radiation Space: 1.25"x0.625"x1.0"/com, PML: 1.25"x0.625"x0.5"/com, Refined meshes near the aperture /nopr/prep7! --- Geometric and operating conditions ---freq=9.5e9lamda=3.e8/freqscal=25.4e-3a1=scal*1.122/2.b1=scal*0.497/2.a2=scal*1.25/2.b2=scal*0.625/2.c1=0c2=c1+scal*0.75c3=c2+scal*0.25c4=c3+scal*0.25c5=c4+scal*0.75c6=c5+scal*0.5! --- Mesh definition ---h1=lamda/12h2=0.5*h1

! --- Define elements and materialet,11,200,5et,1,119,1,,,0et,2,119,1,,,1mp,murx,1,1.mp,perx,1,1.! --- Numerical model ---local,11wpcsys,,11block,-a1,0,-b1,b1,c1,c2block,-a1,0,-b1,b1,c2,c3block,0,a1,-b1,b1,c1,c2block,0,a1,-b1,b1,c2,c3block,-a2,0,-b2,b2,c3,c4block,-a2,0,-b2,b2,c4,c5block,0,a2,-b2,b2,c3,c4block,0,a2,-b2,b2,c4,c5block,-a2,0,-b2,b2,c5,c6block,0,a2,-b2,b2,c5,c6vglue,alltype,11esize,h2asel,s,loc,x,-a2asel,a,loc,y,b2asel,r,loc,z,c3,c4amesh,allesize,h1asel,s,loc,x,-a2asel,a,loc,y,b2asel,r,loc,z,c4,c5amesh,allasel,s,loc,x,-a2asel,a,loc,y,b2asel,r,loc,z,c5,c6amesh,allallsasel,s,loc,x,-a2agen,2,all,,,2*a2asel,s,loc,y,b2


Harmonic Analysis for a Lee-Jones Array Antenna (Command Method)

asel,r,loc,x,-a2,0agen,2,all,,,a2,-2*b2asel,s,loc,y,b2asel,r,loc,x,0,a2agen,2,all,,,-a2,-2*b2allsnummrg,allmat,1type,1 esize,h1vsel,s,loc,z,c1,c2vsel,a,loc,z,c4,c5vmesh,allesize,h2vsel,s,loc,z,c2,c4vmesh,all! --- PML element ---type,2 esize,h1vsel,s,loc,z,c5,c6vmesh,allallsaclear,alletdel,11alls! --- Define master/slave coupling ---nsel,s,loc,y,b2nsel,r,loc,x,-a2,0cm,edge11,nodensel,s,loc,y,b2nsel,r,loc,x,0,a2cm,edge21,nodensel,s,loc,y,-b2nsel,r,loc,x,-a2,0cm,edge22,nodensel,s,loc,y,-b2nsel,r,loc,x,0,a2cm,edge12,nodensel,s,loc,z,c3nsel,r,loc,x,-a1,a1nsel,r,loc,y,-b1,b1cm,ndapt,nodensel,s,loc,x,-a2nsel,a,loc,x,a2cpcyc,ax,,,2*a2,0,0,1nsel,s,,,edge11nsel,a,,,edge12cpcyc,ax,,,a2,-2*b2,0,1nsel,s,,,edge21nsel,a,,,edge22cpcyc,ax,,,-a2,-2*b2,0,1alls! --- Set PEC on waveguide wall & PML wall ---nsel,s,loc,x,-a1nsel,a,loc,x,a1nsel,a,loc,y,-b1nsel,a,loc,y,b1nsel,r,loc,z,c1,c3d,all,ax,0nsel,s,loc,z,c3nsel,u,,,ndaptd,all,ax,0nsel,s,loc,z,c6d,all,ax,0nsel,all! --- Define waveguide port ---hfport,1,rect,11,TE10,impd,2*a1,2*b1,1. nsel,s,loc,z,c1sf,all,PORT,1allssavefini



/solu! --- Perform angle scanning for S-parameter calculation ---spscan,freq,,0,0,,0,55,5,0fini

Target Results

The figure below depicts the S-parameter at the waveguide port over a range of angles, from 0° to 55°.

Figure 3 S-Parameter of Lee-Jones Array with E-Plane Scan at 9.5 GHz


Harmonic Analysis for a Lee-Jones Array Antenna (Command Method)

Harmonic Analysis for Line-fed Microstrip PatchAntenna (Command Method)Problem Description

This example demonstrates how to determine the S-parameter of a line-fed microstrip patch antenna usingANSYS commands.

The line-fed microstrip patch antenna consists of a 16 mm × 12.45 mm metallic rectangular patch on the substratewith the thickness of 0.794 mm and εr = 2.2. The width of the microstrip is 2.46 mm and the characteristic imped-

ance is assumed to be 50 Ohms. The distance from the edge of the microstrip to the edge of the patch is 2.09mm, as shown on the top in the figure below. The structure is enclosed by Perfectly Matched Layers (PML) ofabsorbing material, excepting the ground plane, as shown on the bottom.


Figure 1 Line-fed Microstrip Patch Antenna Geometry and FEA Model



/batch,list/title, Microstrip Rectangular Patch Antenna/com, Problem: Compute S-Parameter of Microstrip Rectangular Patch/com, Microstrip: Width=2.46 mm, Substrate thickness=0.794 mm, er=2.2/com, Patch: 16x12.45 mm^2; Distance from microstrip edge to patch edge: 2.09 mm/nopr/prep7! --- define elements and material ---epsr=2.2et,11,200,7et,1,120,1,,,0et,2,120,1,,,1mp,murx,1,1.mp,perx,1,epsr


Harmonic Analysis for Line-fed Microstrip Patch Antenna (Command Method)

mp,murx,2,1.mp,perx,2,1.! --- define geometry ---ws=2.46wp1=2.09wp2=7.9hp=16.hm=4.hs=0.794scal=1.e-3a3=-wp1a4=0a2=a3-wsa1=a2-wsa5=wsa6=a5+wp2a7=a6+wsa8=a7+wsb5=0.b6=hpb7=b6+hmb8=b7+1.25*hmb4=b5-hmb3=b4-hmb2=b3-hmb1=b2-1.25*hmrect,a2,a3,b2,b3rect,a3,a4,b2,b3rect,a4,a5,b2,b3rect,a5,a6,b2,b3rect,a6,a7,b2,b3rect,a2,a3,b3,b4rect,a3,a4,b3,b4rect,a4,a5,b3,b4rect,a5,a6,b3,b4rect,a6,a7,b3,b4rect,a2,a3,b4,b5rect,a3,a4,b4,b5rect,a4,a5,b4,b5rect,a5,a6,b4,b5rect,a6,a7,b4,b5rect,a2,a3,b5,b6rect,a3,a4,b5,b6rect,a4,a5,b5,b6rect,a5,a6,b5,b6rect,a6,a7,b5,b6rect,a2,a3,b6,b7rect,a3,a4,b6,b7rect,a4,a5,b6,b7rect,a5,a6,b6,b7rect,a6,a7,b6,b7rect,a1,a2,b1,b2rect,a2,a3,b1,b2rect,a3,a4,b1,b2rect,a4,a5,b1,b2rect,a5,a6,b1,b2rect,a6,a7,b1,b2rect,a7,a8,b1,b2rect,a1,a2,b2,b3rect,a7,a8,b2,b3rect,a1,a2,b3,b4rect,a7,a8,b3,b4rect,a1,a2,b4,b5rect,a7,a8,b4,b5rect,a1,a2,b5,b6rect,a7,a8,b5,b6rect,a1,a2,b6,b7rect,a7,a8,b6,b7rect,a1,a2,b7,b8rect,a2,a3,b7,b8rect,a3,a4,b7,b8rect,a4,a5,b7,b8



rect,a5,a6,b7,b8rect,a6,a7,b7,b8rect,a7,a8,b7,b8aglue,all! --- define mesh size ---nx1=8nx2=4nx3=5ny1=4ny2=16nz1=5nz2=4hx1=(a3-a1)/nx1hx2=(a4-a3)/nx2hx3=(a5-a4)/nx3hy1=(b2-b1)/ny1hy2=(b6-b5)/ny2lsel,s,loc,x,(a1+a2)/2lsel,a,loc,x,(a2+a3)/2lsel,a,loc,x,(a6+a7)/2lsel,a,loc,x,(a7+a8)/2cm,lx1,linelesize,lx1,hx1lsel,s,loc,x,(a3+a4)/2lsel,a,loc,x,(a5+a6)/2cm,lx2,linelesize,lx2,hx2lsel,s,loc,x,(a4+a5)/2cm,lx3,linelesize,lx3,hx3lsel,s,loc,y,(b1+b2)/2lsel,a,loc,y,(b2+b3)/2lsel,a,loc,y,(b3+b4)/2lsel,a,loc,y,(b4+b5)/2lsel,a,loc,y,(b6+b7)/2lsel,a,loc,y,(b7+b8)/2cm,ly1,linelesize,ly1,hy1lsel,s,loc,y,(b5+b6)/2cm,ly2,linelesize,ly2,hy2allstype,11asel,allamesh,allallsasel,s,loc,z,0asel,r,loc,x,a2,a7asel,r,loc,y,b2,b7cm,agr1,area! --- meshing ---type,1mat,1esize,,nz1asel,s,area,,agr1vext,all,,,0,0,-hsallsmat,2esize,,nz1asel,s,area,,agr1vext,all,,,0,0,hsalls! --- PML element ---type,2mat,1esize,,nz1asel,s,loc,z,0asel,u,area,,agr1vext,all,,,0,0,-hsmat,2esize,,nz1asel,s,loc,z,0



asel,u,area,,agr1vext,all,,,0,0,hsesize,,nz2asel,s,loc,z,hsvext,all,,,0,0,hsasel,s,loc,z,0aclear,allallsnummrg,all! --- PEC for microstrip and PML wall ---nsel,s,loc,z,0nsel,r,loc,x,a4,a5nsel,r,loc,y,b1,b5d,all,ax,0nsel,s,loc,z,0nsel,r,loc,x,a3,a6nsel,r,loc,y,b5,b6d,all,ax,0nsel,s,loc,x,a1nsel,a,loc,x,a8nsel,a,loc,y,b1nsel,a,loc,y,b8nsel,a,loc,z,-hsnsel,a,loc,z,2*hsd,all,ax,0! --- excitation current ---nsel,s,loc,y,b3nsel,r,loc,x,a4,a5nsel,r,loc,z,-hs,0bf,all,js,0,0,1.e-3,-1! --- define transmission line port ---hfport,1,TLINE,,v1,,50.nsel,s,loc,y,b4nsel,r,loc,z,-hs,hsnsel,r,loc,x,a2,a7bf,all,port,1allsvlscale,all,,,scal,scal,scal,,,1! --- define voltage routines ---y1=scal*b4xv1=scal*0.5*(a4+a5)zv1=0zv2=-scal*hsnv11=node(xv1,y1,zv1)nv12=node(xv1,y1,zv2)path,v1,2ppath,1,nv11ppath,2,nv12pasave,allfini/solu! --- perform a frequency sweep for s-parameter from 1GHz to 20 GHz ---spswp,1.0e9,20.0e9,0.5e9,1,,2,1fini

Target Results

Figure 2: “S-Parameter of Line-Fed Microstrip Patch Antenna” depicts the S-parameter at the microstrip linefeeding port from 1 GHz to 20 GHz. The pattern of the electric field at 7.5 GHz is shown in Figure 3: “Contour ofElectric Field Magnitude at 7.5 GHz”.



Figure 2 S-Parameter of Line-Fed Microstrip Patch Antenna



Figure 3 Contour of Electric Field Magnitude at 7.5 GHz



Harmonic Analysis for Radiation of aWaveguide Antenna with No Flare (CommandMethod)Problem Description

This example demonstrates how to determine the radiation pattern of a waveguide antenna with no flare usingANSYS commands.

The geometry of the modeled three-dimension PEC waveguide radiator with no flare is as follows: width = 2λ0/3,

height = λ0/3 and length = 2λ0. A sinusoidal source is excited on a wide-side-directed monopole feed centered

in the waveguide wide side and λ0/3 from the closed end. One half of the structure is used for numerical modeling,

because of the symmetry of the fields and geometry. A uniform current density is used to model the excitationsource. The PML absorbing material encloses the modeled domain except on the symmetric plane.

Figure 1 Waveguide Radiator with No Flare

λ

λ λ

λ



/batch,list/title, Radiation Pattern of a Rectangular Waveguide Horn Antenna /com, Horn Antenna: 2/3 x 1/3 x 2 wavelength^3/com, Numerical Model: 1/2 structure and line current source from closed end/com, Antenna is enclosed by PML except symmetric plane/com, The equivalent source surface is flagged between waveguide and PML /nopr/prep7! set-up working frequencyfreq=1.e9 lambda=3.e8/freq! define the computational structure*dim,_a,array,5*dim,_b,array,8*dim,_c,array,9*dim,_nz,array,8_a(1)=0_a(2)=_a(1)-lambda/3_a(3)=_a(2)-lambda/8_a(4)=_a(3)-lambda/8_a(5)=_a(4)-lambda/4_b(4)=-lambda/6_b(3)=_b(4)-lambda/8_b(2)=_b(3)-lambda/8_b(1)=_b(2)-lambda/4


_b(5)=lambda/6_b(6)=_b(5)+lambda/8_b(7)=_b(6)+lambda/8_b(8)=_b(7)+lambda/4_c(6)=0_c(5)=_c(6)-5*lambda/3_c(4)=_c(5)-lambda/3_c(3)=_c(4)-lambda/8_c(2)=_c(3)-lambda/8_c(1)=_c(2)-lambda/4_c(7)=_c(6)+lambda/8_c(8)=_c(7)+lambda/6_c(9)=_c(8)+lambda/2et,11,200,7 ! temporary elementet,1,120,1et,2,120,1,,,1 ! PML elementmp,murx,1,1.mp,perx,1,1.h1=lambda/15h2=lambda/12*do,_i,1,8 _nz(_i)=nint((_c(_i+1)-_c(_i))/h2)*enddo*do,_i,1,4 *do,_j,1,7 rect,_a(_i),_a(_i+1),_b(_j),_b(_j+1) *enddo*enddoaglue,allagen,2,all,,,0,0,-(_c(6)-_c(2))asel,s,loc,z,_c(6)adel,allasel,s,loc,z,_c(2)asel,s,loc,x,_a(1),(_a(3)+_a(4))/2asel,r,loc,y,(_b(2)+_b(3))/2,(_b(6)+_b(7))/2cm,airs,areaasel,all! 2-d meshingtype,11 esize,h1amesh,all! 3-d meshingmat,1! PML elementtype,2 asel,s,loc,z,_c(2)esize,,_nz(1)vext,all,,,0,0,-(_c(2)-_c(1))*do,_i,2,7 asel,s,loc,z,_c(_i) *if,_i,eq,2,then asel,u,,,airs *endif esize,,_nz(_i) vext,all,,,0,0,_c(_i+1)-_c(_i)*enddo! normal elementtype,1*do,_i,2,7 asel,s,loc,z,_c(_i) asel,r,loc,x,_a(1),(_a(3)+_a(4))/2 asel,r,loc,y,(_b(2)+_b(3))/2,(_b(6)+_b(7))/2 esize,,_nz(_i) vext,all,,,0,0,_c(_i+1)-_c(_i)*enddo! PML elementtype,2asel,s,loc,z,_c(8)esize,,_nz(8)vext,all,,,0,0,(_c(9)-_c(8))asel,s,loc,z,_c(2)aclear,all


Harmonic Analysis for Radiation of a Waveguide Antenna with No Flare (Command Method)

allsnummrg,all! flag equivalent source surfacensel,s,loc,x,_a(1),_a(3)nsel,r,loc,y,_b(3),_b(6)nsel,r,loc,z,_c(3),_c(7)esln,s,1,allnsel,s,loc,x,_a(3)nsel,a,loc,y,_b(3)nsel,a,loc,y,_b(6)nsel,a,loc,z,_c(3)nsel,a,loc,z,_c(7)sf,all,mxwfalls! define PECnsel,s,loc,x,_a(2)nsel,r,loc,y,_b(4),_b(5)nsel,r,loc,z,_c(4),_c(6)d,all,ax,0nsel,s,loc,y,_b(4)nsel,r,loc,x,_a(1),_a(2)nsel,r,loc,z,_c(4),_c(6)d,all,ax,0nsel,s,loc,y,_b(5)nsel,r,loc,x,_a(1),_a(2)nsel,r,loc,z,_c(4),_c(6)d,all,ax,0nsel,s,loc,z,_c(4)nsel,r,loc,x,_a(1),_a(2)nsel,r,loc,y,_b(4),_b(5)d,all,ax,0nsel,s,loc,x,_a(5)nsel,a,loc,y,_b(1)nsel,a,loc,y,_b(8)nsel,a,loc,z,_c(1)nsel,a,loc,z,_c(9)d,all,ax,0alls! set up excitation line currentnsel,s,loc,z,_c(5)nsel,r,loc,x,_a(1)nsel,r,loc,y,_b(4),_b(5)bf,all,js,0,1.e-3,0allsfini! perform solution/soluantype,harmic harfrq,freqeqslv,sparsesolvefinish! post-processing/post1set,1,1hfsym,,pmc, ! define image symmetric planeprhffar,patt,,0,0,,0,360,360 ! print out radiation patternfini

Target Results

Figure 2: “Radiation Pattern of Waveguide Radiator Without Flare on E-Plane” depicts the radiation pattern ofthe waveguide antenna on the E-plane (φ=0°). Figure 3: “Electric Field Contour of Waveguide Radiator WithoutFlare” shows the electric field contour in the computational domain.



Figure 2 Radiation Pattern of Waveguide Radiator Without Flare on E-Plane


Harmonic Analysis for Radiation of a Waveguide Antenna with No Flare (Command Method)

Figure 3 Electric Field Contour of Waveguide Radiator Without Flare



Harmonic Analysis for a Half WavelengthDipole Antenna (Command Method)Problem Description

This example demonstrates how to determine the radiation far field and antenna parameters of a half wavelengthdipole antenna using ANSYS commands.

Assume that the distribution of current density along the wire is J = 0.08 sin β(h-|z|) z A/m2, where β is the vacuumwave number and h is the half-length of the dipole antenna. Only 1/8 structure is used for the numerical simulation,because of the symmetry of the electromagnetic field. PML is used to truncate the open domain. PEC is imposedon the symmetrical plane perpendicular to the current density vector. The analytic directivity and radiation powerof the antenna are 2.156 dB and 0.058 watt, respectively.



/batch,list/title, Half Wavelength Dipole Antenna /nopr/prep7! structure dimensionsfreq=300e6wavel=3.e8/freqbeta=2.*3.1415926535/wavelcurr=1.e-2 ! 1/8 of total current density_l=wavel/2a=0.5*wavel! define elements and materialet,11,200,7et,1,120,1et,2,120,1,,,1mp,murx,1,1.mp,perx,1,1.! define mesh sizeh=wavel/20_n1=4_nz1=nint(_l/h)+1_nz2=4_nz3=4_npml=6! set up computational domain*dim,_a,array,4_a(1)=0_a(2)=_a(1)+a_a(3)=_a(2)+_n1*h_a(4)=_a(3)+_npml*h_c1=0_c2=_c1+_l/2_c3=_c2+_nz2*h_c4=_c3+_nz3*h_c5=_c4+_npml*h*do,_i,1,3 *do,_j,1,3 rect,_a(_i),_a(_i+1),_a(_j),_a(_j+1) *enddo*enddoaglue,allesize,hamesh,all


asel,s,loc,x,_a(1),_a(3)asel,r,loc,y,_a(1),_a(3)cm,_area1,areatype,1mat,1esize,,_nz1asel,s,area,,_area1vext,all,,,0,0,(_c2-_c1)esize,,_nz2asel,s,loc,z,_c2vext,all,,,0,0,(_c3-_c2)asel,s,loc,z,_c3vext,all,,,0,0,(_c4-_c3)type,2esize,,_nz1asel,s,loc,z,0asel,u,,,_area1vext,all,,,0,0,(_c2-_c1)esize,,_nz2asel,s,loc,z,_c2asel,r,loc,x,_a(1),_a(3)asel,r,loc,y,_a(1),_a(3)cm,_area1,areaasel,s,loc,z,_c2asel,u,,,_area1vext,all,,,0,0,(_c3-_c2)esize,,_nz3asel,s,loc,z,_c3asel,r,loc,x,_a(1),_a(3)asel,r,loc,y,_a(1),_a(3)cm,_area1,areaasel,s,loc,z,_c3asel,u,,,_area1vext,all,,,0,0,(_c4-_c3)esize,,_npmlasel,s,loc,z,_c4vext,all,,,0,0,(_c5-_c4)asel,a,loc,z,_c1aclear,allesel,s,type,,11edel,allallsnummrg,all! define equivalent source surfacensel,s,loc,x,_a(1),_a(2)nsel,r,loc,y,_a(1),_a(2)nsel,r,loc,z,_c1,_c3esln,s,1,allnsel,s,loc,x,_a(2)nsel,a,loc,y,_a(2)nsel,a,loc,z,_c3sf,all,mxwfnsel,allesel,all! define boundary conditionnsel,s,loc,x,_a(4)nsel,a,loc,y,_a(4)nsel,a,loc,z,_c1nsel,a,loc,z,_c5d,all,ax,0.allsel,all_ll=_c2-_c1_hz=_ll/_nz1*do,_i,0,_nz1 !define sinusoid line current source nsel,s,loc,x,0 nsel,r,loc,y,0 nsel,r,loc,z,_i*_hz cc= sin(beta*(_ll-_i*_hz))*curr !current density distribution *if,cc,eq,0,then cc=1.e-9 *endif bf,all,js,0,0,cc


Harmonic Analysis for a Half Wavelength Dipole Antenna (Command Method)

*enddoallsfini! perform solution/solueqslv,sparseantype,harmicharfrq,freqsolvefini/post1set,1,1hfsys,11,pmc,pmc,pec !set up symmetryhfang,,0,360,0,180 !set up radiation solid angleplhffar,field,EF,0,0,,0,180,18,10.,2,Z !plot theta component of E on E-planeplhffar,patt,polar,0,0,,0,180,18 !radiation pattern on E-planeplhffar,dgain,polar,0,0,,0,180,18prhffar,dgain,max !print out directivityprhffar,prad !print out radiation powerfini

The Target Results

The contour of the radiated electric field in the numerical domain is shown in Figure 1: “Contour of the RadiatedElectric Field of a Half Wavelength Dipole”. The far electric field on E-plane at r = 10 m is depicted in Figure 2: “FarElectric Field of a Half Wavelength Dipole on E-Plane at r = 10 m”. Figure 3: “Radiation Pattern of a Half WavelengthDipole on E-Plane” shows the radiation pattern of a half wavelength dipole, and the directive gain is given inFigure 4: “Directive Gain of a Half Wavelength Dipole on E-Plane”. The calculated directivity and radiation powerare 2.13 dB and 0.054 watt, respectively.



Figure 1 Contour of the Radiated Electric Field of a Half Wavelength Dipole



Figure 2 Far Electric Field of a Half Wavelength Dipole on E-Plane at r = 10 m



Figure 3 Radiation Pattern of a Half Wavelength Dipole on E-Plane



Figure 4 Directive Gain of a Half Wavelength Dipole on E-Plane



Part VI. Advanced Wave Propagation Examples

Harmonic Analysis for a Microstrip Low-PassFilter (Command Method)Problem Description

This example demonstrates how to determine the S-parameter of a microstrip low-pass filter using ANSYScommands.

The microstrip low-pass filter is distributed on a dielectric substrate backed by a PEC ground plane. The widthof the input and output microstrip lines are 2.413 mm. The width of the stub is 2.54 mm. The strip is assumed tobe perfectly conducting of thickness 0 m. The substrate material is a lossless dielectric of relative permittivity2.2. The thickness of the substrate is 0.794 mm. The top and side views of the structure are shown in the figurebelow. The characteristic impedance of the microstrip line is assumed to be 50 Ohm. To extract the S-parameter,the current density source is used to excite the system. The PML absorbing material is used to enclose thestructure excepting the ground plane.

Figure 1 Top and Side views of Low-Pass Filter

ε

!"$#&% ')( +*-,.% /&'0#&% ')(



/batch,list/title, Microstrip Filter/nopr/prep7! --- set up elements and materials ---epsr=2.3et,11,200,7et,1,120,1,,,0et,2,120,1,,,1mp,murx,1,1.mp,perx,1,epsrmp,murx,2,1.mp,perx,2,1.! --- set up structure ---w1=2.413w2=2.54s1=5.65s2=4.194c=0.794*dim,_a,array,10


*dim,_b,array,9_a(1)=0_a(2)=_a(1)+s1/2_a(3)=_a(2)+s1/2_a(4)=_a(3)+s1_a(5)=_a(4)+w1_a(6)=_a(5)+s2_a(7)=_a(6)+w1_a(8)=_a(7)+s1_a(9)=_a(8)+s1/2_a(10)=_a(9)+s1/2_b(1)=0_b(2)=_b(1)+s1_b(3)=_b(2)+s1/2_b(4)=_b(3)+s1/4_b(5)=_b(4)+s1/4_b(6)=_b(5)+w2_b(7)=_b(6)+s1/4_b(8)=_b(7)+s1/4_b(9)=_b(8)+s1h1=s1/8h2=w1/5h3=w2/5h4=s2/7nz1=6nz2=4npmlz=3scal=1.e-3*do,_i,1,9 *do,_j,1,8 rect,_a(_i),_a(_i+1),_b(_j),_b(_j+1) *enddo*enddoaglue,all! --- 2d meshing ---type,11esize,h1asel,allasel,u,loc,x,_a(4),_a(7)asel,u,loc,y,_b(5),_b(6)amesh,allallsasel,s,loc,x,_a(4),_a(5)asel,a,loc,x,_a(6),_a(7)asel,u,loc,y,_b(5),_b(6)lsel,s,loc,y,_b(1),_b(9)cm,lgr1,linelesize,lgr1,h1lsel,s,loc,x,(_a(4)+_a(5))/2lsel,a,loc,x,(_a(6)+_a(7))/2cm,lgr2,linelesize,lgr2,h2amesh,allallsasel,s,loc,x,_a(5),_a(6)asel,u,loc,y,_b(5),_b(6)lsel,s,loc,y,_b(1),_b(9)cm,lgr3,linelesize,lgr3,h1lsel,s,loc,x,(_a(5)+_a(6))/2cm,lgr4,linelesize,lgr4,h4amesh,allallsasel,s,loc,y,_b(5),_b(6)asel,u,loc,x,_a(4),_a(7)lsel,s,loc,x,_a(1),_a(10)cm,lgr4,linelesize,lgr4,h1lsel,s,loc,y,(_b(5)+_b(6))/2cm,lgr5,linelesize,lgr5,h3


Harmonic Analysis for a Microstrip Low-Pass Filter (Command Method)

amesh,allallsasel,s,loc,x,_a(4),_a(7)asel,r,loc,y,_b(5),_b(6)asel,u,loc,x,_a(5),_a(6)lsel,s,loc,x,(_a(4)+_a(5))/2lsel,a,loc,x,(_a(6)+_a(7))/2cm,lgr6,linelesize,lgr6,h2lsel,s,loc,y,(_b(5)+_b(6))/2cm,lgr7,linelesize,lgr7,h3amesh,allallsasel,s,loc,x,_a(5),_a(6)asel,r,loc,y,_b(5),_b(6)lsel,s,loc,x,(_a(5)+_a(6))/2cm,lgr8,linelesize,lgr8,h4lsel,s,loc,y,(_b(5)+_b(6))/2cm,lgr9,linelesize,lgr9,h3amesh,allallsasel,s,loc,z,0asel,r,loc,x,_a(2),_a(9)asel,r,loc,y,_b(2),_b(8)cm,agr1,area! --- 3d meshing ---type,1mat,1esize,,nz1asel,s,,,agr1vext,all,,,0,0,-calls

mat,2esize,,nz2asel,s,,,agr1vext,all,,,0,0,calls! --- 3d PML elements ---type,2mat,1esize,,nz1asel,s,loc,z,0asel,u,area,,agr1vext,all,,,0,0,-cmat,2esize,,nz2asel,s,loc,z,0asel,u,area,,agr1vext,all,,,0,0,callstype,2mat,2esize,,npmlzasel,s,loc,z,cvext,all,,,0,0,casel,s,loc,z,0aclear,allallsnummrg,all! --- PEC for strip, ground plane and PML walls ---nsel,s,loc,z,0nsel,r,loc,x,_a(4),_a(5)nsel,r,loc,y,_b(1),_b(5)d,all,ax,0nsel,s,loc,z,0nsel,r,loc,x,_a(6),_a(7)nsel,r,loc,y,_b(6),_b(9)d,all,ax,0



nsel,s,loc,z,0nsel,r,loc,x,_a(3),_a(8)nsel,r,loc,y,_b(5),_b(6)d,all,ax,0nsel,s,loc,x,_a(1)nsel,a,loc,x,_a(10)nsel,a,loc,y,_b(1)nsel,a,loc,y,_b(9)nsel,a,loc,z,-cnsel,a,loc,z,2*cd,all,ax,0! --- excitation current ---nsel,s,loc,y,_b(3)nsel,r,loc,x,_a(4),_a(5)nsel,r,loc,z,-c,0bf,all,js,0,0,1.,-1alls! --- define the ports ---hfport,1,TLINE,,v1,,50.nsel,s,loc,y,_b(4)nsel,r,loc,z,-c,cnsel,r,loc,x,_a(2),_a(9)bf,all,port,1hfport,2,TLINE,,v2,,50.nsel,s,loc,y,_b(7)nsel,r,loc,z,-c,cnsel,r,loc,x,_a(2),_a(9)bf,all,port,2vlscale,all,,,scal,scal,scal,,,1! --- define voltage paths on ports ---y1=scal*_b(4)xv1=scal*0.5*(_a(4)+_a(5))zv1=0zv2=-scal*cnv11=node(xv1,y1,zv1)nv12=node(xv1,y1,zv2)path,v1,2ppath,1,nv11ppath,2,nv12y2=scal*_b(7)xv2=scal*0.5*(_a(6)+_a(7))nv21=node(xv2,y2,zv1)nv22=node(xv2,y2,zv2)path,v2,2ppath,1,nv21ppath,2,nv22pasave,allallssavefini! --- launch the full-method frequency sweep solution ---/soluspswp,0.5e9,20e9,0.5e9,1,,2,1fini

Target Results

Figure 2: “S11 of microstrip low-pass filter” and Figure 3: “S21 of microstrip low-pass filter” depict the S11 andS21 of the microstrip low-pass filter from 0.5 GHz to 20 GHz, respectively.



Figure 2 S11 of microstrip low-pass filter



Figure 3 S21 of microstrip low-pass filter



Harmonic Analysis for a Three-StubRectangular Waveguide Filter (CommandMethod)Problem Description

This example demonstrates how to determine the S-parameter of a three-stub rectangular waveguide filter usingANSYS commands.

The waveguide filter consists of a straight rectangular metallic hollow waveguide with a cross-section 19.05 x

9.252 mm2 and three tuning stubs. The side view of the structure is shown on the left in the figure below, andthe FEA model is shown on the right. Due to the symmetry of the geometry and of the TE10 waveguide excitationto be analyzed, only one-half of the filter needs to be modeled. The perfect electric condition is applied to themetallic surfaces of the waveguide and the impedance matching condition of TE10 mode is imposed at the inputand output ports.

Figure 1 Side View and FEA Model of Filter (Dimensions are in mm)




/batch,list/title, Three-Stub Waveguide Filter/nopr

/prep7! define elements and materialset,11,200,7et,1,120,1,,,0mp,murx,1,1.mp,perx,1,1.! define dimensions of the geometryscal=1.e-3cw=19.05ch=9.525_s1=cw_s2=17.23_gap1=2.86_gap2=2.01_stub=18.9_xg1=_gap1_xg2=_gap2_yg1=0.25*ch! set up 2d numerical domain*dim,_a,array,14*dim,_b,array,5_a(1)=0_a(2)=_a(1)+(_s1-_xg1)_a(3)=_a(2)+_xg1_a(4)=_a(3)+_gap1_a(5)=_a(4)+_xg1_a(6)=_a(5)+(_s2-_xg1-_xg2)_a(7)=_a(6)+_xg2_a(8)=_a(7)+_gap2_a(9)=_a(8)+_xg2_a(10)=_a(9)+(_s2-_xg2-_xg1)_a(11)=_a(10)+_xg1_a(12)=_a(11)+_gap1_a(13)=_a(12)+_xg1_a(14)=_a(13)+(_s1-_xg1)_b(1)=-ch/2_b(2)=_b(1)+ch-_yg1_b(3)=_b(2)+_yg1_b(4)=_b(3)+_yg1_b(5)=_b(4)+(_stub-_yg1)*do,_i,1,13 *do,_j,1,2 rect,_a(_i),_a(_i+1),_b(_j),_b(_j+1) *enddo*enddo*do,_j,3,4 rect,_a(3),_a(4),_b(_j),_b(_j+1) rect,_a(7),_a(8),_b(_j),_b(_j+1) rect,_a(11),_a(12),_b(_j),_b(_j+1)*enddoaglue,all! 2d meshingnx1=20nx2=8nx3=12nx4=18nx5=8nx6=12hx1=(_a(2)-_a(1))/nx1hx2=(_a(3)-_a(2))/nx2hx3=(_a(4)-_a(3))/nx3hx4=(_a(6)-_a(5))/nx4hx5=(_a(7)-_a(6))/nx5hx6=(_a(8)-_a(7))/nx6ny1=8ny2=6ny3=15hy1=(_b(2)-_b(1))/ny1


Harmonic Analysis for a Three-Stub Rectangular Waveguide Filter (Command Method)

hy2=(_b(3)-_b(2))/ny2hy3=(_b(5)-_b(4))/ny3nz=10lsel,s,loc,y,(_b(1)+_b(2))/2cm,ly1,linelesize,ly1,hy1lsel,s,loc,y,(_b(2)+_b(3))/2lsel,a,loc,y,(_b(3)+_b(4))/2cm,ly2,linelesize,ly2,hy2lsel,s,loc,y,(_b(4)+_b(5))/2cm,ly3,linelesize,ly3,hy3lsel,s,loc,x,(_a(1)+_a(2))/2lsel,a,loc,x,(_a(13)+_a(14))/2cm,lx1,linelesize,lx1,hx1lsel,s,loc,x,(_a(2)+_a(3))/2lsel,a,loc,x,(_a(4)+_a(5))/2lsel,a,loc,x,(_a(10)+_a(11))/2lsel,a,loc,x,(_a(12)+_a(13))/2cm,lx2,linelesize,lx2,hx2lsel,s,loc,x,(_a(3)+_a(4))/2lsel,a,loc,x,(_a(11)+_a(12))/2cm,lx3,linelesize,lx3,hx3lsel,s,loc,x,(_a(5)+_a(6))/2lsel,a,loc,x,(_a(9)+_a(10))/2cm,lx4,linelesize,lx4,hx4lsel,s,loc,x,(_a(6)+_a(7))/2lsel,a,loc,x,(_a(8)+_a(9))/2cm,lx5,linelesize,lx5,hx5lsel,s,loc,x,(_a(7)+_a(8))/2cm,lx6,linelesize,lx6,hx6allstype,11amesh,allnummrg,allalls! 3d meshingtype,1mat,1esize,,nzasel,s,loc,z,0vext,all,,,0,0,cw/2asel,s,loc,z,0aclear,alletdele,11allsnummrg,all! PEC on waveguide wall nsel,s,loc,z,cw/2nsel,a,loc,y,_b(1)nsel,a,loc,y,_b(5)d,all,ax,0nsel,s,loc,x,_a(1),_a(3)nsel,a,loc,x,_a(4),_a(7)nsel,a,loc,x,_a(8),_a(11)nsel,a,loc,x,_a(12),_a(14)nsel,r,loc,y,_b(3)d,all,ax,0nsel,s,loc,x,_a(3)nsel,a,loc,x,_a(4)nsel,a,loc,x,_a(7)nsel,a,loc,x,_a(8)nsel,a,loc,x,_a(11)nsel,a,loc,x,_a(12)nsel,r,loc,y,_b(3),_b(5)



d,all,ax,0vlscale,all,,,scal,scal,scal,,,1! define a local coordinates for waveguide portslocal,11,,,,,,,90csys,0! define porthfport,1,rect,11,TE10,IMPD,scal*cw,scal*ch,1.nsel,s,loc,x,_a(1)*scalsf,all,port,1hfport,2,rect,11,TE10,IMPD,cw*scal,ch*scalnsel,s,loc,x,_a(14)*scalsf,all,port,2allssavefini! perform solution/soluspswp,10.e9,15.e9,0.25e9,1,,2,1fini

Target Results

Figure 2: “|S11| of Three-Stub Waveguide Filter” depicts the S11 of simulated 3-stub waveguide filter from 10GHz to 15 GHz. Figure 3: “Electric Field Contour of Three-Stub Waveguide Filter at 15 GHz” shows the electricfield contour at 15 GHz.

Figure 2 |S11| of Three-Stub Waveguide Filter


Harmonic Analysis for a Three-Stub Rectangular Waveguide Filter (Command Method)

Figure 3 Electric Field Contour of Three-Stub Waveguide Filter at 15 GHz



Harmonic Analysis for Multi-layer MicrostripInterconnect (Command Method)Problem Description

This example demonstrates how to determine the S-parameter of a multi-layer microstrip interconnect usingANSYS commands.

The multi-layer microstrip interconnect is distributed over three signal layers. The input and output ports are atthe uppermost layer. The distance to the second signal layer is 0.4 mm. The distance between the second andthird signal layer is 0.4 mm. The third (bottom) layer is 0.8 mm above a perfectly conducting plane. The substratematerial is a lossless dielectric of relative permittivity 0f 9.8. The entire structure is placed inside a perfectly con-ducting box of length 20 mm, width 10 mm and height 6.6 mm. Hence, the uppermost interconnect is 5.0 mmbelow the top of the box. The graphic on the left in the figure below depicts the structure without showing thesubstrate and enclosing box. The graphic on the right shows the geometry of the three-layer interconnect (topview). The microstrip is taken to be infinitesimally thin, perfectly conducting, of width 1.2 mm and the character-istic impedance 55 Ohms. The transitions from one layer to other are effected through perfectly conductingsquare vias of side 1.2 mm. To extract the S-parameter, the current density source is used to excite the system.The PML absorbing material is placed behind the excitation source and terminates the output port.


Figure 1 Three-layer Interconnect



/batch,list/title, Multilayer Microstrip Interconnect/nopr/prep7! --- define elements and material ---epsr=9.8et,11,200,7et,1,120,1,,,0et,2,120,1,,,1mp,murx,1,1.mp,perx,1,epsrmp,murx,2,1.mp,perx,2,1.! --- define geometry ---w=1.2s=2.2l=6.0ls=5.6c1=0.4c2=0.4c3=0.8bw=2.7


Harmonic Analysis for Multi-layer Microstrip Interconnect (Command Method)

bh=5.0*dim,_a,array,6*dim,_b,array,11_a(1)=0_a(2)=_a(1)+bw_a(3)=_a(2)+w_a(4)=_a(3)+s_a(5)=_a(4)+w_a(6)=_a(5)+bw_b(1)=0_b(2)=_b(1)+l/2_b(3)=_b(2)+l/4_b(4)=_b(3)+l/4_b(5)=_b(4)+l_b(6)=_b(5)+w_b(7)=_b(6)+ls_b(8)=_b(7)+w_b(9)=_b(8)+l_b(10)=_b(9)+l/8_b(11)=_b(10)+l/2*do,_i,1,5 *do,_j,1,10 rect,_a(_i),_a(_i+1),_b(_j),_b(_j+1) *enddo*enddoaglue,all! --- choose mesh size ---hx1=w/4hx2=s/6hx3=(_a(2)-_a(1))/5hy1=hx1hy2=(_b(7)-_b(6))/10hy3=(_b(2)-_b(1))/5nz1=4nz2=7nz3=12scal=1.e-3lsel,s,loc,x,(_a(1)+_a(2))/2lsel,a,loc,x,(_a(5)+_a(6))/2cm,lxblnk,linelesize,lxblnk,hx3lsel,s,loc,x,(_a(2)+_a(3))/2lsel,a,loc,x,(_a(4)+_a(5))/2cm,lxstrip,linelesize,lxstrip,hx1lsel,s,loc,x,(_a(3)+_a(4))/2cm,lxstub,linelesize,lxstub,hx2lsel,s,loc,y,(_b(1)+_b(2))/2*do,_i,2,4 lsel,a,loc,y,(_b(_i)+_b(_i+1))/2*enddo*do,_i,8,10 lsel,a,loc,y,(_b(_i)+_b(_i+1))/2*enddocm,lyprp,linelesize,lyprp,hy3lsel,s,loc,y,(_b(5)+_b(6))/2lsel,a,loc,y,(_b(7)+_b(8))/2cm,lystrip,linelesize,lystrip,hy1lsel,s,loc,y,(_b(6)+_b(7))/2cm,lystub,linelesize,lystub,hy2allsasel,s,loc,y,_b(1),_b(2)asel,a,loc,y,_b(10),_b(11)cm,apml,area! --- 2-d meshing ---type,11asel,allamesh,all



alls! --- 3-d meshing ---type,1mat,1esize,,nz1asel,s,loc,z,0asel,u,,,apmlvext,all,,,0,0,-c1asel,s,loc,z,-c1vext,all,,,0,0,-c2esize,,nz2asel,s,loc,z,-(c1+c2)vext,all,,,0,0,-c3mat,2esize,,nz3asel,s,loc,z,0asel,u,,,apmlvext,all,,,0,0,bhalls! --- PML element ---type,2mat,1esize,,nz1asel,s,,,apmlvext,all,,,0,0,-c1asel,s,loc,z,-c1asel,u,loc,y,_b(2),_b(10)vext,all,,,0,0,-c2esize,,nz2asel,s,loc,z,-(c1+c2)asel,u,loc,y,_b(2),_b(10)vext,all,,,0,0,-c3mat,2esize,,nz3asel,s,,,apmlvext,all,,,0,0,bhalls! --- clean up 2-d element ---asel,s,loc,z,0aclear,allesel,s,type,,11edel,allallsnummrg,allalls! --- set up PEC for microstrip, vias, ground plane and PML walls ---nsel,s,loc,z,0nsel,r,loc,x,_a(2),_a(3)nsel,u,loc,y,_b(6),_b(7)d,all,ax,0cm,npec1,nodensel,s,loc,z,-c1nsel,r,loc,x,_a(2),_a(5)nsel,r,loc,y,_b(5),_b(8)nsel,u,loc,y,_b(6),_b(7)d,all,ax,0cm,npec2,nodensel,s,loc,z,-(c1+c2)nsel,r,loc,x,_a(4),_a(5)nsel,r,loc,y,_b(6),_b(7)d,all,ax,0cm,npec3,nodensel,s,loc,x,_a(2),_a(3)nsel,r,loc,y,_b(5),_b(8)nsel,u,loc,y,_b(6),_b(7)nsel,r,loc,z,0,-c1d,all,ax,0cm,npec4,nodensel,s,loc,x,_a(4),_a(5)nsel,r,loc,y,_b(5),_b(8)nsel,u,loc,y,_b(6),_b(7)nsel,r,loc,z,-c1,-(c1+c2)



d,all,ax,0cm,npec5,nodensel,s,,,npec1nsel,a,,,npec2nsel,a,,,npec3nsel,a,,,npec4nsel,a,,,npec5cm,npec,nodensel,s,loc,x,_a(1)nsel,a,loc,x,_a(6)nsel,a,loc,y,_b(1)nsel,a,loc,y,_b(11)nsel,a,loc,z,-(c1+c2+c3)nsel,a,loc,z,bhd,all,ax,0alls! --- assign excitation current ---nsel,s,loc,y,_b(3)nsel,r,loc,x,_a(2),_a(3)nsel,r,loc,z,-(c1+c2+c3),0bf,all,js,0,0,1.,-1alls! --- define transmission line port ---hfport,1,TLINE,,v1,,55.nsel,s,loc,y,_b(4)nsel,r,loc,z,-(c1+c2+c3),bhnsel,r,loc,x,_a(1),_a(6)bf,all,port,1hfport,2,TLINE,,v2,,55.nsel,s,loc,y,_b(9)nsel,r,loc,z,-(c1+c2+c3),bhnsel,r,loc,x,_a(1),_a(6)bf,all,port,2allsvlscale,all,,,scal,scal,scal,,,1! --- define voltage pathsy1=scal*_b(4)xv1=scal*0.5*(_a(2)+_a(3))zv1=0zv2=-scal*(c1+c2+c3)nv11=node(xv1,y1,zv1)nv12=node(xv1,y1,zv2)path,v1,2ppath,1,nv11ppath,2,nv12y2=scal*_b(9)xv2=scal*0.5*(_a(2)+_a(3))nv21=node(xv2,y2,zv1)nv22=node(xv2,y2,zv2)path,v2,2ppath,1,nv21ppath,2,nv22pasave,allallssavefini/solu! --- perform solution over the frequency range ---spswp,55.e6,10.05e9,0.25e9,1,,2,1fini

Target Results

Figure 2: “S11 of the Multi-Layer Microstrip Interconnect” and Figure 3: “S21 of the Multi-Layer Microstrip Inter-connect” depict the magnitude of S11 and S21 fro 0.55 GHz to 10 GHz, respectively. The pattern of electric fieldat 6.5 GHz is shown in Figure 4: “Electric Field Contour of Multi-Layer Microstrip Interconnect at 6.5 GHz”.



Figure 2 S11 of the Multi-Layer Microstrip Interconnect



Figure 3 S21 of the Multi-Layer Microstrip Interconnect



Figure 4 Electric Field Contour of Multi-Layer Microstrip Interconnect at 6.5 GHz

The Touchstone file is listed as follow

! ANSYS S-parameter Data for 2 Ports (Transmission Line). # GHz S DB R 55. ! Freq |S11| <S11 |S21| <S21 |S12| <S12 |S22| <S22 0.5500 -10.586 -139.524 -0.386 -53.065 -0.386 -53.065 -10.586 -139.524 0.8000 -9.474 -163.757 -0.516 -72.785 -0.516 -72.785 -9.474 -163.757 1.0500 -8.519 177.585 -0.657 -93.033 -0.657 -93.033 -8.519 177.585 1.3000 -7.798 159.309 -0.788 -113.339 -0.788 -113.339 -7.798 159.309 1.5500 -7.265 140.275 -0.902 -133.354 -0.902 -133.354 -7.265 140.275 1.8000 -6.920 121.118 -0.986 -153.086 -0.986 -153.086 -6.920 121.118 2.0500 -6.799 101.999 -1.017 187.257 -1.017 187.257 -6.799 101.999 2.3000 -6.952 82.741 -0.978 167.493 -0.978 167.493 -6.952 82.741 2.5500 -7.494 62.693 -0.854 147.187 -0.854 147.187 -7.494 62.693 2.8000 -8.468 42.305 -0.674 126.413 -0.674 126.413 -8.468 42.305 3.0500 -10.071 21.466 -0.456 105.029 -0.456 105.029 -10.071 21.466 3.3000 -12.746 -0.348 -0.238 82.806 -0.238 82.806 -12.746 -0.348 3.5500 -17.579 -24.110 -0.075 59.706 -0.075 59.706 -17.579 -24.110 3.8000 -30.635 -56.537 -0.002 36.011 -0.002 36.011 -30.635 -56.537 4.0500 -23.199 113.152 -0.019 12.185 -0.019 12.185 -23.199 113.152 4.3000 -16.041 86.057 -0.107 -11.287 -0.107 -11.287 -16.041 86.057 4.5500 -12.735 62.480 -0.235 -34.213 -0.235 -34.213 -12.735 62.480 4.8000 -11.057 40.321 -0.352 -56.716 -0.352 -56.716 -11.057 40.321 5.0500 -10.419 18.522 -0.410 -79.079 -0.410 -79.079 -10.419 18.522 5.3000 -10.630 -3.630 -0.390 -101.655 -0.390 -101.655 -10.630 -3.630 5.5500 -11.726 -26.854 -0.299 -124.832 -0.299 -124.832 -11.726 -26.854 5.8000 -13.972 -52.099 -0.174 -148.953 -0.174 -148.953 -13.972 -52.099 6.0500 -18.143 -80.242 -0.063 185.844 -0.063 185.844 -18.143 -80.242



6.3000 -28.815 -115.762 -0.001 159.798 -0.001 159.798 -28.815 -115.762 6.5500 -24.396 56.778 -0.011 133.463 -0.011 133.463 -24.396 56.778 6.8000 -16.846 28.486 -0.085 107.147 -0.085 107.147 -16.846 28.486 7.0500 -14.286 3.056 -0.159 80.676 -0.159 80.676 -14.286 3.056 7.3000 -14.299 -23.299 -0.158 53.411 -0.158 53.411 -14.299 -23.299 7.5500 -17.632 -52.183 -0.069 24.150 -0.069 24.150 -17.632 -52.183 7.8000 -39.377 24.216 0.007 -8.652 0.007 -8.652 -39.377 24.216 8.0500 -12.158 48.036 -0.265 -45.028 -0.265 -45.028 -12.158 48.036 8.3000 -5.417 13.873 -1.470 -82.412 -1.470 -82.412 -5.417 13.873 8.5500 -2.522 -19.324 -3.599 -116.859 -3.599 -116.859 -2.522 -19.324 8.8000 -1.312 -45.705 -6.028 215.285 -6.028 215.285 -1.312 -45.705 9.0500 -0.625 -77.587 -8.700 187.522 -8.700 187.522 -0.625 -77.587 9.3000 -0.425 -92.929 -10.332 170.339 -10.332 170.339 -0.425 -92.929 9.5500 -2.705 10.910 -7.750 212.830 -7.750 212.830 -2.705 10.910 9.8000 -8.146 66.104 -8.762 221.922 -8.762 221.922 -8.146 66.104 10.0500 -4.729 173.671 -12.306 222.941 -12.306 222.941 -4.729 173.671



Harmonic Analysis for Microstrip Meander Line(Command Method)Problem Description

This example demonstrates how to determine the S-parameter of a microstrip meander line using ANSYS com-mands.

Microstrip meander lines are used to introduce delay (or phase shift in the case of time-harmonic excitations).The figure below depicts the top view of the meander line. The strip is assumed to be perfectly conducting ofthickness 0 mm and width 0.4 mm. The microstrip meander line is embedded in a lossless substrate of relativepermittivity 9.8. The meander line is placed 0.5 mm above a perfectly conducting plane. The entire structure isplaced inside a perfectly conducting box of width 5 mm and height 2.5 mm. Hence the top wall of the box is 2.0mm above the meander line. For these dimensions, the characteristic impedance of the buried microstrip isabout 45 Ohm.

Figure 1 Microstrip Meander Line (Top View)



/batch,list/title, Microstrip meander line/nopr/prep7! --- define elements and materials ---epsr=9.8et,11,200,7et,1,120,1,,,0et,2,120,1,,,1mp,murx,1,1.mp,perx,1,epsr! --- set up geometry ---w=0.4gap=0.6lz1=5.0lz2=5.6stub=2.2xleft=0.8xright=1.2blow=0.5bup=2.0Z0=45*dim,_a,array,6*dim,_b,array,27_a(1)=0_a(2)=_a(1)+xleft_a(3)=_a(2)+w_a(4)=_a(3)+stub


_a(5)=_a(4)+w_a(6)=_a(5)+xright_b(1)=0_b(2)=_b(1)+lz1/2_b(3)=_b(2)+lz1/4_b(4)=_b(3)+lz1/4_b(5)=_b(4)+lz1*do,_i,6,22,2 _b(_i)=_b(_i-1)+w _b(_i+1)=_b(_i)+gap*enddo_b(24)=_b(23)+w_b(25)=_b(24)+lz2_b(26)=_b(25)+lz2/4_b(27)=_b(26)+lz2/2*do,_i,1,5 *do,_j,1,26 rect,_a(_i),_a(_i+1),_b(_j),_b(_j+1) *enddo*enddoaglue,allasel,allasel,s,loc,x,_a(2),_a(3)*do,_i,1,4 asel,u,loc,y,_b(_i),_b(_i+1)*enddo*do,_i,8,20,4 asel,u,loc,y,_b(_i),_b(_i+1)*enddo*do,_i,24,26 asel,u,loc,y,_b(_i),_b(_i+1)*enddocm,strip1,areaasel,allasel,s,loc,x,_a(3),_a(4)*do,_i,1,4 asel,u,loc,y,_b(_i),_b(_i+1)*enddo*do,_i,6,22,2 asel,u,loc,y,_b(_i),_b(_i+1)*enddo*do,_i,24,26 asel,u,loc,y,_b(_i),_b(_i+1)*enddocm,strip2,areaasel,allasel,s,loc,x,_a(4),_a(5)*do,_i,6,22,4 asel,u,loc,y,_b(_i),_b(_i+1)*enddocm,strip3,areaasel,allasel,s,,,strip1asel,a,,,strip2asel,a,,,strip3cm,strip,areaasel,allasel,s,loc,y,_b(1),_b(2)asel,a,loc,y,_b(26),_b(27)cm,apml,areaasel,all! --- set up element size ---hx1=w/5hx2=stub/14hx3=(_a(2)-_a(1))/4hy1=hx1hy2=gap/6hy3=(_b(2)-_b(1))/6nz1=4nz2=16scal=1.e-3lsel,s,loc,y,(_b(1)+_b(2))/2


Harmonic Analysis for Microstrip Meander Line (Command Method)

*do,_i,2,4 lsel,a,loc,y,(_b(_i)+_b(_i+1))/2*enddo*do,_i,24,26 lsel,a,loc,y,(_b(_i)+_b(_i+1))/2*enddocm,ly3,linelesize,ly3,hy3lsel,s,loc,y,(_b(5)+_b(6))/2*do,_i,7,23,2 lsel,a,loc,y,(_b(_i)+_b(_i+1))/2*enddocm,ly1,linelesize,ly1,hy1lsel,s,loc,y,(_b(6)+_b(7))/2*do,_i,6,22,2 lsel,a,loc,y,(_b(_i)+_b(_i+1))/2*enddocm,ly2,linelesize,ly2,hy2lsel,s,loc,x,(_a(1)+_a(2))/2lsel,a,loc,x,(_a(5)+_a(6))/2cm,lx3,linelesize,lx3,hx3lsel,s,loc,x,(_a(2)+_a(3))/2lsel,a,loc,x,(_a(4)+_a(5))/2cm,lx1,linelesize,lx1,hx1lsel,s,loc,x,(_a(3)+_a(4))/2cm,lx2,linelesize,lx2,hx2alls! --- meshing the model ---type,11amesh,allallstype,1mat,1esize,,nz1asel,s,loc,z,0asel,u,,,apmlvext,all,,,0,0,-blowesize,,nz2asel,s,loc,z,0asel,u,,,apmlvext,all,,,0,0,bup! --- PML elements ---type,2mat,1esize,,nz1asel,s,,,apmlvext,all,,,0,0,-blowesize,,nz2asel,s,,,apmlvext,all,,,0,0,bupalls! --- clean up 2-d element ---asel,s,loc,z,0aclear,allesel,s,type,,11edel,allallsnummrg,all! --- PEC for microstrip and exterior walls except portsasel,s,,,stripda,all,ax,0.allsnsel,s,loc,x,_a(1)nsel,a,loc,x,_a(6)nsel,a,loc,y,_b(1)nsel,a,loc,y,_b(27)nsel,a,loc,z,-blow



nsel,a,loc,z,bupd,all,ax,0! --- excitation current ---nsel,s,loc,y,_b(3)nsel,r,loc,x,_a(4),_a(5)nsel,r,loc,z,-blow,0bf,all,js,0,0,1.,-1alls! --- transmission line port ---hfport,1,TLINE,,v1,,Z0nsel,s,loc,y,_b(4)nsel,r,loc,z,-blow,bupnsel,r,loc,x,_a(1),_a(6)bf,all,port,1hfport,2,TLINE,,v2,,Z0nsel,s,loc,y,_b(25)nsel,r,loc,z,-blow,bupnsel,r,loc,x,_a(1),_a(6)bf,all,port,2vlscale,all,,,scal,scal,scal,,,1! --- define voltage routines ---y1=scal*_b(4)xv1=scal*0.5*(_a(4)+_a(5))zv1=0zv2=-scal*blownv11=node(xv1,y1,zv1)nv12=node(xv1,y1,zv2)path,v1,2ppath,1,nv11ppath,2,nv12y2=scal*_b(25)nv21=node(xv1,y2,zv1)nv22=node(xv1,y2,zv2)path,v2,2ppath,1,nv21ppath,2,nv22pasave,allallssavefini! --- launch the solution ---/soluspswp,100.e6,10.1e9,200.e6,1,,2,0fini

Target Results

Figure 2: “S11 of the Microstrip Meander Line” depicts the S11 of the microstrip meander line from 0.5 GHz to10 GHz. Figure 3: “The Contour of Electric Field Magnitude” shows the contour of electric field magnitude.



Figure 2 S11 of the Microstrip Meander Line



Figure 3 The Contour of Electric Field Magnitude



Harmonic Analysis for a RectangularWaveguide with a Ridge Discontinuity(Command Method)Problem Description

This example demonstrates how to determine the S-parameter of a rectangular waveguide with a ridge discon-tinuity using ANSYS commands.

The metallic ridge discontinuity is located at the center of the rectangular waveguide, shown in the figure below.Due to the symmetry of the geometry and of the TE10 waveguide excitation to be analyzed, only one-half of the

structure needs to be modeled. The perfect electric condition is applied to the metallic surfaces of the waveguideand perfectly matched layers (PML) terminate the input and output ports.

Figure 1 Waveguide with Ridge Discontinuity (Dimensions are in mm)



/batch,list/title, Rectangular Waveguide with a ridge discontinuity/nopr/prep7! define elements and materialset,11,200,7et,1,120,1,,,0et,2,120,1,,,1mp,murx,1,1.mp,perx,1,1.! define the geometry and numerical domainscal=1.e-3cw=19.05ch=9.524_l=5.08_w=1.016_h=7.619_dp=cw/8_dw=2*cw/3_ds=_l/4_dpml=cw/5*dim,_a,array,4*dim,_b,array,3_a(1)=0


_a(2)=_a(1)+_w/2_a(3)=_a(2)+_w_a(4)=cw/2_b(1)=-ch/2_b(2)=_b(1)+_h_b(3)=ch/2_c3=0_c2=_c3-_dp_c1=_c2-_dpml_c4=_c3+_dw_c5=_c4+_ds_c6=_c5+_l_c7=_c6+_ds_c8=_c7+_dw_c9=_c8+_dp_c10=_c9+_dpml*do,_i,1,3 *do,_j,1,2 rect,_a(_i),_a(_i+1),_b(_j),_b(_j+1) *enddo*enddoaglue,all! set up the mesh_nx1=4_nx2=8_nx3=18_ny1=18_ny2=8_nz1=2_nz2=14_nz3=3_nz4=15_nzpml=4hx1=(_a(2)-_a(1))/_nx1hx2=(_a(3)-_a(2))/_nx2hx3=(_a(4)-_a(3))/_nx3hy1=(_b(2)-_b(1))/_ny1hy2=(_b(3)-_b(2))/_ny2lsel,s,loc,y,(_b(1)+_b(2))/2cm,ly1,linelesize,ly1,hy1,,ny1,1.0lsel,s,loc,y,(_b(2)+_b(3))/2cm,ly2,linelesize,ly2,hy2,,ny2,1.0lsel,s,loc,x,(_a(1)+_a(2))/2cm,lx1,linelesize,lx1,hx1lsel,s,loc,x,(_a(2)+_a(3))/2cm,lx2,linelesize,lx2,hx2lsel,s,loc,x,(_a(3)+_a(4))/2cm,lx3,linelesize,lx3,hx3alls! 2d mshingtype,11amesh,allalls! 3d meshingtype,1mat,1esize,,_nz1asel,s,loc,z,_c3vext,all,,,0,0,-(_c3-_c2)esize,,_nz2asel,s,loc,z,_c3vext,all,,,0,0,_c4-_c3esize,,_nz3asel,s,loc,z,_c4vext,all,,,0,0,_c5-_c4esize,,_nz4asel,s,loc,z,_c5


Harmonic Analysis for a Rectangular Waveguide with a Ridge Discontinuity (Command Method)

vext,all,,,0,0,_c6-_c5esize,,_nz3asel,s,loc,z,_c6vext,all,,,0,0,_c7-_c6esize,,_nz2asel,s,loc,z,_c7vext,all,,,0,0,_c8-_c7esize,,_nz1asel,s,loc,z,_c8vext,all,,,0,0,_c9-_c8type,2esize,,_nzpmlasel,s,loc,z,_c2vext,all,,,0,0,-(_c2-_c1)asel,s,loc,z,_c9vext,all,,,0,0,_c10-_c9asel,s,loc,z,0aclear,alletdele,11allsnummrg,all! PEC on waveguide wallnsel,s,loc,x,cw/2nsel,a,loc,y,-ch/2nsel,a,loc,y,ch/2nsel,a,loc,z,_c1nsel,a,loc,z,_c10d,all,ax,0nsel,s,loc,x,_a(1),_a(2)nsel,r,loc,y,_b(1),_b(2)nsel,r,loc,z,_c5,_c6d,all,ax,0allsvlscale,all,,,scal,scal,scal,,,1! define input and output porthfport,1,rect,,TE10,SOFT,cw*scal,ch*scal,1.nsel,s,loc,z,scal*_c3bf,all,port,1hfport,2,rect,,TE10,SOFT,cw*scal,ch*scalnsel,s,loc,z,_c8*scalbf,all,port,2allssavefini! perform the solution/soluspswp,10e9,15e9,0.25e9,1,,2,1fini

Target Results

Figure 2: “|S21| of the Rectangular Waveguide with a Ridge Discontinuity” depicts the |S21| of the simulatedstructure from 10 GHz to 15 GHz. Figure 3: “Electric Field Contour of the Waveguide with a Ridge at 15 GHz”shows the electric field contour at 15 GHz.



Figure 2 |S21| of the Rectangular Waveguide with a Ridge Discontinuity


Harmonic Analysis for a Rectangular Waveguide with a Ridge Discontinuity (Command Method)

Figure 3 Electric Field Contour of the Waveguide with a Ridge at 15 GHz



Harmonic Analysis for a RectangularWaveguide with a Dielectric Post on AdaptiveMesh (Command Method)Problem Description

This example demonstrates how to determine the S-parameter of a rectangular waveguide with a dielectric postby adaptive meshing using ANSYS commands.

The dielectric post (12 × 10.16 × 6 mm3, εr = 8.2) is located at the center of the rectangular waveguide (22.86 ×

10.16 mm2), shown in Figure 1: “Waveguide with Dielectric Post (Dimensions are in mm)”. The perfect electriccondition is applied to the metallic surfaces of the waveguide and the impedance matching boundary conditionof TE10 mode is used at the input and output ports. Four iterations of adaptive meshes are used to approach an

accurate solution for the S-parameter at 10 GHz. Then, the S-parameters are calculated on the refined mesh from8 GHz to 12 GHz.

Figure 1 Waveguide with Dielectric Post (Dimensions are in mm)



/title, Dielectric Post in a Rectangular Waveguide/com, Waveguide Dimension: 22.86x10.16 mm^2 (Cutoff Frequency: 6.56 GHz)/com, Dielectric Post: 12 x 10.16 x 6 mm^3 at the center of waveguide, epsr = 8.2/com, Frequency Range: 8 - 12 GHz for TE10 mode/nopr/prep7! define the structurech=10.16e-3 cw=22.86e-3c=12e-3 d=6e-3 epsr=8.2 freq=10e9 cl=5*d ! define the elements and materialset,1,HF119,1mp,murx,1,1.mp,perx,1,1.mp,murx,2,1.


mp,perx,2,epsr block,-cw/2,cw/2,-ch/2,ch/2,-cl/2,cl/2 block,-c/2,c/2,-ch/2,ch/2,-d/2,d/2 vsbv,1,2,,delete,keepvglue,all! 3-d meshingh1=cw/5 esize,h1type,1mat,1 vmesh,3mat,2 vmesh,2! Tangential E is zero on all side wallsasel,s,loc,y,-ch/2asel,a,loc,y,ch/2asel,a,loc,x,-cw/2asel,a,loc,x,cw/2da,all,ax,0.! define waveguide portsasel,s,loc,z,-cl/2 sfa,all,,port,1hfport,1,rect,,te10,impd,cw,ch,1 asel,s,loc,z,cl/2sfa,all,,port,2hfport,2,rect,,te10,impd,cw,challsfini! set up adaptive loop and perform solution at 10 GHz_n=4*do,_i,1,_n *if,_i,gt,1,then /prep7 hferefine,_i-1 fini *endif /solu ANTYPE,harmic harfre,10e9 eqslv,sparse solve fini /post1 sparm,1,1 fini*enddo! perform final solution on refined mesh over frequency band/soluspswp,8e9,12e9,0.25e9,1,,2,1fini

The Target Results

The first four figures below show the mesh densities during the initial mesh and three iterations of mesh refine-ment. The results for |S11| on each mesh are 0.266, 0.230, 0.241 and 0.246, respectively. Figure 6: “|S11| of Rectan-

gular Waveguide with a Dielectric Post from 8 GHz to 12 GHz” depicts the |S11| of the simulated structure from

8 GHz to 12 GHz on the final refined mesh.


Harmonic Analysis for a Rectangular Waveguide with a Dielectric Post on Adaptive Mesh (Command

Figure 2 Initial Mesh Density



Figure 3 Mesh Density after First Mesh Refinement Iteration



Figure 4 Mesh Density after Second Mesh Refinement Iteration



Figure 5 Mesh Density after Third Mesh Refinement Iteration



Figure 6 |S11| of Rectangular Waveguide with a Dielectric Post from 8 GHz to 12 GHz



Harmonic Analysis of a Parallel-PlateWaveguide with a Lumped Circuit Load(Command Method)Problem Description

This example demonstrates how to determine the s-parameter of a parallel-plate waveguide with a lumped circuitload using ANSYS commands.

The finite element model is shown in Figure 1: “3-D Parallel-plate Waveguide Model”. The waveguide is 15 mmhigh by 5 mm wide. A perfect electric conductor boundary condition is applied to the top and bottom walls ofthe waveguide. The impedance matching boundary condition of TEM mode is used at the input and outputports. The lumped circuit load is shown in Figure 2: “1-D Transmission Line Impedance Load”. The calculationsare performed at a frequency of 5 GHz.

Figure 1 3-D Parallel-plate Waveguide Model

Figure 2 1-D Transmission Line Impedance Load

The circuit loads applied are equivalent to the circuit load for the 1-D transmission line. As shown in Fig-ure 3: “Lumped Circuit Loads”, since there are three elements on a cross section and the lumped loads are appliedat the vertical edges of the hexahedral elements, 2Z/3 is applied at the mid-nodes of the edges using the BF


command with Lab = LUMP. HF Emag imposes the lumped circuit loads on the end nodes of the element edgesas well as the mid-nodes. Impedance Z represents a shunt RCL circuit as shown in Figure 4: “Shunt RCL Circuit”.

Figure 3 Lumped Circuit Loads

Figure 4 Shunt RCL Circuit



/batch,list/title, Lumped Circuit in Parallel-plate Waveguide /com,/nopr/prep7ch=0.015 ! height of the parallel-plate waveguidecw=0.005 ! width of the parallel-plate waveguide freq=5.e9 ! frequencylamda=0.06_omega=2.*3.1415926535*freqh=lamda/10 ! mesh sizecl=0.5*lamdaZc=(ch/cw)*377.0 ! wave impedance of parallel-plate waveguide_R=Zc/3 ! resistance_C=1.0d0/(_R*_omega) ! capacitance_L=_R/(_omega) ! inductance! define element and materialet,1,120,1 ! 1st order hex elementmp,murx,1,1. ! permeabilitymp,perx,1,1. ! permittivitylocal,11wpcsys,,11! define structureblock,-cw/2,cw/2,-ch/2,ch/2,0,clblock,-cw/2,cw/2,-ch/2,ch/2,0,-clvglue,all! meshing the structureesize,htype,1mat,1vmesh,all! PEC on top and bottom wallnsel,s,loc,y,-ch/2


Harmonic Analysis of a Parallel-Plate Waveguide with a Lumped Circuit Load (Command Method)

nsel,a,loc,y,ch/2d,all,ax,0.! define input and output porthfport,1,para,11,tem,impd,cw,ch,1hfport,2,para,11,tem,impd,cw,chnsel,s,loc,z,clsf,all,port,1nsel,s,loc,z,-clsf,all,port,2! define shunt RCL circuit at vertical edgesnsel,s,loc,x,-cw/2nsel,a,loc,x,cw/2nsel,r,loc,z,0bf,all,lump,1,_R,_C,_Lallssavefini! perform solution/solueqslv,sparseantype,harmicharfrq,freqsolvefini! extract s-parameter/post1sparm,1,1fini

Target Results

A S11 value of 0.5002 is calculated for 5 GHz. Transmission line theory gives value of 0.5.



Postprocessing Scattering, Admittance, andImpedance ParametersProblem Description

This example demonstrates how to convert, list, and plot S (scattering), Y (admittance), and Z (impedance)parameters of a T-type transmission line using the ANSYS postprocessor. The T-type transmission line networkis shown in the following figure.

Figure 1 T-type Transmission Line Network

where:

Z1 = 1/jωC, Z2 = jωL; Z3 = R + j(ωL -1/ωC)

R = 10 Ω

C = 10-11 F

L = 7 x 10-9 H

Z01 = 50 Ω; Z02 = 75 Ω

ω = angular frequency

The Touchstone file T_network.s2p of S-parameters for the T-type network follows:

# GHz S MA R 50. 75.1.000 0.6297 169.6 0.5316 26.08 0.5316 26.08 0.7363 99.682.000 0.6470 100.7 0.6755 -9.873 0.6755 -9.873 0.7126 65.893.000 0.7459 73.82 0.6105 -28.45 0.6105 -28.45 0.7846 51.314.000 0.8192 58.46 0.5315 -40.29 0.5315 -40.29 0.8442 41.825.000 0.8681 48.31 0.4622 -48.53 0.4622 -48.53 0.8855 35.09

Smith Charts

To plot network parameters on a Smith chart, the following commands are issued in interactive mode:

/post1PLSCH,T_network,s2p,S,1 ! plot S11 on Smith ChartPLSCH,T_network,s2p,Y,1 ! plot Y11 on Smith Chartfini

S11 and Y11 plots are shown in the following figures. PLSCH,T_network,s2p,Y,1 converts the S-parameters to Y-parameters and plots them.


Figure 2 S11 on Smith Chart


Postprocessing Scattering, Admittance, and Impedance Parameters

Figure 3 Y11 on Smith Chart

Network Parameters vs. Frequency Plots

To plot S11, S21, Z11, and Z21 parameters versus frequency, the following commands are issued in interactivemode:

/post1PLSYZ,T_network,s2p,S,MAG,1,1,2,1 ! plot S11 and S21 versus frequencyPLSYZ,T_network,s2p,Z,MAG,1,1,2,1 ! plot Z11 and Z21 versus frequencyfini

PLSYZ,T_network,s2p,Z,1 converts the S-parameters to Z-parameters and plots them.



Figure 4 S11 and S21 Magnitude vs. Frequency


Postprocessing Scattering, Admittance, and Impedance Parameters

Figure 5 Z11 and Z21 Magnitude vs. Frequency

Touchstone File Conversion

To generate a Touchstone file of Y-parameters, the following commands are issued in interactive mode:

/post1PRSYZ,T_network,s2p,Y,MAfini

PLSYZ T_network,s2p,Y,MA converts the S-parameters to Y-parameters and creates the following Touchstonefile with the name T_network_SYZ.s2p.

! 2-port Y-parameter file, 5 frequency points# GHz Y MA R 50. 75.!freq magY11 angY11 magY21 angY21 magY12 angY12 magY22 angY221.00000 0.24744 -25.2489 0.10135 143.034 0.10135 143.034 0.05352 -56.81502.00000 0.02924 -85.4203 0.01401 90.8503 0.01401 90.8503 0.01264 -89.92503.00000 0.01681 -87.4959 0.00826 90.1989 0.00826 90.1989 0.00791 -89.99314.00000 0.01203 -88.2378 0.00596 90.0865 0.00596 90.0865 0.00582 -89.99475.00000 0.00943 -88.6262 0.00468 90.0374 0.00468 90.0374 0.00461 -90.0011



Part VII. Advanced Wave Resonance Examples

Modal Analysis for Resonant Frequencies of aDielectric Resonator on Microstrip Substrate(Command Method)Problem Description

This example demonstrates how to determine the resonant frequencies of a dielectric resonator (DR) on a mi-crostrip substrate using ANSYS commands.

A cylindrical dielectric resonator is located on the top of a microstrip substrate with metallic enclosure (D = 10mm, h = 5 mm, εr = 36, εs = 9.6, Hs = 1 mm, H = 6 mm, R = 15 mm), as shown on the left in the figure below.

Modal analysis is used to find the resonant frequencies in the structure. One quarter of the structure is used forthe numerical model because of the symmetry of the fields and geometry. Since the structure is open and thefringe fields exist in the space, the metallic enclosure should be placed far enough away from the resonator inorder to minimize the effect of the metallic enclosure that is necessary for modal analysis. The resonant modescan be obtained by the combination of boundary conditions on two symmetric planes, in other words, PMC-PEC, PMC-PMC or PEC-PEC. The wedge element is used for analysis as shown on the right in the figure below.

Figure 1 Geometry and FEA Model of Dielectric Resonator



/batch,list/title, Dielectric Resonator on Microstrip Substrate /nopr/prep7 ! define the structurer1=5.r2=15h=5.hc=6hs=1.eps1=9.6


eps2=36scal=1.e-3

! set up boundary key: _bc=0 PMC-PMC; _bc=1 PEC-PMC; _bc=2 PEC-PEC_bc=1! define elements and materialset,11,200,5et,1,120,1mp,perx,1,1.mp,murx,1,1.mp,perx,2,eps1mp,murx,2,1.mp,perx,3,eps2mp,murx,3,1.! set up computational domainhsize=r1/8hz=h/12_nz1=4_nz2=nint(h/hz)+1_nz3=nint((hc-h)/hz)+1_c1=0_c2=_c1+hs_c3=_c2+h_c4=_c3+(hc-h)pcirc,r1,0,0,90pcirc,r2,0,0,90asba,2,1,,delete,keepaglue,all! 2d-meshingesize,hsizetype,11amesh,all! 3d-meshingmat,2esize,,_nz1type,1asel,s,loc,z,0vext,all,,,0,0,(_c2-_c1)csys,1asel,s,loc,z,_c2asel,r,loc,x,0,r1cm,_area1,areacsys,0esize,,_nz2mat,3type,1asel,s,,,_area1vext,all,,,0,0,(_c3-_c2)mat,1asel,s,loc,z,_c2asel,u,,,_area1vext,all,,,0,0,(_c3-_c2)asel,s,loc,z,_c3esize,,_nz3mat,1vext,all,,,0,0,(_c4-_c3)allsasel,s,loc,z,0aclear,allesel,s,type,,11edele,allallsnummrg,allalls! set up PEC boundary conditioncsys,1nsel,s,loc,x,r2d,all,ax,0csys,0nsel,s,loc,z,_c1nsel,a,loc,z,_c4*if,_bc,eq,1,then


Modal Analysis for Resonant Frequencies of a Dielectric Resonator on Microstrip Substrate (Command

nsel,a,loc,x,0*elseif,_bc,eq,2,then nsel,a,loc,x,0 nsel,a,loc,y,0*endifd,all,ax,0vlscale,all,,,scal,scal,scal,,,1fini! perform a solution/soluantype,modalmodopt,lanb,2,1.e6,10.e9,,onmxpand,,,,yessolvefini

Target Results

The three lowest resonant modes are TM01δ, HEM and TE01δ. The corresponding resonant frequencies are 3.98

GHz, 5.18 GHz and 5.94 GHz, respectively. The electric fields of the three lowest modes are shown in the followingthree figures.

Figure 2 The Electric Field of TM01δ Mode in a DR with a Metallic Enclosure



Figure 3 The Electric Field of HEM Mode in a DR with a Metallic Enclosure


Modal Analysis for Resonant Frequencies of a Dielectric Resonator on Microstrip Substrate (Command

Figure 4 The Electric Field of TE01δ Mode in a DR with a Metallic Enclosure



Modal Analysis for Dispersion of a MicrostripLine (Command Method)Problem Description

This example demonstrates how to determine the dispersion of a microstrip line using ANSYS commands.

Modal analysis is used to find the dispersion of the fundamental mode of the microstrip line, shown on the leftin the figure below. One half of the structure is used for the numerical model because of the symmetry of thefields and geometry. The metallic enclosure should be placed far enough away from the resonator to minimizethe effect of the metallic enclosure that is necessary for modal analysis. The triangular element is used for ana-lysis as shown on the right in the figure below.

Figure 1 Geometry and FEA Model of the Microstrip Line

ε




/batch, list/title, Dispersion of Isotropic Microstrip Line/com, Freq = 1-20 GHz/com, w=h=1.27 mm,er=8.875,X=12.7 mm,Y=12.7 mm /nopr/prep7! set up structurew=1.27e-3h=1.27e-3X=12.7e-3Y=12.7e-3er=8.875! define elements and materialset,1,118,1emunit,mksmp,murx,1,1.mp,perx,1,1.mp,murx,2,1.mp,perx,2,er! define numerical model and meshingrect,0,w/2,0,hrect,w/2,X/2,0,hrect,0,w/2,h,Yrect,w/2,X/2,h,Yaglue,allmshkey,0mshape,1mat,2lsel,s,line,,1,3,2lesize,all,,,4lsel,s,line,,2,4,2lesize,all,,,6amesh,1lsel,s,line,,17,18lesize,all,,,20,2lsel,s,line,,6lesize,all,,,3amesh,5mat,1lsel,s,line,,11lesize,all,,,1lsel,s,line,,19,20lesize,all,,,25,3amesh,6lsel,s,line,,22lesize,all,,,6lsel,s,line,,21lesize,all,,,18,2amesh,7lsel,all! set up PEClsel,s,line,,3lsel,a,loc,y,0,lsel,a,loc,y,Ylsel,a,loc,x,X/2dl,all,,ax,0.lsel,allfinish! perform solution/soluhfpcswp,1.e9,20.e9,0.5e9,1finish


Modal Analysis for Dispersion of a Microstrip Line (Command Method)

The Target Results

The output file generated by the HFPCSWP command is listed below for the dispersion, and the electric field ofthe fundamental mode at 20 GHz is shown in Figure 2: “Electric field of the Fundamental Mode in the MicrostripLine at 20 GHz”.

_________________________ HFPCSWP RESULTS_____________________________

MODE NUMBER: 1.

FREQ (GHz) BETA (RAD/M) 1.0000 0.5112E+02 1.5000 0.7683E+02 2.0000 0.1027E+03 2.5000 0.1288E+03 3.0000 0.1550E+03 3.5000 0.1815E+03 4.0000 0.2082E+03 4.5000 0.2352E+03 5.0000 0.2623E+03 5.5000 0.2896E+03 6.0000 0.3172E+03 6.5000 0.3449E+03 7.0000 0.3727E+03 7.5000 0.4008E+03 8.0000 0.4290E+03 8.5000 0.4573E+03 9.0000 0.4858E+03 9.5000 0.5144E+03 10.0000 0.5432E+03 10.5000 0.5721E+03 11.0000 0.6011E+03 11.5000 0.6303E+03 12.0000 0.6595E+03 12.5000 0.6889E+03 13.0000 0.7184E+03 13.5000 0.7480E+03 14.0000 0.7777E+03 14.5000 0.8075E+03 15.0000 0.8374E+03 15.5000 0.8673E+03 16.0000 0.8974E+03 16.5000 0.9275E+03 17.0000 0.9577E+03 17.5000 0.9880E+03 18.0000 0.1018E+04 18.5000 0.1049E+04 19.0000 0.1079E+04 19.5000 0.1110E+04 20.0000 0.1141E+04 ______________________________________________________________________



Figure 2 Electric field of the Fundamental Mode in the Microstrip Line at 20 GHz


Modal Analysis for Dispersion of a Microstrip Line (Command Method)

Part VIII. Advanced Wave Scattering Examples

Harmonic Analysis for Scattering of a MetallicSphere Coated by Lossy Dielectric Layer(Command Method)Problem Description

This example demonstrates how to determine the radar cross section (RCS) of a metallic sphere coated by a lossydielectric layer using ANSYS commands.

The radius of the metallic sphere is 0.8 cm. The relative complex permittivity of the lossy dielectric layer is εr=4-

i, with thickness 0.2 cm. To calculate the normalized RCS of the lossy dielectric-coated metallic sphere, the incidentplane wave is taken as -x-polarized with incident angles φ=0° and θ=180°. One half of the structure is used forthe numerical model, because of the symmetry of the fields and geometry as shown in Figure 1: “FEA Model forScattering Analysis of a Lossy Dielectric-Coated Metallic Sphere”. The PML absorbing material encloses themodeled domain except on the symmetric planes. To improve the accuracy, a 3-element buffer is placed betweenthe dielectric sphere and the equivalent source surface. Also, a 3-element buffer is placed between the equivalentsource surface and the PML interface.


Figure 1 FEA Model for Scattering Analysis of a Lossy Dielectric-Coated Metallic Sphere



/batch,list/title, RCS from a Lossy Dielectric-coated Metallic Sphere/com, Problem: The radius of sphere = 0.8 cm, the thickness of dielectric layer = 0.2 cm/com, Incident Wave: +x polirazation with PHI =0, THETA=180 (degree) at 15 GHz/com,/nopr/prep7! frequency, material and structure dimensionsfreq=15.e9lambda=3.e8/freqra=8.e-3rb=ra+2.e-3epsr=4.loss=1./epsrwave1=3.e8/(sqrt(epsr)*freq)wave2=3.e8/freq! define the computational domainh=wave2/15a=rb+3*h


Harmonic Analysis for Scattering of a Metallic Sphere Coated by Lossy Dielectric Layer (Command Method)

b=a+3*hc=b+4*h! define the elements and materialset,1,HF119,1et,2,HF119,1,,,1mp,murx,1,1.mp,perx,1,epsrmp,lsst,1,lossmp,murx,2,1.mp,perx,2,1.! set up numerical modelsphere,ra,rb,0,180block,-a,a,0,a,-a,ablock,-b,b,0,b,-b,bblock,-c,c,0,c,-c,cvsbv,4,3,,delete,keepvsbv,3,2,,delete,keepvsbv,2,1,,delete,keepcsys,2vsel,s,loc,x,0,ra/2vdel,allallscsys,0vglue,all! meshingesize,wave1/10type,1mat,1vmesh,1esize,hmat,2vmesh,4,6,2type,2vmesh,5allsnummrg,all! define equivalent source surfacensel,s,loc,x,-a,ansel,r,loc,y,0,ansel,r,loc,z,-a,aesln,s,1,allnsel,s,loc,x,ansel,a,loc,x,-ansel,a,loc,y,ansel,a,loc,z,-a,nsel,a,loc,z,asf,all,mxwfalls! define boundary conditionnsel,s,loc,x,cnsel,a,loc,x,-cnsel,a,loc,y,cnsel,a,loc,z,-cnsel,a,loc,z, cd,all,ax,0.nsel,allcsys,2nsel,s,loc,x,rad,all,ax,0.csys,0allsel,all! define incident plane waveplwave,1,0,0,0,180fini! perform solution/soluhfscat,scateqslv,sparseantype,harmicharfrq,freqsolvefini



! calculate normalized RCS/post1set,1,1hfsym,11,,pmcprhffar,rcsn,,0,0,,0,180,36,,prhffar,rcsn,,90,90,,0,180,36,,fini

Target Results

The contour of the scattering electric field from the lossy dielectric-coated metallic sphere is shown in Fig-ure 2: “Scattering Electric Field Contour of the Lossy Dielectric-Coated Metallic Sphere”. Figure 3: “NormalizedRCS of the Lossy Dielectric-Coated Metallic Sphere on E-plane and H-plane” depicts the RCS of the dielectric-coated metallic sphere on the E-plane (φ=0°) and H-plane (φ=90°), respectively.

Figure 2 Scattering Electric Field Contour of the Lossy Dielectric-Coated Metallic Sphere


Harmonic Analysis for Scattering of a Metallic Sphere Coated by Lossy Dielectric Layer (Command Method)

Figure 3 Normalized RCS of the Lossy Dielectric-Coated Metallic Sphere on E-plane andH-plane



Harmonic Analysis for Scattering of a DielectricSphere (Command Method)Problem Description

This example demonstrates how to determine the radar cross section (RCS) from the scattering of a dielectricsphere using ANSYS commands.

The relative permittivity of the dielectric sphere is εr = 2.56. To calculate the bistatic RCS of the dielectric sphere,

the incident plane wave is taken as x-polarized with incident angles φ = 0° and θ = 0°. The electric size is k0a = 1

(k0 is the wave number in free space). One half of the structure is used for the numerical model, because of the

symmetry of the fields and geometry, as shown in Figure 1: “FEA Model for Scattering Analysis of a DielectricSphere”. The PML absorbing material encloses the modeled domain except on the symmetric planes. To improvethe accuracy, a 4-element buffer is placed between the dielectric sphere and the equivalent source surface. Also,a 4-element buffer is placed between the equivalent source surface and the PML interface.

Figure 1 FEA Model for Scattering Analysis of a Dielectric Sphere




/batch,list/title, RCS of a Dielectric Sphere/com, Problem: Calculate RCS of a Dielectric Sphere/com, Structure: ka=1 (a - radius of sphere, k - vacuum wavenumber), er=2.56/com, Numerical Model: 1/2 Structure/com, PML enclosure except on symmetric planes/com, Plane Wave: +x polarization, Phi=0 (deg), Theta=0 (deg)/nopr/prep7! define structure and frequencyra=1freq=4.7746e7epsr=2.56! define computational domainlamda1=3.e8/(sqrt(epsr)*freq)lamda2=3.e8/freqh1=lamda1/20h2=lamda2/20a=ra+4*h1b=a+4*h2c=b+4*h2! define elements and materialset,1,HF119,1et,2,HF119,1,,,1mp,murx,1,1.mp,perx,1,epsrmp,murx,2,1.mp,perx,2,1.! set up numerical domainsphere,0,ra,0,180block,-a,a,0,a,-a,ablock,-b,b,0,b,-b,bblock,-c,c,0,c,-c,cvsbv,4,3,,dele,keepvsbv,3,2,,dele,keepvsbv,2,1,,dele,keepvglue,all! volume definition: v1 - dielectric sphere; v5 - PML; v3, v4 - air! meshingesize,h1type,1mat,1vmesh,1mat,2vmesh,3esize,h2vmesh,4type,2vmesh,5! define equivalent source surfacensel,s,loc,x,-a,ansel,r,loc,y,0,ansel,r,loc,z,-a,aesln,s,1,allnsel,s,loc,x,ansel,a,loc,x,-ansel,a,loc,y,ansel,a,loc,z,-ansel,a,loc,z,asf,all,mxwfnsel,allesel,all! define PEC boundary conditionnsel,s,loc,x,cnsel,a,loc,x,-cnsel,a,loc,y,c


Harmonic Analysis for Scattering of a Dielectric Sphere (Command Method)

nsel,a,loc,z,-cnsel,a,loc,z, cd,all,ax,0.nsel,allalls! incident plane waveplwave,1,0,0,0,0fini! perform solution/soluhfscat,scateqslv,sparseantype,harmicharfrq,freqsolvefini! RCS calculation/post1set,1,1! set up image symmetric planehfsym,,,pmc prhffar,rcs,,0,90,1,0,180,36fini

Target Results

Figure 2: “RCS of the Dielectric Sphere” depicts the RCS of the dielectric sphere on E-plane (φ=0°) (black line) andH-plane (φ=90°) (gray line). The contour of the scattering electric field is shown in Figure 3: “Contour of theScattering Electric Field from a Dielectric Sphere”.

Figure 2 RCS of the Dielectric Sphere



Figure 3 Contour of the Scattering Electric Field from a Dielectric Sphere


Harmonic Analysis for Scattering of a Dielectric Sphere (Command Method)

Harmonic Analysis for Scattering of a MetallicCube (Command Method)Problem Description

This example demonstrates how to determine the radar cross section (RCS) of a metallic cube using ANSYScommands.

The edge lengths of the metallic cube are 0.755 wavelength. To calculate the bistatic RCS of the metallic cube,the incident plane wave is taken as x-polarized with incident angles φ=90° and θ=0°. One half of the structure isused for the numerical model, because of the symmetry of the fields and geometry. The PML absorbing materialencloses the modeled domain except on the symmetric planes. To improve the accuracy, a 4-element buffer isplaced between the metallic cube and the equivalent source surface. Also, a 4-element buffer is placed betweenthe equivalent source surface and the interface of 6-layer PML.



/batch,list/title, RCS of Metallic Cube (0.755x0.755x0.755 wavelength**3) /com, Incident Wave: +X polirazation with PHI = 90 (deg), THETA = 180 (deg)/nopr/prep7! structure dimensionsfreq=300e6wavel=3.e8/freqa=0.755*wavelb=a! define elements and materialet,11,200,7et,1,120,1et,2,120,1,,,1mp,murx,1,1.mp,perx,1,1.! define mesh sizeh=wavel/14_n1=4_n2=4_npml=6! set up computational domain*dim,_a,array,5*dim,_b,array,9_a(1)=0_a(2)=_a(1)+a/2_a(3)=_a(2)+_n1*h_a(4)=_a(3)+_n2*h_a(5)=_a(4)+_npml*h_b(5)=0_b(6)=_b(5)+b/2_b(7)=_b(6)+_n1*h_b(8)=_b(7)+_n2*h_b(9)=_b(8)+_npml*h_b(4)=_b(5)-b/2_b(3)=_b(4)-_n1*h_b(2)=_b(3)-_n2*h_b(1)=_b(2)-_npml*h_c4=-a/2_c5=_c4+a_c6=_c5+_n1*h_c7=_c6+_n2*h


_c8=_c7+_npml*h_c3=_c4-_n1*h_c2=_c3-_n2*h_c1=_c2-_npml*h_nz=nint((_c5-_c4)/h)+1*do,_i,1,4 *do,_j,1,8 rect,_b(_j),_b(_j+1),_a(_i),_a(_i+1) *enddo*enddoaglue,allasel,allagen,2,all,,,,,-a/2asel,s,loc,z,_c4asel,r,loc,y,_a(1),_a(2)asel,r,loc,x,_b(4),_b(6)cm,_soli,areaasel,s,loc,z,_c4asel,u,,,_solicm,_air,areaasel,alllsel,s,loc,y,(_a(1)+_a(2))/2lsel,a,loc,x,(_b(4)+_b(5))/2lsel,a,loc,x,(_b(5)+_b(6))/2cm,_lxy,linelesize,_lxy,hlsel,alllsel,u,,,_lxycm,_lair,linelesize,_lair,htype,11asel,s,loc,z,_c4amesh,allasel,s,area,,_soliagen,2,all,,,,,(_c5-_c4)esize,,_nztype,1mat,1asel,s,area,,_airvext,all,,,0,0,(_c5-_c4)esize,,_n1asel,s,loc,z,_c5vext,all,,,0,0,(_c6-_c5)asel,s,loc,z,_c4vext,all,,,0,0,-(_c4-_c3)esize,,_n2asel,s,loc,z,_c6vext,all,,,0,0,(_c7-_c6)asel,s,loc,z,_c3vext,all,,,0,0,-(_c3-_c2)type,2esize,,_npmlasel,s,loc,z,_c7vext,all,,,0,0,(_c8-_c7)asel,s,loc,z,_c2vext,all,,,0,0,-(_c2-_c1)asel,s,loc,z,_c4asel,a,loc,z,_c5aclear,allesel,s,type,,11edel,allallsnsel,s,loc,y,_a(1),_a(4)nsel,r,loc,x,_b(2),_b(8)nsel,r,loc,z,_c2,_c8cm,_inte,nodensel,s,loc,z,_c2,_c7nsel,u,,,_inteesln,s,1emodif,all,type,2allsnummrg,all


Harmonic Analysis for Scattering of a Metallic Cube (Command Method)

! define equivalent source surfacensel,s,loc,x,_b(3),_b(7)nsel,r,loc,y,_a(1),_a(3)nsel,r,loc,z,_c3,_c6esln,s,1,allnsel,s,loc,x,_b(3)nsel,a,loc,x,_b(7)nsel,a,loc,y,_a(3)nsel,a,loc,z,_c3nsel,a,loc,z,_c6sf,all,mxwfnsel,allesel,all! define boundary conditionnsel,s,loc,x,_b(1)nsel,a,loc,x,_b(9)nsel,a,loc,y,_a(5)nsel,a,loc,z,_c1nsel,a,loc,z,_c8d,all,ax,0.nsel,s,loc,x,_b(4),_b(6)nsel,r,loc,y,_a(1),_a(2)nsel,r,loc,z,_c4,_c5d,all,ax,0.allsel,all! incident plane waveplwave,1,0,0,90,0fini! perform solution/soluhfscat,scateqslv,sparseantype,harmicharfrq,freqsolvefini! calculate RCS/post1set,1,1hfsym,,,pmcprhffar,rcsn,,0,0,,0,180,36prhffar,rcsn,,90,90,,0,180,36fini

Target Results

The contour of the scattering electric field from the metallic cube is shown in Figure 1: “Scattering Electric FieldContour from the Metallic Cube”. Figure 2: “Normalized RCS of the Metallic Cube on E-Plane and H-Plane” depictsthe RCS of the metallic cube on E-plane (φ=0°) and H-plane (φ=90°), respectively.



Figure 1 Scattering Electric Field Contour from the Metallic Cube


Harmonic Analysis for Scattering of a Metallic Cube (Command Method)

Figure 2 Normalized RCS of the Metallic Cube on E-Plane and H-Plane



Harmonic Analysis for Scattering of a MetallicSphere Coated by a Dielectric Layer (CommandMethod)Problem Description

This example demonstrates how to determine the radar cross section (RCS) of a metallic sphere coated by adielectric layer using ANSYS commands.

The radius of the metallic sphere is 0.333 wavelength. The relative permittivity of the dielectric layer is εr = 4 with

thickness 0.067 wave length. To calculate the bistatic RCS of the dielectric-coated dielectric sphere, the incidentplane wave is taken as - x-polarized with incident angles φ = 0° and θ = 0°. One half of the structure is used forthe numerical model, because of the symmetry of the fields and geometry as shown in Figure 1: “FEA Model forScattering Analysis of a Dielectric-Coated Metallic Sphere”. The PML absorbing material encloses the modeleddomain except on the symmetric planes. To improve the accuracy, a 4-element buffer is placed between thedielectric-coated metallic sphere and the equivalent source surface. Also, a 3-element buffer is placed betweenthe equivalent source surface and the PML interface.


Figure 1 FEA Model for Scattering Analysis of a Dielectric-Coated Metallic Sphere



/batch,list/title, RCS of a Dielectric-coated Metallic Sphere/com, Problem: A metallic sphere (radiu=0.333 wavelength) coated by dielectric layer/com, (thickness=0.067 wavelength, Er=4)/com, Incident Wave: -x polirazation with PHI = 0 (degree), THETA = 0 (degree)/nopr/prep7! problem dimensions and set-upfreq=300e6lambda=3.e8/freqepsr=4wave1= lambda /sqrt(epsr)wave2=lambdah1=wave1/16h2=wave2/16ra=0.333*lambdas=0.067*lambdarb=ra+sa=rb+4*h2


Harmonic Analysis for Scattering of a Metallic Sphere Coated by a Dielectric Layer (Command Method)

b=a+3*h2c=b+4*h2! --- define elements and materials ---et,1,HF119,1et,2,HF119,1,,,1mp,murx,1,1.mp,perx,1,epsrmp,murx,2,1.mp,perx,2,1.! --- set up the geometry ---sphere,ra,rb,0,180sphere,rb,a,0,180vsel,allcm,vequi,volublock,-b,b,0,b,-b,bblock,-c,c,0,c,-c,cvsbv,4,3,,delete,keepvsbv,3,vequi,,delete,keepcsys,2vsel,s,loc,x,0,ra/2vdel,allallscsys,0vglue,all! --- meshing ---csys,0smrtsize,4! meshingesize,h1type,1mat,1vmesh,1mat,2esize,h2vmesh,3esize,h2vmesh,6! --- PML element ---type,2vmesh,5allsnummrg,all! define equivalent source surfacecsys,2nsel,s,loc,x,0,aesln,s,1,allnsel,s,loc,x,asf,all,mxwfalls! define boundary conditioncsys,0nsel,s,loc,x,cnsel,a,loc,x,-cnsel,a,loc,y,cnsel,a,loc,z,-cnsel,a,loc,z,cd,all,ax,0.nsel,allcsys,2nsel,s,loc,x,rad,all,ax,0.csys,0allsel,all! incident plane waveplwave,-1,0,0,0,0fini/soluhfscat,scateqslv,sparseantype,harmicharfrq,freqsolve



fini/post1set,1,1hfsym,,,pmcprhffar,rcsn,,0,0,,0,180,36,,fini

Target Results

The contour of the scattering electric field from the dielectric-coated metallic sphere is shown in Figure 2: “Scat-tering Electric Field Contour of The Dielectric-Coated Metallic Sphere”. Figure 3: “Normalized RCS of the Dielectric-Coated Metallic Sphere on E-Plane” depicts the RCS of the dielectric-coated metallic sphere on the E-plane (φ=0°).

Figure 2 Scattering Electric Field Contour of The Dielectric-Coated Metallic Sphere


Harmonic Analysis for Scattering of a Metallic Sphere Coated by a Dielectric Layer (Command Method)

Figure 3 Normalized RCS of the Dielectric-Coated Metallic Sphere on E-Plane



Harmonic Analysis of a Thick BandpassFrequency Selective Surface (CommandMethod)Problem Description

This example demonstrates how to determine the power transmission coefficient for a thick bandpass frequencyselective surface using ANSYS commands. The frequency selective surface is a thick perfectly conducting screenperforated with a periodic array of annular apertures. The conducting screen is 0.1 cm thick. The outer radius ofthe annular slot is 0.45 cm. The inner radius is 0.40 cm. A square grid is selected with a periodic spacing of 1 cm.

The FEA model is shown in Figure 1: “Unit Cell”. Perfect electric conductor boundary conditions are applied tothe aperture and PML wall. The calculations are performed at normal incidence and a frequency of 10 GHz.

Figure 1 Unit Cell



/batch,list/com,Thick Annular-Slot Band-pass FSS


/com/nopr/prep7_frq=10e9 ! working frequencylamda=3.e8/_frqscal=1.e-2phi=0 ! incident phi angle! define element and geometrytheta=0 ! incident theta angleet,1,119,1 ! normal elementet,2,119,1,,,1 ! PML elementmp,murx,1,1.mp,perx,1,1.x0=scal*0.5y0=scal*0.5rb=scal*0.45ra=rb/1.125plate_h=scal*0.1cyl4,0,0,ra,0,rb,360,plate_hh1=lamda/15h2=0.3*h1_n1=6_n2=4_npml=6*dim,_c,array,10_c(4)=0_c(3)=_c(4)-0.05*lamda_c(2)=_c(3)-0.25*lamda_c(1)=_c(2)-_npml*h1_c(5)=_c(4)+plate_h_c(6)=_c(5)+0.05*lamda_c(7)=_c(6)+0.25*lamda_c(8)=_c(7)+0.25*lamda_c(9)=_c(8)+_npml*h1*do,_i,5,8 block,-x0,x0,-y0,y0,_c(_i),_c(_i+1)*enddo*do,_i,4,2,-1 block,-x0,x0,-y0,y0,_c(_i),_c(_i-1)*enddoallsvglue,allnumcmp,all/number,1! meshing master surfaces and copy mesh to slave surfaceset,3,200,5type,3esize,h2asel,s,loc,x,-x0asel,a,loc,y,-y0asel,r,loc,z,_c(3),_c(6)amesh,allesize,h1asel,s,loc,x,-x0asel,a,loc,y,-y0asel,u,loc,z,_c(3),_c(6)amesh,allallsasel,s,loc,x,-x0agen,2,all,,,2*x0asel,s,loc,y,-y0agen,2,all,,,0,2*y0allsnummrg,all! meshing volumestype,1esize,h2vsel,s,loc,z,_c(3),_c(6)vmesh,allesize,h1vsel,s,loc,z,_c(2),_c(3)vsel,a,loc,z,_c(6),_c(8)


Harmonic Analysis of a Thick Bandpass Frequency Selective Surface (Command Method)

vmesh,all! create PML element type,2 esize,h1vsel,s,loc,z,_c(1),_c(2)vsel,a,loc,z,_c(8),_c(9)vmesh,allallsaclear,alletdel,3alls! coupling master/slave nodesnsel,s,loc,x,-x0nsel,a,loc,x,x0cpcyc,ax,,,2*x0,0,0,1nsel,s,loc,y,-y0nsel,a,loc,y,y0cpcyc,ax,,,0,2*y0,0,1alls! set up PEC on aperture and PML wallnsel,s,loc,z,_c(1)nsel,a,loc,z,_c(9)d,all,ax,0csys,1nsel,s,loc,z,_c(4)nsel,a,loc,z,_c(5)nsel,u,loc,x,ra,rbd,all,ax,0nsel,s,loc,x,ransel,a,loc,x,rbnsel,r,loc,z,_c(4),_c(5)d,all,ax,0allscsys,0! port definitionsnsel,s,loc,z,_c(7)bf,all,port,1hfport,1,PLAN,,,SOFT,0.,1.,0.,phi,thetaallssavefini! perform a solution/solueqslv,sparseantype,harmicharfrq,_frqsolvefini! calculate power transmission coefficient/post1fssparmfini

Target Results

A 0.50 power transmission coefficient is calculated for 10 GHz. The mode matching method presented in thepaper “Bandpass Grids with Annular Apertures” by Ann Roberts and Ross C. McPhedran, IEEE Transactions onAntennas and Propagation, Vol. 36, No. 5., May 1988, pp. 607–611 gives a value of 0.47.



Harmonic Analysis for Scattering of a DielectricGrating (Command Method)Problem Description

This example demonstrates how to determine scattering of a dielectric grating using ANSYS commands.

The dielectric grating has the dimensions and material properties shown in the following figure. Period D = 11.28mm, thickness h = 4.37 mm, l1 = l2 = 5.64 mm. The relative permittivities are: ε1 = 6.13 (E-glass) and ε2 = 3.7 (silica)

The oblique incident wave is a transverse electric polarization (TE) wave, E = Eox, with incident angles φ = 90o

and θ = 5o. A unit cell is under investigation. PML absorbing elements are used to truncate the model in the zdirection.

Figure 1 Dielectric Grating

ε ε

θ

φ



/batch,list/nopr/prep7! define structure and numerical modelfrq=15.5e9 ! central frequencylamda=3.e8/frqtheta=5 ! incident theta anglephi=90 ! incident phi angleD=11.28e-3 ! grating periodh=4.37e-3 ! grating thickness_xd=D/4zpml=lamda/4 ! thickness of PML layerzprt=lamda/2 ! distance between port and PMLeps1=6.13 ! E-glass (relat. permit.)eps2=3.7 ! silica (relat. permit.)h_grt=lamda/(12*sqrt(eps1)) ! mesh size ! define element and materialset,1,120,1 ! normal elementet,2,120,1,,,1 ! PML elementet,3,200,7 ! temp. surface mesh

mp,murx,2,1. ! E-glassmp,perx,2,eps1mp,murx,1,1. ! silicamp,perx,1,eps2


mp,murx,3,1. ! airmp,perx,3,1.! generate volumes for numerical model*dim,_z,array,7*dim,_y,array,4_z(4)=0_z(3)=_z(4)-h_z(2)=_z(3)-lamda/4_z(1)=_z(2)-zpml_z(5)=_z(4)+zprt_z(6)=_z(5)+lamda/4_z(7)=_z(6)+zpml_y(1)=-D/2_y(2)=_y(1)+D/4_y(3)=_y(2)+D/2_y(4)=_y(3)+D/4*do,_i,1,6 *do,_j,1,3 block,-_xd,_xd,_y(_j),_y(_j+1),_z(_i),_z(_i+1) *enddo*enddovglue,allnumcmp,allalls! mesh master surfacestype,3esize,h_grtasel,s,loc,x,-_xdasel,a,loc,y,_y(1)asel,u,loc,z,_z(2),_z(6)amesh,all asel,s,loc,x,-_xdasel,a,loc,y,_y(1)asel,r,loc,z,_z(3),_z(4)amesh,all asel,s,loc,x,-_xdasel,a,loc,y,_y(1)asel,u,loc,z,_z(1),_z(2)asel,u,loc,z,_z(3),_z(4)asel,u,loc,z,_z(6),_z(7)amesh,allalls ! copy mesh to slave surfacesasel,s,loc,x,-_xdagen,2,all,,,2*_xdasel,s,loc,y,-D/2agen,2,all,,,0,Dallsnummrg,all! mesh the volumestype,1 mat,1esize,h_grtvsel,s,loc,z,_z(3),_z(4)vsel,u,loc,y,_y(2),_y(3)vmesh,all mat,2vsel,s,loc,z,_z(3),_z(4)vsel,r,loc,y,_y(2),_y(3)vmesh,all mat,3 esize,h_grtvsel,s,loc,z,_z(2),_z(3)vsel,a,loc,z,_z(4),_z(6)vmesh,all! PML meshestype,2 mat,3esize,h_grtvsel,s,loc,z,_z(1),_z(2)vsel,a,loc,z,_z(6),_z(7)vmesh,all


Harmonic Analysis for Scattering of a Dielectric Grating (Command Method)

alls! delete surface meshaclear,allalls! coupling master/slave nodesnsel,s,loc,x,-_xd nsel,a,loc,x,_xdcpcyc,ax,,,2*_xd,0,0,1nsel,s,loc,y,-D/2nsel,a,loc,y,D/2cpcyc,ax,,,0,D,0,1alls! define portsnsel,s,loc,z,_z(5)bf,all,port,1hfport,1,PLAN,,,SOFT,1.,0.,0.,phi,thetaalls! set up PEC nsel,s,loc,z,_z(1)nsel,a,loc,z,_z(7)d,all,ax,0.0 allsfini! perform the solution/soluspswp,12.5e9,17.5e9,0.25e9,1,,2,0fini! postprocessing/post1/yrange,0,1plsyz,file,s1p,s,mag,1,1fini

Target Results

The following figure depicts the magnitude of the reflection coefficient |S11| from 12.5 to 17.5 GHz.

Note — Reflectance is equal to the power reflection coefficient and the square of the reflection coefficient.



Figure 2 Reflection Coefficient of Dielectric Grating


Harmonic Analysis for Scattering of a Dielectric Grating (Command Method)

IndexAadaptive remeshing, 6–1analysis

high-frequency electromagnetic, 1–1antenna arrays, 4–12

Bboundary conditions

harmonic high-frequency analysis, 4–5perfect electric conductor, 4–6perfect magnetic conductor, 4–7perfectly matched layers, 4–9surface impedance, 4–7

CCutoff frequencies, 29, 101

Ddispersion characteristics, 5, 29, 101

Eelements

high-frequency, 3–1EMF command, 4–39example problems

high-frequency advanced analysis, 39high-frequency basic analysis, 5wave propagation, advanced, 73wave propagation, basic, 9wave radiation, advanced, 39wave radiation, basic, 5wave resonance, advanced, 127wave resonance, basic, 21wave scattering, advanced, 139wave scattering, basic, 33

Ffrequency selective surface, 4–39

HHF 118 element, 3–1HF119 element, 3–1HF120 element, 3–1HFANG command, 4–37HFEIGOPT command, 5–2HFEREFINE command, 3–1HFNEAR command, 4–34HFPORT command, 4–16

HFSCAT command, 4–29HFSYM command, 4–36high-frequency analysis, 1–1

advanced example problems, 39basic example problems, 5boundary conditions, 4–5circuit parameters, 4–38current source, 4–21electric field source, 4–24elements, 3–1excitation sources, 4–15field calculations, 4–34material properties, 4–3mesh refinement, 3–1modal analysis, 5–1physics environment, 4–2plane wave source, 4–23quality factor, 5–4S-parameters, 4–38scattering field analysis, 4–29surface magnetic field source, 4–23units, 4–3waveguide modal source, 4–16

IIMPD command, 4–39

Llumped circuits, 4–26

MMMF command, 4–39modal analysis, 5–1

Nnetwork parameter conversion, 4–41

Pperfect electric conductor, 4–6perfect magnetic conductor, 4–7perfectly matched layers, 4–9

attenuation factors, 4–9normal reflection coefficients, 4–9

periodic arrays, 4–12periodic boundary conditions, 4–12permittivity, 4–3physics environment

high-frequency electromagnetic analysis, 4–2plane wave source port, 4–16PLHFFAR command, 4–35PLSP command, 4–38PLWAVE command, 4–23


postprocessing, 4–33power parameters, 4–39PRHFFAR command, 4–35Propagating constants, 5, 29, 101

QQFACT command, 5–4

Rrelative permittivity, 4–3

Sscattering field analysis, 4–29Smith chart, 4–41SPARM command, 4–38specific absorption rate, 4–32SPSWP command, 4–38surface impedance, 4–7

Ttransmission line port, 4–16

Uunits, 4–3

Wwave propagation

advanced examples, 73basic examples, 9

wave raditionadvanced examples, 39basic examples, 5

wave resonanceadvanced examples, 127basic examples, 21

wave scatteringadvanced examples, 139basic examples, 33

waveguide port, 4–16

ANSYS High-Frequency Electromagnetic Analysis Guide . ANSYS Release 9.0 . 002114 . © SAS IP, Inc.Index–2

Index

ansys high-frequency electromagnetic analysis guide

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