january 2010 empro 2009 - keysight

EMPro 2009 - EMPro FEM Simulation

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EMPro 2009January 2010


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Calculating S-Parameters in FEM Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Creating a Microstrip Line for FEM Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Creating Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Creating the Microstrip line Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Modeling the Microstrip Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Defining the Outer Boundary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Adding a Waveguide Feed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Setting up new FEM simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Defining Radiation Patterns and Antenna Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 About Radiation Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 About Antenna Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Viewing Results Automatically in Data Display . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Exporting Far-Field Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Displaying Radiation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Performing Multimode Analysis on Rectangular Waveguide . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Setting up Waveguide Geometry Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Setting up Waveguide Ports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Setting up Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Viewing Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Specifying FEM Simulation Setup in EMPro . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Specifying the Mesh Refinement Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Specifying Frequency Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Specifying the Solver Type Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Specifying the Parameter Sweep Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 Using the Notes Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

Troubleshooting Mesh Failures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Best practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

Understanding the Process of FEM Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 The Finite Element Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 Implementation Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 The Solution Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 The Mesher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 The 2D Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 The 3D Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Ports-only Solutions and Impedance Computations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

Using Ports in EMPro FEM Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 Component feeds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

Using the Advanced Visualization Feature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Starting the Advanced Visualizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Using the Advanced Visualizer on PC and Linux Machines . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

Using the Finite Element Method (FEM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 Major Features and Benefits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 FEM Simulator Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

Viewing and Analyzing Parameters in FEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Starting FEM Simulator Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 FEM Simulator Visualization on PC and Linux Machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

Viewing FEM Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Viewing the Default Output of FEM Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Creating a Line Graph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 Viewing S-parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Viewing Results Using FEM Simulator Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 S-parameter Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Viewing S-parameters in graphical format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86


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Plotting S-parameter Magnitude . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Plotting S-parameter Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 Plotting S-parameters on a Smith Chart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 Exporting S-parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 EMPro FEM-Specific Sensors and Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Viewing the Output in Advanced Visualizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89


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Calculating S-Parameters in FEMSimulationA generalized S-matrix describes what fraction of power associated with a given fieldexcitation is transmitted or reflected at each port.

The S-matrix for a three port structure is shown below:

where:

All quantities are complex numbers.The magnitudes of a and b are normalized to a field carrying one watt of power.|a i |

2 represents the excitation power at port i.

|b i | 2 represents the power of the transmitted or reflected field at port i.

The full field pattern at a port is the sum of the port's excitation field and allreflected/transmitted fields.The phase of a i and b i represent the phase of the incident and reflected/transmitted

field at t=0, Represents the phase angle of the excitation field on port i at t=0. (By default, it iszero.)

Represents the phase angle of the reflected or transmitted field with respect to theexcitation field.S ij is the S-parameter describing how much of the excitation field at port j is

reflected back or transmitted to port i.

For example, S 31 is used to compute the amount of power from the port 1 excitation field

that is transmitted to port 3. The phase of S 31 specifies the phase shift that occurs as the

field travels from port 1 to port 3.

NoteWhen the 2D solver computes the excitation field for a given port, it has no information indicating whichway is up or down. Therefore, if ports have not been calibrated, it is possible to obtain solutions in whichthe S-parameters are out of phase with the expected solution.

Frequency Points

The S-parameters associated with a structure are a function of frequency. Therefore,separate field solutions and S-matrices are generated for each frequency point of interest.FEM Simulator supports two types of frequency sweeps:

Discrete frequency sweeps, in which a solution is generated for the structure at each


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frequency point you specify.Fast frequency sweeps, in which asymptotic waveform evaluation is used toextrapolate solutions for a range of frequencies from a single solution at a centerfrequency.

Fast frequency sweeps are useful for analyzing the behavior of high Q structures. For widebands of information, they are much faster than solving the problem at individualfrequencies.

NoteWithin a fast frequency solution, there is a bandwidth where the solution results are most accurate. Thisrange is indicated by an error criterion using a matrix residue that measures the accuracy of the solution.For complex frequency spectra that have many peaks and valleys, a fast sweep may not be able toaccurately model the entire frequency range. In this case, additional fast sweeps with different expansionfrequencies will automatically be computed and combined into a single frequency response.

Renormalized S-Matrices

Before a structure's generalized S-matrix can be used in a high frequency circuit simulatorto compute the reflection and transmission of signals, the generalized S-matrix must benormalized to the appropriate impedance. For example, if a generalized S-matrix has beennormalized to 50 ohms, it can be used to compute reflection and transmission directlyfrom signals that are normalized to 50 ohms, as in:

where the input signals, Vi i , and output signals, Vo i , are both normalized to 50 ohms.

To renormalize a generalized S-matrix to a specific impedance, the system first calculatesa unique impedance matrix associated with the structure. This unique impedance matrix,Z, is defined as follows:

where:

S is the n x n generalized S-matrix.I is an n x n identity matrix.Z 0 is a diagonal matrix having the characteristic impedance (Z 0 ) of each port as a

diagonal value.

The renormalized S-matrix is then calculated from the unique impedance matrix using thisrelationship:

Where, Z is the structure's unique impedance matrix.


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and are diagonal matrices with the desired impedance and admittance as diagonal

values. For example, if the matrix is being renormalized to 50 ohms, then would havediagonal values of 50.

Visualize the generalized S-matrix as an S-matrix that has been renormalized to thecharacteristic impedances of the structure. Therefore, if a diagonal matrix containing the

characteristic impedances of the structure is used as in the above equation, the resultwould be the generalized S-matrix again.

Z- and Y-Matrices

Calculating and displaying the unique impedance and admittance matrices (Z and Y)associated with a structure is performed in the post processor.

Characteristic Impedances

FEM Simulator calculates the characteristic impedance of each port in order to compute arenormalized S-matrix, Z-matrix, or Y-matrix. The system computes the characteristicimpedance of each port in three ways-as Z pi , Z pv , and Z vi impedances.

You have the option of specifying which impedance is to be used in the renormalizationcalculations.

PI Impedance

The Z pi impedance is the impedance calculated from values of power (P) and current (I):

The power and current are computed directly from the simulated fields. The power passingthrough a port is equal to the following:

where the surface integral is over the surface of the port.

The current is computed by applying Ampere's Law to a path around the port:

While the net current computed in this way will be near zero, the current of interest is thatflowing into the structure, I- or that flowing out of the structure, I+ . In integrating aroundthe port, the system keeps a running total of the contributions to each and uses theaverage of the two in the computation of impedances.


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PV Impedance

The Z pv impedance is the impedance calculated from values of power (P) and voltage (V):

where the power and voltage are computed directly from the simulated fields. The poweris computed in the same way as for the Z pi impedance. The voltage is computed as

follows:

The path over which the system integrates is referred to as the impedance line, which isdefined when setting up the ports. To define the impedance line for a port, select the twopoints across which the maximum voltage difference occurs. FEM Simulator cannotdetermine where the maximum voltage difference will be unless you define an impedanceline.

VI Impedance

The Z vi impedance is given by:

For TEM waves, the Z pi and Z pv impedances form upper and lower boundaries to a port's

actual characteristic impedance. Therefore, the value of Z vi approaches a port's actual

impedance for TEM waves.

Choice of Impedance

When the system is instructed to renormalize the generalized S-matrix or compute aY- or Z-matrix, you must specify which value to use in the computations, Z pi , Z pv ,

or Z vi.

For TEM waves, the Z vi impedance converges on the port's actual impedance and

should be used.

When modeling microstrips, it is sometimes more appropriate to use the Z pi

impedance.


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For slot-type structures (such as finline or coplanar waveguides), Z pv impedance is

the most appropriate.

De-embedding

If a uniform length of transmission line is added to (or removed from) a port, the S-matrixof the modified structure can be calculated using the following relationship:

Where, is a diagonal matrix with the following entries:

γ = α + jβ is the complex propagation constant, where:

αi is the attenuation constant of the wave of port i.βi is the propagation constant associated with the uniform transmission line at port i.l i is the length of the uniform transmission line that has been added to or removedfrom the structure at port i. A positive value indicates that a length of transmissionline has been removed from the structure.

The value of γ for the dominant mode of each port is automatically calculated by the 2Dsolver.

EquationsThe sections below describe some of the equations that are solved in a simulation or usedto define elements of a structure.

Derivation of Wave Equation

The solution to the following wave equation is found during a simulation:

where:

E( x,y,z ) is a phasor representing an oscillating electric field

k is the free space wave number, .


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0ω is the angular frequency, 2πf.µr( x,y,z ) is the complex relative permeability.

εr( x,y,z ) is the complex relative permittivity.

The difference between the 2D and 3D solvers is that the 2D solver assumes that theelectric field is a traveling wave with this form:

while the 3D solver assumes that the phasor E is a function of x, y, and z:

Maxwell's Equations

The field equation solved during a simulation is derived from Maxwell's Equations, which intheir time-domain form are:

Where:

E (t) is the electric field intensity.

D (t) is the electric flux density, ε E (t), and ε is the complex permittivity.

H (t) is the magnetic field intensity.

B (t) is the magnetic flux density, µ H (t), and µ is the complex permeability.

J (t) is the current density, σ E (t).

ρ is the charge density.

Phasor Notation

Because all time-varying electromagnetic quantities are oscillating at the same frequency,they can be treated as phasors multiplied by ej ω t (in the 3D solver) or by ej ω t -γ z (inthe 2D solver).In the general case with the 3D solver, the equations become:


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By factoring out the quantity ej ω t and using the following relationships:

Maxwell's Equations in phasor form reduce to:

where B , H , E , and D are phasors in the frequency domain. Now, using the relationshipsB = µ H , D = ε E , and J = α E , Maxwell's Equations in phasor form become:

for σ = 0

Where:

H and E are phasors in the frequency domain, µ is the complex permeability, and ε isthe complex permittivity.

H and E are stored as phasors, can be visualized as a magnitude and phase or as acomplex quantity.


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Electric and Magnetic Fields Can Be Represented as Phasors

Assumptions

To generate the final field equation, place H in the equation in terms of E to obtain:

Then, substitute this expression for H in the equation to produce:

Conductivity

Although good conductors can be included in a model, the system does not solve for anyfields inside these materials. Because fields penetrate lossy conductors only to one skindepth (which is a very small distance in good conductors), the behavior of a field can berepresented with an equivalent impedance boundary.

For perfect conductors, the skin depth is zero and no fields exist inside the conductor.Perfect conductors are assumed to be surrounded with Perfect E boundaries.

Dielectric Loss Tangent

Dielectric losses can be modeled by assuming that the relative permittivity, , iscomplex:


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Expressed in terms of the dielectric (electric) loss tangent, , the complex

relative permittivity, becomes:

Magnetic Loss Tangent

Losses in magnetic materials can be modeled by assuming that µr is complex.

Expressed in terms of the magnetic loss tangent, , the complex relativepermeability becomes:

Definition of Freespace Phase Constant

Using the relationships and , the wave equation being solved can beplaced in this form:

Now, if the freespace phase constant (or wave number) is defined as, , theabove reduces to:

which is the equation that the 2D and 3D engines solve.


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Creating a Microstrip Line for FEMSimulationIn this project, you will learn how to:

Create a Microstrip Line geometryAssign a Waveguide portSetup an FEM simulation

Getting StartedOpen a new project and make FEM tab active on bottom left of GUI.

In the Project Properties Editor window, navigate to the Display Units tab:

Select SI Metric in the Unit Set drop-down list.1.Change Length to millimeters (mm). This changes the Unit Set value to Custom.2.Click Done.3.

Creating MaterialsRight-click Definitions:Materials branch of the project tree and select New Material1.Definition.Double-click the new material to edit its properties. Specify the following properties2.for the electric conductor material:

Name: AluminaElectric: Isotropic


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Magnetic: FreespaceRelative Permittivity = 9.9Conductivity = 0 S/mDepending on your requirements, you can also set the display color of the PECmaterial in the Appearance tab, as shown in the following figure.

Right-click Definitions:Materials branch of the project tree and select from the3.Default material library. Double-click Cu (copper). This material will be added inthe list.

Creating the Microstrip line GeometryYou will create the patch antenna geometry from of 2 simple components: a rectangularsubstrate and a Microstrip line. For this example, you will use the Geometry Toolsinterface to create a rectangular Extrusion and a pair of rectangular Sheet Bodies.Modeling the SubstrateFirst, you will create the rectangular substrate named Substrate. This object will stretchfrom (-7.5, -10, 0) to (7.5, 10, 2) and have a 2mm extrusion in the +Z direction.

Right-click the Parts branch of the Project Tree. Choose Create New>Extrude from1.the context menu.


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Name the substrate by typing Substrate in the Name text box in the upper-right2.corner of the window.Choose the Rectangle tool from the Shapes toolbar.3.

The Creation dialog box allows exact entry of coordinates. Press the Tab key in the4.geometry space to activate the Creation dialog window. Specify the position of firstpoint.

NoteIf the Creation dialog box does not appear, right-click in the geometry space to activate the window.

Press the Tab key to display the creation dialog for the second point. Enter (7.5 mm,5.10 mm) and click OK to complete the rectangle.

Navigate to the Extrude tab to extrude the rectangular region. Enter a distance of 26.mm.


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Click Done to finish the Substrate geometry.7.

Modeling the Microstrip LineThe Microstrip Line will be created with a Sheet Body object that rests on top of theSubstrate. This shape comprises of one rectangle. The line will stretch from (-7.5, -1, 2)to (7.5, 1, 2).

Right-click the Parts branch of the Project Tree. Choose Create New Sheet Body1.from the context menu.

Navigate to the Specify Orientation tab. Set the origin to (0, 0, 2 mm) to place the2.Sheet Body on top of the Substrate.

Navigate to the Edit Profile tab. Type Microstrip Line into the Name text box.3.To draw the Microstrip line, select the Rectangle tool. Use the Creation dialog box4.to enter the corners of the microstrip rectangle:o Endpoint 1: (-7.5 mm, -1 mm)o Endpoint 2: (7.5mm, 1 mm)

Meshing Priority

Ensure that the meshing priority of the Microstrip Line is greater than the Substrate for anaccurate calculation.Right-click the Microstrip in the Project Tree. Under Meshing Order, select Move to Topif it is an available option.


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Assigning Materials

Click and drag the PEC material object located in the project tree and drop it on top1.of the Microstrip Line objects in the Parts branch of the tree.Assign the Cu material to the Substrate object using the same procedure.2.

The following figure displays the project tree after material objects have been dropped ontheir respective parts.

The following image shows the Microstrip Line geometry with materials applied and colorsset for each.

Defining the Outer BoundaryDouble-click the Simulation Domain> Boundary Conditions branch of the project1.tree to open the Outer Boundary Editor.Set the outer boundary properties as follows:2.

Boundary: Absorbing for all boundaries except Lower Boundary Z, which shouldbe PEC

Click Done to apply the outer boundary settings.3.Double-click the Simulation Domain> FEM Bounding Box branch of the project4.tree to open the bounding box. Set the upper and lower limits as shown:


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Click Done to apply the FEM Bounding Box setting.5.

Adding a Waveguide FeedYou can now add a Waveguide Feed to the patch antenna geometry. It will consist of avoltage source and series 50Ω resistor connected between the base of the stub portion ofthe Microstrip Line and the ground plane.

NoteWaveguide Port with Modal power needs to be used for WG or Coaxial structures.

For TEM -type waveguides (e.g. microstrips), you need to use a feed circuit component definition.For TE/TM-type waveguies (e.g. hollow waveguides), you need to use a modal circuit componentdefinition.

Define a new circuit component definition from project tree Definition, as shown1.below:

The Circuit Component Definition Editor dialog box is displayed:2.


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Define Waveguide ports from Project Tree> Circuit Components/Ports as shown:3.

From the Waveguide Port Editor dialog box in location tab use to select4.edge of Substrate coinciding X=-7.5 mm plane as shown below:


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Under properties tab chose 50 ohm Voltage source in Waveguide Port Definition as5.shown below:

Under Impedance Line define Endpoint1 and Endpoint2 as shown below:6.


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Click OK.7.The impedance line will appear on the waveguide port as shown below:

Waveguide port so defined still show invalid symbol:

As per the message waveguide port should lie on the faces of the geometry. Toaccommodate this we need to change padding in x direction. Both lower and upperpadding in X direction should be 0mm in FEM bounding box as waveguide port lie onX plane as shown in figure:


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Click Done. This will make waveguide port valid.8.Similarly define another waveguide port at X=7.5 mm plane. Once both waveguideport is defined the waveguide ports on the structure look like as shown in followingfigure:

Setting up new FEM simulationClick the Simulation tab on right side of GUI. This opens the Simulation window, as1.shown in following figure.


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Click FEM Simulations following window for FEM simulation appears.2.Add following frequency plan:3.

Under Setup Mesh/Discretisation use following settings in basic and advance tabs:4.

Under Setup matrix solver choose Direct solver:5.

Click Create and Queue Simulation on FEM simulation window to start FEM6.simulation.


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Defining Radiation Patterns andAntenna CharacteristicsThis section describes how to calculate the radiation fields. It also provides generalinformation about the antenna characteristics that can be derived based on the radiationfields.

About Radiation PatternsOnce the currents on the circuit are known, the electromagnetic fields can be computed.The electric and magnetic fields contain terms that vary as 1/r, 1/r 2 etc. It can be shownthat the terms that vary as 1/r 2, 1/r3, ... are associated with the energy storage aroundthe circuit. They are called the reactive field or near-field components. The terms having a1/r dependence become dominant at large distances and represent the power radiated bythe circuit. Those are called the far-field components (Eff, Hff).

NoteIn the direction parallel to the substrate (theta = 90 degrees), parallel plate modes or surface wavemodes, that vary as 1/sqrt(r), may be present, too. Although they will dominate in this direction, andaccount for a part of the power emitted by the circuit, they are not considered to be part of the far-fields.

The radiated power is a function of the angular position and the radial distance from thecircuit. The variation of power density with angular position is determined by the type anddesign of the circuit. It can be graphically represented as a radiation pattern.

The far-fields can only be computed at those frequencies that were calculated during asimulation. The far-fields will be computed for a specific frequency and for a specificexcitation state. They will be computed in all directions (theta, phi) in the open half spaceabove and/or below the circuit. Besides the far-fields, derived radiation pattern quantitiessuch as gain, directivity, axial ratio, etc. are computed.

About Antenna CharacteristicsBased on the radiation fields, polarization and other antenna characteristics such as gain,directivity, and radiated power can be derived.

Polarization

The far-field can be decomposed in several ways. You can work with the basicdecomposition in (!emds-13-1-03.gif!, !emds-13-1-04.gif!). However, with linear polarized


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antennas, it is sometimes more convenient to decompose the far-fields into (Eco, Ecross)

which is a decomposition based on an antenna measurement set-up. For circular polarizedantennas, a decomposition into left and right hand polarized field components (Elhp, Erhp)

is most appropriate. Below you can find how the different components are related to eachother.

is the characteristic impedance of the open half sphere under consideration.

The fields can be normalized with respect to:

Circular Polarization

Below is shown how the left hand and right hand circular polarized field components arederived. From those, the circular polarization axial ratio (ARcp) can be calculated. The

axial ratio describes how well the antenna is circular polarized. If its amplitude equals one,the fields are perfectly circularly polarized. It becomes infinite when the fields are linearlypolarized.

Linear Polarization

Below, the equations to decompose the far-fields into a co and cross polarized field aregiven (!emds-13-1-14.gif! is the co polarization angle). From those, a "linear polarization


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axial ratio" (ARlp) can be derived. This value illustrates how well the antenna is linearly

polarized. It equals to one when perfect linear polarization is observed and becomesinfinite for a perfect circular polarized antenna.

Note Eco is defined as colinear and Ecross implies a component orthogonal to Eco. For a perfect linearpolarized antenna, Ecross is zero and the axial ratio AR=1. If Ecross = Eco you no longer have linearpolarization but circular polarization, resulting in AR = infinity.

Co-polarization angle

Radiation Intensity

The radiation intensity in a certain direction, in watts per sterad ian, is given by:

For a certain direction, the radiation intensity will be maximal and equals:


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Radiated Power

The total power radiated by the antenna, in Watts, is represented by:

Effective Angle

This parameter is the solid angle through which all power emanating from the antennawould flow if the maximum radiation intensity is constant for all angles over the beamarea. It is measured in steradians and is represented by:

Directivity

Directivity is dimensionless and is represented by:

The maximum directivity is given by:

Gain

The gain of the antenna is represented by:

where Pinj is the real power, in watts, injected into the circuit.

The maximum gain is given by:


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Efficiency

The efficiency is given by:

Effective Area

The effective area, in square meters, of the antenna circuit is given by:

Planar (Vertical) Cut

For the planar cut, the angle phi ( Cut Angle ), which is relative to the x-axis, is keptconstant. The angle theta, which is relative to the z-axis, is swept to create a planar cut.Theta is swept from 0 to 360 degrees. This produces a view that is perpendicular to thecircuit layout plane.

Planar (vertical) cut

NoteIn layout, there is a fixed coordinate system such that the monitor screen lies in the XYplane. The X-axisis horizontal, the Y-axis is vertical, and the Z-axis is normal to the screen. To choose which plane isprobed for a radiation pattern, the cut angle must be specified. For example, if the circuit is rotated by 90degrees, the cut angle must also be changed by 90 degrees if you wish to obtain the same radiationpattern from one orientation to the next.

Conical Cut

For a conical cut, the angle theta, which is relative to the z-axis, is kept constant. Phi,which is relative to the x-axis, is swept to create a conical cut. Phi is swept from 0 to 360degrees. This produces a view that is parallel to the circuit layout plane.

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Conical cut

Viewing Results Automatically in Data DisplayIf you choose to view results immediately after the far-field computation is complete,enable Open display when computation completed. When Data Display is used for viewingthe far-field data, a data display window containing default plot types of the data displaytemplate of your choice will be automatically opened when the computation is finished.The default template, called FarFields, bundles four groups of plots:

Linear Polarization with Eco, Ecross, ARlp.

Circular Polarization with Elhp, Erhp, ARcp.

Absolute Fields with .Power with Gain, Directivity, Radiation Intensity, Efficiency.

Exporting Far-Field DataIf 3D Visualization is selected in the Radiation Pattern dialog, the normalized electric f ar-field components for the complete hemisphere are saved in ASCII format in the file <project_dir>/ mom_dsn /<design_name>/ proj.fff. The data is saved in the followingformat:

#Frequency <f> GHz /* loop over <f> */

#Excitation # /* loop over */

#Begin cut /* loop over phi */

<theta> <phi_0> <real(E_theta)> <imag(E_theta)> <real(E_phi)> <imag(E_phi)>

/* loop over <theta> */

#End cut

#Begin cut

<theta> <phi_1> <real(E_theta)> <imag(E_theta)> <real(E_phi)> <imag(E_phi)>

\* loop over <theta> */

#End cut

:

:

#Begin cut

<theta> <phi_n> <real(E_thet\)> <imag\(E_theta\)> <real(E_phi)> <imag(E_phi)>

/* loop over <theta> */

#End cut

In the proj.fff file, E_theta and E_phi represent the theta and phi components,respectively, of the far-field values of the electric field. Note that the fields are described

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in the spherical co-ordinate system (r, theta, phi) and are normalized. The normalizationconstant for the fields can be derived from the values found in the proj.ant file andequals:

The proj.ant file, stored in the same directory, contains the antenna characteristics. Thedata is saved in the following format:

Excitation /* loop over */

Frequency <f> GHz /* loop over <f> */

Maximum radiation intensity /* in Watts/steradian */

Angle of U_max <theta> <phi> /* both in deg */

E_theta_max <mag(E_theta_max)> ; E_phi_max <mag(E_phi_max)>

E_theta_max <real(E_theta_max)> <imag(E_theta_ma\)>

E_phi_max <real(E_phi_max\)> <imag(E_phi_max)>

Ex_max <real(Ex_max)> <imag(Ex_max)>

Ey_max <real(Ey_max)> <imag(Ey_ma\)>

Ez_max <real(Ez_max)> <imag(Ez_max)>

Power radiated <excitation #i> <prad> /* in Watts */

Effective angle <eff_angle_st> steradians <eff_angle_deg> degrees

Directivity <dir> dB /* in dB */

Gain <gain> dB /* in dB */

The maximum electric field components (E_theta_max, E_phi_max, etc.) are those foundat the angular position where the radiation intensity is maximal. They are all in volts.

Displaying Radiation ResultsIn FEM Visualization, you can view the following radiation data:

Far-fields including E fields for different polarizations and axial ratio in 3D and 2DformatsAntenna parameters such as gain, directivity, and direction of main radiation intabular formatThis section describes how to view the data. In the FEM Simulator RF mode, radiationresults are not available for display.

Loading Radiation Results

In FEM Simulator, computing the radiation results is included as a post processing step.The Far Field menu item appears in the main menu bar only if radiation results areavailable. If a radiation results file is available, it is loaded automatically.

Note The command Set Port Solution Weights (in the Current menu) has no effect on the radiation results. Theexcitation state for the far-fields is specified in the radiation pattern dialog box before computation.

You can also read in far-field data from other projects. First, select the project containingthe far-field data that you want to view, then load the data:

Choose Projects > Select Project.1.Select the name of the Momentum or Agilent FEM project that you want to use.2.Click Select Momentum or Select Agilent FEM.3.


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Choose Projects > Read Field Solution.4.When the data is finished loading, it can be viewed in far-field plots and as antenna5.parameters.

Displaying Far-fields in 3D

The 3D far-field plot displays far-field results in 3D.

To display a 3D far-field plot:

Choose Far Field > Far Field Plot.1.Select the view in which you want to insert the plot.2.Select the E Field format:3.

E = sqrt(mag(E Theta)2 + mag(E Phi)2)E ThetaE PhiE LeftE RightCircular Axial RatioE CoE CrossLinear Axial Ratio

If you want the data normalized to a value of one, enable Normalize. For Circular and4.Linear Axial Ratio choices, set the Minimum dB. Also set the Polarization Angle for ECo, E Cross, and Linear Axial Ratio.By default, a linear scale is used to display the plot. If you want to use a logarithmic5.scale, enable Log Scale. Set the minimum magnitude that you want to display, in dB.Click OK.6.

Selecting Far-field Display Options

You can change the translucency of the far-field and set a constant phi angle:

Click Display Options.1.A white, dashed line appears lengthwise on the far-field. You can adjust the position2.of the line by setting the Constant Phi Value, in degrees, using the scroll bar.Adjust the translucency of the far-field by using the scroll bar under Translucency.3.Click Done.4.

Defining a 2D Cross Section of a Far-field

You can take a 2D cross section of the far-field and display it on a polar or rectangularplot. The cut type can be either planar (phi is fixed, theta is swept) or conical (theta isfixed, phi is swept). The figure below illustrates a planar cut (or phi cut) and a conical cut(or theta cut), and the resulting 2D cross section as it would appear on a polar plot.

The procedure that follows describes how to define the 2D cross section.


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To define a cross section of the 3D far-field:

Choose Far Field > Cut 3D Far Field.1.If you want a conical cut, choose Theta Cut. If you want a planar cut, choose Phi Cut.2.Set the angle of the conical cut using the Constant Theta Value scroll bar or set the3.angle of the planar cut using the Constant Phi Value scroll bar.Click Apply to accept the setting. The cross section is added to the Cut Plots list.4.Repeat these steps to define any other cross sections.5.Click Done to dismiss the dialog box6.

Displaying Far-fields in 2D

Once you have defined a 2D cross section of the 3D far-field plot, you can display thecross section on one of these plot types:

On a polar plotOn a rectangular plot, in magnitude versus angle

In the figure below, a cross section is displayed on a polar and rectangular plot.


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To display a 2D far-field plot:

Choose Far Field > Plot Far Field Cut.1.Select a 2D cross section from the 2D Far Field Plots list. The type of cut (phi or2.theta) and the angle identifies each cross section.Select the view that you want to use to display the plot.3.Select the E-field format.4.Select the plot type, either Cartesian or Polar.5.If you want the data normalized to a value of one, enable Normalize.6.By default, a linear scale is used to display the plot. If you want to use a logarithmic7.scale, enable Log Scale. If available, set the minimum magnitude that you want todisplay, in dB; also, set the polarization angle.Click OK.8.

Displaying Antenna Parameters

Choose Far Field > Antenna Parameters to view gain, directivity, radiated power,maximum E-field, and direction of maximum radiation. The data is based on the frequencyand excitation state as specified in the radiation pattern dialog. The parameters include:

Radiated power, in wattsEffective angle, in degreesDirectivity, in dBGain, in dBMaximum radiation intensity, in watts per steradianDirection of maximum radiation intensity, theta and phi, both in degreesE_theta, in magnitude and phase, in this directionE_phi, in magnitude and phase, in this directionE_x, in magnitude and phase, in this directionE_y, in magnitude and phase, in this directionE_z, in magnitude and phase, in this direction

NoteIn the antenna parameters, the magnitude of the E-fields is involts.


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Performing Multimode Analysis onRectangular WaveguideIn this section, you will learn how to create a multimode analysis on any structure inEMPro. To demonstrate the design flow we have used a square waveguide. Perform thefollowing steps to analyze a rectangular waveguide:

Set up Waveguide Geometry ModelSet up Waveguide PortsSet up SimulationView Results

Setting up Waveguide Geometry ModelYou can set up a waveguide geometry model by performing the following steps:

Select Create>Extrude to draw a square waveguide.1.Choose rectangle and specify the inner dimensions as ( -20 mm, -20 mm) and (202.mm,20 mm). Also, specify the outer dimensions as (-21mm, -21 mm) and (21mm,21mm).Extrude the waveguide to 50 mm length. This will draw a square waveguide of 403.mm x 40 mm cross section and length 50 mm.

NoteThis waveguide will support TE10 and TE01 mode at C band.

Specify the name the of the waveguide as Square Waveguide and assign the4.material Aluminum. The resulting waveguide appears as follows:


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Setting up Waveguide PortsYou can set up a waveguide port by performing the following steps:

Right-click Circuit Components/Ports> and select New Waveguide Port to a new1.waveguide port. This opens the EMPro Waveguide Port Editor, as shown in thefollowing figure:

Choose view Bottom( +z)to define the Waveguide port at Z equals to 0mm value.2.

From Waveguide Port Editor > Location, choose to select the face:


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Under the Edit cross section, remove the selection of Auto Extend to simulation3.domain boundaries. This will restrict waveguide port to waveguide cross sectiononly.Under Properties, choose Waveguide Port Definition and choose the number of4.modes equals to 2. Also, for Waveguide port definition choose 1 W Modal power feed,as shown in the following figure:

Under Impedance for Endpoint 1, choose center of the lower edge.5.


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For endpoint 2, choose center point of the upper edge.6.

This defines mode 1 for port 1. Similarly define mode 2 for port 1.


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If Waveguide port 1 still show invalid please change the padding as shown below:

While doing the FEM padding of waveguide structure, consider the following guidelines:

The +/- Z padding MUST be zero for a valid waveguide port definition. The padding inthe orthogonal direction of waveguide plane should be 0 mm. In this case, the Z axisis orthogonal to waveguide planes. After placing these paddings, the waveguide portwill become valid.The +/- X and Y padding COULD be set to zero for a more efficient simulation ChooseTop(-z) view to define second waveguide port at z=50 mm. Repeat the same stepsas defined above to create second waveguide port and two modes.

A Waveguide with waveguide ports having two excited modes appears as follows:


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Setting up SimulationSelect simulation and New FEM simulation. Define the frequency plan as shown1.below:

Choose following Mesh/Convergence properties.2.

Choose direct solver and press Create and Queue simulation.3.


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Viewing Results

Viewing S Parameter

For waveguide port 1, port 1 and port 2 are defined for 2 modes. And for waveguide port2, port3 and port4 are defined for 2 modes. So port 1 of waveguide port 1 will couple toport 3 of waveguide port2 since they are for same mode. Similar coupling will take placefor port 2 and port 4. The S13 and S24 plot is:

Cross mode coupling S14 and S23 is shown below:

The set of equations solved by FEM become ill-conditioned at waveguide mode cut-offfrequencies. This leads to the spike in S14 and S23 seen around 3.75 GHz

Viewing Propagation Constant

TE10 and TE01 mode is degenerate mode in square waveguide. For degenerate mode’s


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the propagation constant is same as shown in plot below:

Viewing Field

Viewing field for different modes. From Result window> Choose project and then AdvanceVisualization. In advance visualization choose solution setup and select one of thefrequency in pass band. For following plots frequency of 6.9 GHz is selected. Also choosePort 1 mode 1 to see TE10 mode in the waveguide.In Plot properties, choose Z=0 in field plot planes. Choose Shaded plot and log scale. Theplot will appear as

Select animate to see the progress of the field with phase. Remove the selection fromShaded plot and select Arrow plot. This is TE01 mode, as shown below:


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Go to Solution setup and select Port 1 mode2. Choose shaded plot in solution setup.

Uncheck shaded plot and check arrow plot. This is TE01 mode:

Add a plane by choosing Add in field plot planes to see the field along the length of thewaveguide section.

Move this plane on the centre of the waveguide by using edit option. Choose Shade plot tosee fields on this plane.


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Similarly arrow plot on the plane is shown below:


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Specifying FEM Simulation Setup inEMProYou can specify the simulation options that are specific to the FEM Simulator in theCreate FEM Simulation dialog box. This dialog box enables you to control how the FEMsimulation mesh is generated. In the Simulations workspace window, click New FEMSimulation.

Specifying the Mesh Refinement SettingsAn FEM simulation mesh is a sub-division of the entire 3D problem domain into a set oftetrahera (or cells). This pattern of cells is based on the geometry of a circuit andoptionally, user-defined parameters, so each circuit will have a unique mesh calculated forit. The mesh is then applied to the circuit in order to compute the electric within each celland identify any coupling effects in the circuit during simulation. From these calculations,S-parameters are then calculated for the circuit.The FEM Simulator implements an adaptive mesh algorithm, where an initial mesh isgenerated and the electric fields (and S-parameters) are computed on that initial mesh fora single frequency. An error estimate is generated for each tetrahedron. The tetrahedrawith the largest estimated error are refined to create a new mesh on which the electricfields (and S-parameters) are computed. The S-parameters from consecutive meshes arecompared. If the S-parameters do not change significantly, then electric fields (and S-parameters) are computed for all the requested frequencies. If the S-parameters dochange significantly, then new error estimates are computed, a new mesh is generatedand new electric fields (and S-parameters) are computed.

Click Setup Mesh/Discretisation- (Delta Error: 0.01). This displays the SetupMesh/Discretisation- (Delta Error: 0.01) screen, which consists of two tabs: Basic andAdvanced.

Specifying Basic tab settings


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Option Description

Delta Error Global Delta S-parameter sets a value that is applied to all S-parameters in the solution.Enter a value in the Delta Error field. This is the allowable change in the magnitude of thevector difference for all S-parameters for at least two consecutive refinement passes.

Minimumnumber ofadaptive passes

Enter the number of consecutive passes that must meet or exceed the delta error. If youhave concerns about convergence, you can increase this value, otherwise, use the defaultvalue of 1.

Maximumnumber ofadaptive passes

Enter the maximum number of passes to be attempted. If the number of refinement passesentered is reached before the delta error criteria is met, the refinement process will end,based upon this limit. The number of passes from all prior simulations is also displayed.Typically, a value between 10 and 20 is recommended.

Refine atspecificfrequency

Select this option to enable the The mesh will be refined at text box. By default, the meshrefinement is performed at the highest frequency specified in the simulation. To change thefrequency at which the mesh refinement is performed, enable `Refine at SpecifiedFrequency' and enter a value in `The mesh will be refined at' field, in GHz.

The mesh willbe refined at

Enable `Refine at Specified Frequency' and enter a value in `The mesh will be refined at'field, in GHz.

Specifying Advanced tab Settings

Option Description

Consecutive passes ofdelta error required

Specify the required consecutive passes of delta error.

Maximum RefinementPoints (400 to 30000)

Max Refinement Points enables you to specify the maximum number of points addedat each mesh refinement iteration. You can set this limit between 400 and 30,000. Thelocations of the refinement points are determined by FEM Simulator.

Merge objects withsame material

Select this checkbox to merge objects with same material.

Specifying Frequency PlansUsing the Create FEM Simulation dialog box, you can specify the frequency settings foryour FEM simulation.


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In the Frequencies Plans screen, Specify the options listed in the following table:

Option Description

Sweep type Specify the type of sweep: Adaptive,Logarithmic, Linear, and Single.

Start Frequency Specify the start frequency value in GHz

Stop Frequency Specify the stop frequency value in GHz

Sample Points Limit Specify the value of sample points limit.

Add To List Adds the specified values to the box present on the screen.

Update Updates the values in the box present on the screen.

Delete Deletes the values specified in the box.

Specifying the Solver Type SettingsUsing the Create FEM Simulation dialog box, you can specify the solver type settings. ClickSetup Matrix Solver- (Direct) to display the Setup Matrix Solver- (Direct) screen, asshown in the following figure:


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You can select the following solver types to be used by FEM during a simulation.

Direct: When selecting Direct, the FEM Simulator will choose the direct densematrix solver to be used in the simulation. This implies that the matrix is stored in adense matrix format (requiring order N2 memory) and solved using a direct matrixfactorization technique (requiring order N3 computer time). The direct dense matrixsolver guarantees to always provide a solution using a predetermined number ofoperations. The main disadvantage is that the computer time it requires scales qubicwith the matrix size N, yielding larger simulation times for large problem sizes.

Iterative: When selecting Iterative, FEM Simulator will choose the iterative densematrix solver to be used in the simulation. This implies that the matrix is stored in adense matrix format (requiring order N2 memory) and solved using aniterative matrix solve technology (requiring order N2 computer time). The computertime scales quadratic with the matrix size N, yielding faster simulation times for largeproblem sizes when compared to the direct dense matrix solver. The maindisadvantage is that the iterative solver does not guarantee to converge fast. Theiterative solver will monitor its convergence rate and will automatically switch to theDirect matrix solver when it observes that the convergence stagnates or theconvergence rate is too slow. This is the default matrix solver selection option.

NoteAuto-select is not available at this time.

Specifying the Parameter Sweep ValuesClick Setup Parameter Sweep- (Off) to display the Setup Parameter Sweep- (Off)screen, as shown in the following figure:


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Select the Perform parameter Sweep to enable the options available on the screen:

Option Description

Parameter tosweep

Specify the required parameter

Values Specify the value

Sweep type Select the required sweep type

Starting value Specify the start value for the parameter

Ending Value Specify the end value for the parameter

Using the Notes SectionIf you want to add any notes or observation with your simulation, you can specify it in theNotes text box. Click Notes in the Create FEM Simulation dialog box to display theNotes screen, as shown in the following figure:


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After you have completed entering your FEM Simulation options, click the Done button toapply the current settings in the Create FEM Simulation dialog box, or click CreateSimulation Only to accept the settings. You can also click Create and QueueSimulation, alternatively, you can click the Cancel button to abort the changes anddismiss the dialog box.


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Troubleshooting Mesh FailuresIf the mesh generation fails in the surface meshing a list of failed faces assembled in anSAT file will be generated in the design directory. The exact location of this file will beshown in the output window of the simulation.

Best practicesSimplify the design by removing unnecessary (for the EM-modeling) detail. Variousgeometry modification tools are available within the EMPro GUI to achieve this.Avoid shelled objects where the thickness of the shell is much smaller than the totaldimensions of the object. In this case, replace the thick shell with a thin sheet.Visually inspect the design for small gaps between two 3D objects. Considerremoving the gaps by moving one of the objects to create overlap between objects.Avoid using complex Boolean subtractions: use the mesh priority to set the correctobject precedence for meshing. For example, a metal object sticking through adielectric object will be meshed as such if the priority of the metal object is set to ahigher value than the dielectric object.

To isolate specific objects that are causing mesh failures, you can selectively include orexclude objects from a simulation by using the Include In Mesh option in the contextmenu of objects.


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Understanding the Process of FEMSimulationThe simulation technique used to calculate the full three-dimensional electromagnetic fieldinside a structure is based on the finite element method. This section provides anoverview of the FEM simulation process, its implementation in EMPro, and a description ofhow S-parameters are computed from the simulated electric and magnetic fields.

The Finite Element MethodThe finite element method divides the full problem space into many smaller regions(elements) and represents the field in each element by a local function. The FEMimplementation in EMPro uses tetrahedral elements.

Representation of a Field Quantity

The value of a vector field quantity (such as the H-field or the E-field) at points insideeach tetrahedron is interpolated from the vertices of the tetrahedron. At each vertex, FEMSimulator stores the components of the field that are tangential to the three edges of thetetrahedron. In addition, the component of the vector field at the midpoint of selectededges that is tangential to a face and normal to the edge can also be stored. The fieldinside each tetrahedron is interpolated from these nodal values.

Field Quantities are Interpolated from Nodal Values

The components of a field that are tangential to the edges of an element are explicitlystored at the vertices.The component of a field that is tangential to the face of an element and normal to anedge is explicitly stored at the midpoint of the selected edges.

The value of a vector field at an interior point is interpolated from the nodal values.By representing field quantities in this way, Maxwell's equations can be transformed intomatrix equations that are solved using traditional numerical methods.

Basis Functions


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A first-order tangential element basis function interpolates field values from both nodalvalues at vertices and on edges. First-order tangential elements have 20 unknowns pertetrahedra.

Size of Mesh Versus Accuracy

There is a trade-off between the size of the mesh, the desired level of accuracy, and theamount of available computing resources.

On one hand, the accuracy of the solution depends on how small each of the individualelements (tetrahedra) are. Solutions based on meshes that use a large number ofelements are more accurate than solutions based on coarse meshes using relatively fewelements. To generate a precise description of a field quantity, each tetrahedron mustoccupy a region that is small enough for the field to be adequately interpolated from thenodal values.

On the other hand, generating a field solution for meshes with a large number of elementsrequires a significant amount of computing power and memory. Therefore, it is desirableto use a mesh that is fine enough to obtain an accurate field solution but not so fine that itoverwhelms the available computer memory and processing power.

To produce the optimal mesh, FEM Simulator uses an iterative process in which the meshis automatically refined in critical regions. First, it generates a solution based on a coarseinitial mesh. Then, it refines the mesh based on suitable error criteria and generates anew solution. When selected S-parameters converge to within a desired limit, the iterationprocess ends.

Field Solutions

During the iterative solution process, the S-parameters typically stabilize before the fullfield solution. Therefore, when you are interested in analyzing the field solution associatedwith a structure, it may be desirable to use convergence criteria that is tighter than usual.

In addition, for any given number of adaptive iterations, the magnetic field (H-field) is lessaccurate than the solution for the electric field (E-field) because the H-field is computedfrom the E-field using the following relationship:

thus making the polynomial interpolation function an order lower than those used for theelectric field.

Implementation OverviewTo calculate the S-matrix associated with a structure, the following steps are performed:

The structure is divided into a finite element mesh.1.The waves on each port of the structure that are supported by a transmission line2.having the same cross section as the port are computed.The full electromagnetic field pattern inside the structure is computed, assuming that3.


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each of the ports is excited by one of the waves.The generalized S-matrix is computed from the amount of reflection and transmission4.that occurs.

The final result is an S-matrix that allows the magnitude of transmitted and reflectedsignals to be computed directly from a given set of input signals, reducing the full three-dimensional electromagnetic behavior of a structure to a set of high frequency circuitvalues.

The Solution ProcessThere are three variations to the solution process:

Adaptive solutionNon-adaptive discrete frequency sweepNon-adaptive fast frequency sweep

Adaptive Solution

An adaptive solution is one in which a finite element mesh is created and automaticallyrefined to increase the accuracy of succeeding adaptive solutions. The adaptive solution isperformed at a single frequency. (Often, this is the first step in generating a non-adaptivefrequency sweep or a fast frequency sweep).

Non-adaptive Discrete Frequency Sweep

To perform this type of solution, an existing mesh is used to generate a solution over arange of frequencies. You specify the starting and ending frequency, and the interval atwhich new solutions are generated. The same mesh is used for each solution, regardlessof the frequency.

Non-adaptive Fast Frequency Sweep

This type of solution is similar to a discrete frequency sweep, except that a single fieldsolution is performed at a specified center frequency. From this initial solution, the systememployes asymptotic waveform evaluation (AWE) to extrapolate an entire bandwidth ofsolution information. While solutions can be computed and viewed at any frequency, thesolution at the center frequency is the most accurate.

The MesherA mesh is the basis from which a simulation begins. Initially, the structure's geometry isdivided into a number of relatively coarse tetrahedra, with each tetrahedron having fourtriangular faces. The mesher uses the vertices of objects as the initial set of tetrahedra


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vertices. Other points are added to serve as the vertices of tetrahedra only as needed tocreate a robust mesh. Adding points is referred to as seeding the mesh.

After the initial field solution has been created, if adaptive refinement is enabled, themesh is refined further.

2D Mesh Refinement

For 2D objects or ports, the mesher treats its computation of the excitation field patternas a two-dimensional finite element problem. The mesh associated with each port issimply the 2D mesh of triangles corresponding to the face of tetrahedra that lie on theport surface.

The mesher performs an iterative refinement of this 2D mesh as follows:

Using the triangular mesh formed by the tetrahedra faces of the initial mesh,1.solutions for the electric field, E, are calculated.The 2D solution is verified for accuracy.2.If the computed error falls within a pre-specified tolerance, the solution is accepted.3.Otherwise, the 2D mesh on the port face is refined and another iteration isperformed.Any mesh points that have been added to the face of a port are incorporated into thefull 3D mesh.

The 2D SolverBefore the full three-dimensional electromagnetic field inside a structure can becalculated, it is necessary to determine the excitation field pattern at each port. The 2Dsolver calculates the natural field patterns (or modes) that can exist inside a transmissionstructure with the same cross section as the port. The resulting 2D field patterns serve asboundary conditions for the full three-dimensional problem.

Excitation Fields

The assumption is that each port is connected to a uniform waveguide that has the samecross section as the port. The port interface is assumed to lie on the z=0 plane. Therefore,the excitation field is the field associated with traveling waves propagating along thewaveguide to which the port is connected:

Where:

Re is the real part of a complex number or function.E(x,y) is a phasor field quantity.

j is the imaginary unit, ω is angular frequency, 2πf.γ=α + j β is the complex propagation constant, α is the attenuation constant of the


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wave.β is the propagation constant associated with the wave that determines, at a giventime t , how the phase angle varies with z.

In this context, the x and y axes are assumed to lie in the cross section of the port; the zaxis lies along the direction of propagation.

Wave Equation

The field pattern of a traveling wave inside a waveguide can be determined by solvingMaxwell's equations. The following equation that is solved by the 2D solver is deriveddirectly from Maxwell's equation.

where:

E(x,y) is a phasor representing an oscillating electric field.

k 0 is the free space wave number, .

ω is the angular frequency, 2πf.µr( x, y ) is the complex relative permeability.

εr( x, y ) is the complex relative permittivity.

To solve this equation, the 2D solver obtains an excitation field pattern in the form of aphasor solution, E(x,y). These phasor solutions are independent of z and t ; only afterbeing multiplied by e-γz do they become traveling waves.

Also, note that the excitation field pattern computed is valid only at a single frequency. Adifferent excitation field pattern is computed for each frequency point of interest.

ModesFor a waveguide or transmission line with a given cross section, there is a series of basicfield patterns (modes) that satisfy Maxwell's equations at a specific frequency. Any linearcombination of these modes can exist in the waveguide.

Modes, Reflections, and Propagation

It is also possible for a 3D field solution generated by an excitation signal of one specificmode to contain reflections of higher-order modes which arise due to discontinuities in ahigh frequency structure. If these higher-order modes are reflected back to the excitationport or transmitted onto another port, the S-parameters associated with these modesshould be calculated.

If the higher-order mode decays before reaching any port-either because of attenuation


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due to losses or because it is a non-propagating evanescent mode-there is no need toobtain the S-parameters for that mode. Therefore, one way to avoid the need forcomputing the S-parameters for a higher-order mode is to include a length of waveguidein the geometric model that is long enough for the higher-order mode to decay.

For example, if the mode 2 wave associated with a certain port decays to near zero in 0.5mm, then the "constant cross section" portion of the geometric model leading up to theport should be at least 0.5 mm long. Otherwise, for accurate S-parameters, the mode 2 S-parameters must be included in the S-matrix.

The length of the constant cross section segment to be included in the model depends onthe value of the mode's attenuation constant, α.

Modes and Frequency

The field patterns associated with each mode generally vary with frequency. However, thepropagation constants and impedances always vary with frequency. Therefore, when afrequency sweep has been requested, a solution is calculated for each frequency point ofinterest.

When performing frequency sweeps, be aware that as the frequency increases, thelikelihood of higher-order modes propagating also increases.

Modes and Multiple Ports on a Face

Visualize a port face on a microstrip that contains two conducting strips side by side astwo separate ports. If the two ports are defined as being separate, they are treated as twoports are connected to uncoupled transmission structures. It is as if a conductive wallseparates the excitation waves.

However, in actuality, there will be electromagnetic coupling between the two strips. Theaccurate way to model this coupling is to analyze the two ports as a single port withmultiple modes.

The 3D SolverTo calculate the full 3D field solution, the following wave equation is solved:

where:

E(x,y,z) is a complex vector representing an oscillating electric field.mr( x, y ) is the complex relative permeability.

k 0 is the free space phase constant, ,

ω is the angular frequency, 2πf.


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εr( x, y ) is the complex relative permittivity.

This is the same equation that the 2D solver solves for in calculating the 2D field patternat each port. The difference is that the 3D solver does not assume that the electric field isa traveling wave propagating in a single direction. It assumes that the vector E is afunction of x, y, and z. The physical electric field, E(x,y,z,t) , is the real part of the productof the phasor, E(x,y,z) , and εj ω t :

Boundary Conditions

FEM Simulator imposes boundary conditions at all surfaces exposed to the edge of themeshed problem region. This includes all outer surfaces and all surfaces exposed to voidsand surface discontinuities within the structure.The following types of boundary conditions are recognized by the 3D solver:

PortPerfect HSymmetric HPerfect ESymmetric EGround planeConductorResistorRadiationRestore

Port Boundaries

The 2D field solutions generated by the 2D solver for each port serve as boundaryconditions at those ports. The final field solution that is computed for the structure mustmatch the 2D field pattern at each port.

FEM Simulator solves several problems in parallel. Consider the case of analyzing modes 1and 2 in a two-port device. To compute how much of a mode 1 excitation at port 1 istransmitted as a mode 2 wave at port 2, the 3D mesher uses the following as boundaryconditions:

A "mode 1" field pattern at port 1.A "mode 2" field pattern at port 2.

To compute the full set of S-parameters, solutions involving other boundary conditionsmust also be solved. Because the S-matrix is symmetric for reciprocal structures (that is,S 12 is the same as S 21 ), only half of the S-parameters need to be explicitly computed.

Perfect H Boundaries


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A Perfect H boundary forces the magnetic field (H-field) to have a normal component only.A symmetric H boundary can be used to model a plane of symmetry for a mode in whichthe H-field is normal to the symmetry plane.

Perfect E Boundaries

By default, the electric field is assumed to be normal to all surfaces exposed to thebackground, representing the case in which the entire structure is surrounded by perfectlyconducting walls. This is referred to as a Perfect E boundary. The final field solution mustmatch the case in which the tangential component of the electric field goes to zero atPerfect E boundaries.

It is also possible to assign Perfect E boundaries to surfaces within a structure. UsingPerfect E boundaries in this way enables users to model perfectly conducting surfaces. Thesurfaces of all objects that have been defined to be perfectly conducting materials areautomatically assigned to be Perfect E boundaries.

Conductor Boundaries

Conductor boundaries can be assigned to surfaces of imperfect conductors or resistiveloads such as thick film resistors. At such boundaries, the following condition holds:

where:

is the unit vector that is normal to the surface.E tan is the component of the E-field that is tangential to the surface.H is the H-field.Z s is the surface impedance of the boundary. (1+ j )/(δσ).

δ is the skin depth, , of the conductor being modeled.ω is the frequency of the excitation wave.σ is the conductivity of the conductor.

The fact that the E-field has a tangential component at the surface of imperfectconductors simulates the case in which the surface is lossy. The amount of loss will beproportional to the component of that flows into the surface.

The field inside these objects is not computed; the conductor boundary approximates thebehavior of the field at the surfaces of the objects.

Resistor Boundaries

Resistor boundaries model surfaces that represent resistive loads such as thin films onconductors. The following condition holds at resistor boundaries:


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where:

E tan is the component of the E-field that is tangential to the surface.H is the H-field.R is the resistance at the boundary in ohms per square meter.

Radiation Boundaries

Radiation boundaries model surfaces that represent open space. Energy is allowed toradiate from these boundaries instead of being contained within them. At these surfaces,the second order radiation boundary condition is employed:

where:

E tan is the component of the E-field that is tangential to the surface.

is the unit vector normal to the radiation surface.

k 0 is the free space phase constant, .

j is equal to .

To ensure accurate results, radiation boundaries should be applied at least one quarter ofa wavelength away from the source of the signal. However, they do not have to bespherical. The only restriction regarding their shape is that they be convex with regard tothe radiation source.

Computing Radiated Fields

Electromagnetic Design System maps the E-field computed by the 3D solver on theradiation surfaces to plane registers and then calculates the radiated E-field using thefollowing equation:

where:

s represents the radiation surfaces.

j is the imaginary unit, .ω is the angular frequency, 2πf.µ0 is the relative permeability of the free space.


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H tan is the component of the magnetic field that is tangential to the surface.H normal is the component of the magnetic field that is normal to the surface.E tan is the component of the electric field that is tangential to the surface.G is the free space Green's Function, given by:

where:

k 0 is the free space wave number, .

r and represent, respectively.

Implementing Green's Function When Computing Radiated Fields

Displaying Field Solutions

The 3D solver is also used to manipulate field quantities for display. The system enablesyou to display or manipulate the field associated with any excitation wave at any port-forexample, the field inside the structure due to a discrete mode 2 excitation wave at port 3.Waves excited on different modes can also be superimposed, even if they have differentmagnitudes and phases-for example, the waves excited on mode 1 at port 1 and mode 2at port 2. In addition, far-field radiation in structures with radiation boundaries can bedisplayed.

The available fields depend on the type of solution that was performed:

For adaptive solutions, the fields associated with the solution frequency are available.For frequency sweeps, the fields at each solved frequency point are available.For fast frequency sweeps, the fields associated with the center frequency point areinitially available.

Ports-only Solutions and Impedance ComputationsThis section addresses how impedances are computed for multi-conductor transmissionline ports. Some examples of such structures are:


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Two coupled microstrip linesCoplanar waveguide modeled with 3 separate stripsShielded twin-wire leads

For structures with one or two conductors, you will need to define a single line segment,called an "impedance line", for each mode. Some examples of such structures include:

microstrip transmission line (two-conductor structure)grounded CPW (two-conductor structure) where the CPW ground fins are alsoattached to the OUTER ground

For these structures, the port solver will compute the voltage V along the impedance linewhich is used to calculate Z pv = V 2 /(2*Power). The power is always normalized to 1

Watt.

If one models N-conductor structures where N>2, then FEM Simulator uses a differentalgorithm for computing Z pv and Z pi . The user must define an impedance line for each

interior conductor. The impedance lines should go from the center of each interiorconductor to the outer conductor.

The port solver computes a voltage along the first N line segments for each of the first Nmodes when the port solver detects that there are N+1 conductors. This becomes a

"voltage vector" (of length N) for each of the N quasi-TEM modes. Then, when computing Z pv , the square

of the scalar voltage is now replaced by the dot product of the voltage vectors, forexample:

For a more detailed explanation as to why this is done, refer to reference \1\ at the end ofthis section.For Z pi , the current is generally computed by adding the currents flowing into and out of

the port and taking the average of the two. (If the simulator computed currents to perfectaccuracy, the inward and outward currents would be identical.) For all mode numbers >=N, where N = number of conductors, the currents are calculated in this way.For the first (N-1) quasi-TEM modes, the currents are computed on the N-1 interiorconductors producing a current eigenvector. Then the impedance:

The result is that the FEM Simulator impedance computations for such structures ascoupled microstrip lines match the published equations for even- and odd-modeimpedances.

As an example, take a CPW modeled as three interior strips surrounded by an enclosure.The ground strips do not touch the enclosure. Such a model is in the examples directory ofFEM Simulator and is called cpwtaper . The port solver shows us that the desired CPWmode is not the dominant mode, but is actually mode 3. To identify the modes, one canuse the arrow plots in the Port Calibration menu or the Arrow display of the E-field in thepost processor.


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Each port consists of a 4 conductor system, the outer (ground) conductor, the inner strip,and the two "ground" strips. This results in 3 quasi-TEM modes. Mode 1 has E-field linespredominately in the substrate, all pointing in the same direction. This is the commonmode (+V, +V, +V). Mode 2 also has E-field lines predominately in the substrate, but inopposite directions under the two "ground" strips. This is the slot mode (-V, 0, +V). Mode3 has nearly zero E-fields everywhere because the fields are predominately between theinner strip and the "ground" strips. This is the CPW mode (0, +V, 0).

For further help in identifying modes in such a structure, one can look at the distributionswith the "full" scale. One will notice that modes 1 and 3 obviously have the same "even"symmetry in the E fields, while mode 2 has an odd symmetry. The CPW mode has an"even" symmetry, so it has to be mode 1 or 3.

Modes 1 and 2 have significant E-field strengths in the substrate, especially under the"ground" strips. So, there is a potential difference between the "ground" strips and theouter ground for these two modes. However, for mode 3, the "ground" strips are at thesame potential as the outer ground, which is consistent with the CPW mode.

Thus one can identify the modes. For mode 3, the "ground" strips are at 0 volts withrespect to the outer ground, and the signal line has +V. The Z pv impedance computed for

this mode using a dot product of the voltage vector for mode 3 gives the same Z pv as by

computing the simple voltage between center strip and either "ground" strip. That is

because the voltage vector for mode 3 along the three impedance lines is =[0,V,0] and

However, the impedances for the other modes now match accepted impedance definitionsfound in the literature for multi-conductor transmission lines.

G.G. Gentili and M. Salazar-Palma, "The definition and computation of modal1.characteristic impedance in quasi-TEM coupled transmission lines," IEEE Trans.Microwave Theory Tech., Feb. 1995, pp. 338-343.


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Using Ports in EMPro FEM Simulation Component feedsEMPro 2009 supports the Component Feed port in the FEM simulation setup. TheComponent Feed ports are direct point feeds having a negative and positive connectionpoint to the metallization the design. Refer to the Defining Circuit Components andExcitations section for more information about Component feeds.

Note that for FEM simulations only the following component feed definition is allowed,which specifies the voltage sources with a termination impedance:


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Using the Advanced VisualizationFeatureThe Advanced Visualization feature enables you to view and analyze the following typesof simulation data:

E FieldsFar-fieldsAntenna parametersTransmission line data

Data can be analyzed in a variety of 3D plot formats. This section gives an overview onhow to use the Advanced Visualization feature. Viewing FEM Simulation Results (fem)describes in detail how to use FEM Simulator Visualization for viewing specific types ofdata, such as S-parameters or currents.

Starting the Advanced VisualizerYou can invoke the Advanced Visualization feature by clicking the AdvancedVisualization button in the Results window. The following figure highlights this button.The current project must run through a complete simulation use Visualization to viewdata. If simulation has been previously completed for a project, you can start thevisualizer directly to view the existing data.

Using the Advanced Visualizer on PC and LinuxMachinesOn the PC and Linux platforms, FEM Simulator Visualization is based on the AdvancedVisualizer. The following figure highlights the basic window which comes up whenAdvanced Visualizer is invoked.


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Upon startup, the following window appears having:

All the object shading removed.Two additional tabs for controlling the view are added to the window.

The left side of the Advanced Visualizer contains the basic controls for the view in thedocking widget.

Types of Plots

The Advanced Visualization supports three basic types of plots:

Shaded Plot - This plot displays the E Field on the selected planar surfaces.Arrow Plot - This plot displays a vector representation of the E Field on the selectedplanes.Mesh Plot - This plot displays the FEM Simulator Mesh which is used to computethe field.

Only one current plot and one arrow plot can be displayed. The arrow and current plot willalways correspond to the selected excitation. Once an excitation is changed, the plot willautomatically update using the new excitation values at the current phase.

The Solution Configuration Tab


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The solution configuration tab is used to select the current excitation for the plots. All ofthe plots will automatically reflect the current solution configuration once it has beenselected. By simply selecting either a port or frequency, the excitation is changed and theplots are automatically updated.

The excitations in the visualization are modal. This means that the solutions arerepresented using ports and modes. Excitations are based on these modal solutions.

Maximum Value

All of the plot properties for a given plot are retained when the excitation is changed with the exception ofthe maximum value. This value is reset when the plot is regenerated.

The Plot Properties Tab

The Plot Properties tab enables you to control the three basic plots, as well as, theanimation settings.


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Plane Entry

FEM Simulator Visualization automatically creates z planes at all the surfaces where thereis horizontial xy plane at a z coordinate. These are displayed in the plane list. Each planehas a separate button, allowing you to control the individual display on the plane.

Vis - Display the two dimensional triangular mesh which is the intersection of the 3Dmesh with the 2D plane.Plot - Plots the selected plots within the plane. The plost are determined by thearrow and shade check boxes.

Besides the default planes, you can enter a new plane using the Add button. The Addbutton lets you select three points which define the plane. Once entered, you can plot onthis plane.

Planes can also be moved using the Modify button. When a plane is moved, it is movedperpindicular to its surface. Anything that is plotted on the place is automatically updatedduring this move.

Shaded Plot


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Displaying the shaded current plot is controlled by using the check box next to the plotname. When it is selected, the plot is visible. Within the plot there are some basiccontrols:

Log Scale - This controls whether the scaling and color representation uses alogarithmic scale or a linear one.Transparency - This controls the transparency of the shaded plot.

Arrow Plot

Displaying the arrow plot is controlled by using the check box next to the plot name.When it is selected, the plot is visible. Within the plot there are some basic controls:

Scale - This controls whether the arrows are scaled, based on the relative magnitudeof the current density through out the design. When it is selected, the arrows will bescaled, making the lower current density areas have smaller arrows. If it is notselected all of the arrows will be the same size. However, their size can still bechanged by changing the Arrow Size.Log Scale - This controls whether the scaling and color representation use alogarithmic scale or a linear one. If scaling is not enabled, only the color weighting isaffected.Arrow Size - This controls the relative size of the arrow on the screen. Keep in mindthat if the arrows are not scaled, the default size of the arrow will often appear to belarger than when the arrows are scaled.

Mesh Plot

When this plot is enabled the FEM Simulator mesh which is used to compute the field isdisplayed. If the surface box is checked, the surface of the 3D mesh is displayed.Otherwise a 3 dimension wire representation of the mesh is shown.

Boundary Plot

When this plot is enabled the FEM Simulator boundary surface meshes are displayed.These meshes are used by the solution process to represent specific boundary conditions,such as port surfaces and radiation boundaries. By individually selecting the variousboundary types, you can see what surfaces were used for each type of boundarycondition.

Unassigned surfaces can also be seen. These surfaces are those which could be assigned,but were not assigned during the solution process. If you are not getting the expectedsolution, this view is an excellent way to determine if the problem is set up correctly.

Advanced Options

The advanced options dialogs, selectable from the Shaded and Arrow plot areas enableyou to control the color ranges for the plots and the maximum and minimum values forthe respective plots.


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Shaded Advanced Options Arrow Advanced Options

The arrow advanced options also enables you to change the sampling for the arrow plotwhen you change from the default multiplier of 1.

Arrow SamplingWhen the arrow sampling is changed, it may take a few seconds for the system to update thedisplay.

Animation

Animation of arrow and shaded plots is controlled by the animation section. There are twocontrols within this area.

Display Update - This option determines the minimal time between display updatesin milliseconds. Since some updates may take longer than this setting, it is aminimum number and not an absolute one.Phase Increment- This controls the number of degrees added to the current phasewhen an update occurs.

Far Field Plots

When a problem contains far field data, a second window will be enabled within FEMVisualization. This window is used to display the far field plots in 3D. By default, thewindow is initialized displaying the E field as shown below:


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A new docking widget is also added to this widget, which controls the far field options.

These options are:

Plot - Controls the type of plot which will be displayed. Once the plot type isselected, the window is updated with the plot.Normalize - This control is used to normalize the data.Log Scale - This control is used to enable the scaling of the data logarithmically.Minimum dB - This is the minimum dB value which is used when plotting the datausing the Log Scale.Polarization Angle - This is the polarization angle in degrees.Transparency - Controls the transparency of the plot.

The antenna parameters for the far field can be displayed by selecting the AntennaParameters button.


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Using the Finite Element Method (FEM)The Finite Element Method (FEM) Simulator within EMPro provides a complete solution forelectromagnetic simulation of arbitrarily-shaped and passive three-dimensional structures.It provides a complete 3D EM simulation for designers working with RF circuits, MMICs, PCboards, modules, and Signal Integrity applications. The FEM simulation provides the bestprice/performance, 3D EM simulator on the market, with a full 3D electromagnetic fieldsolver, and fully automated meshing and convergence capabilities for modeling arbitrary3D shapes such as bond wires and finite dielectric substrates.

Developed with the designer of high-frequency/high-speed circuits in mind, FEM Simulatoroffers a powerful finite-element EM simulator that solves a wide array of applications withimpressive accuracy and speed.

By combining fast solution times, efficient memory usage, and powerful displaycapabilities, FEM Simulator for ADS delivers leading price/performance solution to complexhigh-frequency problems. FEM Simulator for ADS users need very little background inelectromagnetic field theory in order to operate and achieve accurate, meaningfulsolutions.

Major Features and BenefitsFEM in EMPro provides the following key technological features, which demonstrate theadvantages of full 3D EM design and verification:

Conductors, resistors, isotropic dielectrics, isotropic linear magnetic materialmodeling that allow a wide range of application coverage.An unlimited number of ports, which enables simulating multi-I/O design applicationssuch as packages.Electric and magnetic fields modeling, enabling visualization of EM fields in a design.Absorbing boundary condition (free space), enabling antenna modeling.Full-wave, EM-accuracy for first-pass design success.Antenna parameters (gain, directivity, polarization, and so on), to enable betterinsight into antenna design.FEM Simulator/ADS integration providing an integrated approach to EM/Circuitdesign.

Application Areas

EM modeling tools are known for their great accuracy. FEM Simulator redefines this termwith broad application coverage, including the following:

Microstrip, stripline, CPW elements (filters, couplers, spiral inductors, via holes, air


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bridges, meander lines...)Multilayer structuresCeramic filtersAdapters/transitionsAntennasCouplersPower splitters/combiners

Visualization and Display of Results

The visualization and animation capabilities in FEM Simulator enable you to evaluatesimulation results thoroughly. For analyzing designs, you can perform the EM fieldanimation and dynamic rotation of structures simultaneously. Choose from shaded plots,contour lines, or vectors. 3D far-field plots illustrate beam shapes in both azimuth andelevation on a single plot. To aid in analyzing your designs, EM field animation anddynamic rotation of structures can be performed simultaneously. Choose from shadedplots, contour lines, or vectors. 3D far-field plots illustrate beam shapes in both azimuthand elevation on a single plot.

FEM Simulator OverviewThe FEM Simulator commands are available from the Layout window. The following stepsdescribe a typical process for creating and simulating a design with the FEM Simulator:

Create a physical design: Create a physical design for your FEM simulation in1.EMPro.Set Simulation Options: A mesh is a pattern of tetrahedra that is applied to a2.design in order to break down (discretize) the design into small cells. A mesh isrequired in order to simulate the design effectively. You can specify a variety of meshparameters to customize the mesh to your design, or use default values and let FEMgenerate an optimal mesh automatically.Simulate the circuit: You set up a simulation by specifying the parameters of a3.frequency plan, such as the frequency range of the simulation and the sweep type.When the setup is complete, you run the simulation. The simulation process uses themesh pattern, and the electric fields in the design are calculated. S-parameters arethen computed based on the electric fields. If the Adaptive Frequency Sample sweeptype is chosen, a fast, accurate simulation is generated, based on a rational fitmodel.View the results: The data from an FEM simulation is saved as S-parameters or as4.fields.FEM Visualization: The FEM visualization enables you to view and analyze, S-5.parameters, currents, far-fields, antenna parameters, and transmission line data.Data can be analyzed in a variety of 2D and 3D plot formats. Some types of data aredisplayed in tabular form.Radiation patterns: Once the electric fields on the circuit are known, the6.electromagnetic fields can be computed. They can be expressed in the sphericalcoordinate system attached to your circuit.


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Viewing and Analyzing Parameters inFEMFEM Simulator Visualization enables you to view and analyze these types of simulationdata:

E FieldsFar-fieldsAntenna parametersTransmission line data

Data can be analyzed in a variety of 3D plot formats.

You can view the simulation results from any FEM Simulator or Agilent FEM project.This section gives an overview on how to use the FEM Simulator Visualization. ViewingResults (fem) describes in detail how to use FEM Simulator Visualization for viewingspecific types of data, such as S-parameters or currents.

Starting FEM Simulator VisualizationTo start the FEM Visualization choose FEM > Post-Processing > Visualization. The currentproject must run through a complete simulation use Visualization to view data. Ifsimulation has been previously completed for a project, you can start Visualization directlyto view the existing data.

FEM Simulator Visualization on PC and LinuxMachinesOn the PC and Linux platforms, FEM Simulator Visualization is based on the FEM SimulatorPreviewer. The following figure highlights the basic window which comes up when FEMSimulator Visualization is invoked.


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Upon startup, the window appears similar to the FEM Simulator 3D Previewer with a fewmodifications:

All of the object shading has been removed.Two additional tabs for controlling the view are added to the window.

The initial window's layout is similar to that of the FEM Simulator previewer. The left sidecontains the basic controls for the view in the docking widget. The Properties tab providesthe same functionality as the FEM Previewer properties tab.

Types of Plots

FEM Simulator Visualization supports three basic types of plots. These are

Shaded Plot - This plot displays the E Field on the selected planar surfaces.Arrow Plot - This plot displays a vector representation of the E Field on the selectedplanes.Mesh Plot - This plot displays the FEM Simulator Mesh which is used to computethe field.

Only one current plot and one arrow plot can be displayed. The arrow and current plot willalways correspond to the selected excitation. Once an excitation is changed, the plot willautomatically update using the new excitation values at the current phase.

The Solution Configuration Tab


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The solution configuration tab is used to select the current excitation for the plots. All ofthe plots will automatically reflect the current solution configuration once it has beenselected. By simply selecting either a port or frequency, the excitation is changed and theplots are automatically updated.

The excitations in the visualization are modal. This means that the solutions arerepresented using ports and modes. Excitations are based on these modal solutions.

Maximum Value

All of the plot properties for a given plot are retained when the excitation is changed with the exception ofthe maximum value. This value is reset when the plot is regenerated.

The Plot Properties Tab

The Plot Properties tab enables you to control the three basic plots, as well as, theanimation settings.


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Plane Entry

FEM Simulator Visualization automatically creates z planes at all the surfaces where thereis horizontial xy plane at a z coordinate. These are displayed in the plane list. Each planehas a separate button, allowing you to control the individual display on the plane.

Vis - Display the two dimensional triangular mesh which is the intersection of the 3Dmesh with the 2D plane.Plot - Plots the selected plots within the plane. The plost are determined by thearrow and shade check boxes.

Besides the default planes, you can enter a new plane using the Add button. The Addbutton lets you select three points which define the plane. Once entered, you can plot onthis plane.

Planes can also be moved using the Modify button. When a plane is moved, it is movedperpindicular to its surface. Anything that is plotted on the place is automatically updatedduring this move.

Shaded Plot


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Displaying the shaded current plot is controlled by using the check box next to the plotname. When it is selected, the plot is visible. Within the plot there are some basiccontrols:

Log Scale - This controls whether the scaling and color representation uses alogarithmic scale or a linear one.Transparency - This controls the transparency of the shaded plot.

Arrow Plot

Displaying the arrow plot is controlled by using the check box next to the plot name.When it is selected, the plot is visible. Within the plot there are some basic controls:

Scale - This controls whether the arrows are scaled, based on the relative magnitudeof the current density through out the design. When it is selected, the arrows will bescaled, making the lower current density areas have smaller arrows. If it is notselected all of the arrows will be the same size. However, their size can still bechanged by changing the Arrow Size.Log Scale - This controls whether the scaling and color representation use alogarithmic scale or a linear one. If scaling is not enabled, only the color weighting isaffected.Arrow Size - This controls the relative size of the arrow on the screen. Keep in mindthat if the arrows are not scaled, the default size of the arrow will often appear to belarger than when the arrows are scaled.

Mesh Plot

When this plot is enabled the FEM Simulator mesh which is used to compute the field isdisplayed. If the surface box is checked, the surface of the 3D mesh is displayed.Otherwise a 3 dimension wire representation of the mesh is shown.

Boundary Plot

When this plot is enabled the FEM boundary surface meshes are displayed. These meshesare used by the solution process to represent specific boundary conditions, such as portsurfaces and radiation boundaries. By individually selecting the various boundary types,you can see what surfaces were used for each type of boundary condition.

Unassigned surfaces can also be seen. These surfaces are those which could be assigned,but were not assigned during the solution process. If you are not getting the expectedsolution, this view is an excellent way to determine if the problem is set up correctly.

Advanced Options

The advanced options dialogs, selectable from the Shaded and Arrow plot areas enableyou to control the color ranges for the plots and the maximum and minimum values forthe respective plots.


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Shaded Advanced Options Arrow Advanced Options

The arrow advanced options also enables you to change the sampling for the arrow plotwhen you changefrom the default multiplier of 1.

Arrow SamplingWhen the arrow sampling is changed, it may take a few seconds for the system to update thedisplay.

Animation

Animation of arrow and shaded plots is controlled by the animation section. There are twocontrols within this area.

Display Update - This option determines the minimal time between display updatesin milliseconds. Since some updates may take longer than this setting, it is aminimum number and not an absolute one.Phase Increment- This controls the number of degrees added to the current phasewhen an update occurs.

Far Field Plots

When a problem contains far field data, a second window will be enabled within FEMVisualization. This window is used to display the far field plots in 3D. By default, thewindow is initialized displaying the E field as shown below:


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A new docking widget is also added to this widget, which controls the far field options.

These options are:

Plot - Controls the type of plot which will be displayed. Once the plot type isselected, the window is updated with the plot.Normalize - This control is used to normalize the data.Log Scale - This control is used to enable the scaling of the data logarithmically.Minimum dB - This is the minimum dB value which is used when plotting the datausing the Log Scale.Polarization Angle - This is the polarization angle in degrees.Transparency - Controls the transparency of the plot.

The antenna parameters for the far field can be displayed by selecting the AntennaParameters button.


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Viewing FEM Simulation ResultsAfter running the calculation, you can view the results from the Results workspacewindow. Some results are displayed in the form of numerical values, while other resultsare displayed in the form of plots. There are several types of plots available to view resultsbased on whether they are time-dependent, frequency-dependent, or angle-dependent:

S-parameterSensorsAdvanced Visualization

In this section, you will learn about how to display FEM Simulator results.

Viewing the Default Output of FEM SimulationTo view the default results of a specific project:

Open the Results workspace window by clicking Results in EMPro.1.

Click List Project to open the required project. This opens the EMPro- List Project2.Results dialog box.Select the required project and click Choose.3.In the Results window, you can select the required Output Object, Result Type,4.and Simulation Number.


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Right-click the required result type in the Results pane, which is present at the5.bottom.Select View (default) to display the default output, as shown in the following figure:6.

Creating a Line GraphRight-click the required result type in the Results pane, which is present at the1.bottom.Select the Create Line Graph option. This opens the Create Line Graph dialog box:2.


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Select the plot type by selecting the required option: XY, Polar, or Smith.3.Select the required component from the Component drop-down list.4.Specify Data Transformation option from the drop-down list.5.From the Complex Part drop-down list select the required option for displaying6.results: Magnitude, Real, Phase, and Imaginary.In the Target Graph, select New graph.7.Click View to view the data.8.

Viewing S-parameters

Standard and AFS Datasets

If the Adaptive sweep type is used for a simulation, both the adaptive and discrete S-parameter results are available in the Results for plotting. The adaptive results contain theS-parameters from the rational fitting model resamples with a very dense frequencydistribution. The discrete frequency S-parameter results are indicated with 'DiscreteFrequencies' in the Domain column. The adaptive S-parameter results are indicated with'Frequencies' in the Domain column.

Typically, when viewing data adaptive S-parameter results, you should see very smoothresults, which reflect the behavior of the circuit. Viewing the discrete S-parameter resultson the same plot will show the frequency points for which the simulator was invoked,superimposed on the smooth curve. Those frequency points will be scattered over thewhole range, with relatively more points grouped in areas where the S-parameters showmore variation. Viewing both datasets can help you determine the quality of the AFSprocess on your simulation.

Viewing Results Using FEM Simulator VisualizationIn FEM Simulator Visualization, you can display S-parameters in tabular or plottedformats. This section describes how to view and work with S-parameters. It also givesgeneral information about S-parameters.

S-parameter OverviewWhen viewing and working with S-parameters, you should be aware how impedance isspecified and what naming convention is used. These are described in the followingsections.

Normalization Impedance


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The S-parameters that you can display are S-parameters with respect to a normalizationimpedance as defined in the Impedance fields of the Port Editor dialog box. If an

impedance is not specified, 50 is assumed.

Naming Convention

The S-parameter naming convention, which is based on the name of the project, indicateswhich set of S-parameters you are viewing or working with. There are only two datasetsavailable for a project. One is named design_name which contains the discrete frequenciesthat were actually simulated. The second is design_name(afs) is available only when anadaptive frequency sweep is specified in the simulation setup. An adaptive frequencysweep dataset contains a high resolution sampling based on the pole-zero model fitted onthe simulated frequencies.

Viewing S-parameters in graphical formatYou can view the S-parameter results retrieved with the port sensor placed at the locationof the Feed. To filter the list accordingly, select the following options in the columns in thetop pane of the Results window (You may need to change your column headings first).

Output Object: FeedData Type: Circuit ComponentResult Type: S-Parameters

You can view the following formats for displaying S-parameter values for each port:

MagnitudeRealImaginaryPhase

To view S-parameters:

Right-click the result with a Domain value of Frequency to view transient S-1.parameter results.Select the the Create Line Graph option.2.Select the data format from the Complex Part drop-down list:3.

Magnitude Displays the magnitude of the S-parametersReal Displays the S-parameters as complex numbersPhase Displays the magnitude and phase of the S-parametersImaginary Displays the S-parameters as complex numbers

Click View to display the result.4.

Plotting S-parameter MagnitudeThe S-parameter magnitude plot displays magnitude in dB with respect to frequency.


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To display an S-parameter magnitude plot:

Select the the data you want to view from the S Parameters list.1.Open the Create Line Graph dialog box.2.From the Complex Part drop-down list, select Magnitude.3.Click View.4.

Plotting S-parameter PhaseThe S-parameter phase plot displays phase in degrees with respect to frequency. Notethat when viewing S-parameter phase, in some cases the phase delay is plotted. Forexample, a layout of an electrical length with a phase of 60 degrees, S21 represents a

phase delay, and appears as -60 degrees. For phases greater than 180 degrees, it mayappear that the phase predicted from Gamma compared to S21 is incorrect, but this is not

so if delay is taken into account.

To display an S-parameter phase plot:

Select the data you want to view from the S Parameters list.1.Open the Create Line Graph dialog box.2.From the Complex Part drop-down list, select Phase.3.Click View.4.


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Plotting S-parameters on a Smith ChartThe Smith chart displays real and imaginary components of S-parameters.

To display a Smith chart:

Right-click the data you want to view from the S Parameters list.1.Choose the View Smith Chart option.2.The Smith chart is displayed:3.


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Exporting S-parametersS-parameters can be exported to a Citi file by selecting the S-paramater data in the resultbrowser, and after right-clicking select Export of CITI file ...

EMPro FEM-Specific Sensors and OutputFrom within the results browser, the following sensors can be used for FEM simulations:

• Planar sensors

• Far field sensors

More post processing is possible by using the Advanced Visualization tool available in theResults browser:

Viewing the Output in Advanced VisualizerBefore simulating your design using the FEM simulator, it is recommended to validate thatthe three dimensional design has been properly constructed. This will give youconfirmation of your design and also simulation of designs which are not correct. Therepresentation seen in the viewer is the same definition that will be used in FEM. If theview does not appear to be correct, it is essential that the the design is corrected beforeattempting a simulation.

The key benefits of this visual confirmation are:

Correct Substrate Set Up - The substrate information within ADS is defined usingthe Substrate menu options. Using these commands, the height of each substrate isdefined and the corresponding layers are assigned. The visualizer enables you tovalidate that the proper mappings have been set up and that they are the correctheight.

Correct Bondwire and Dielectric Brick Placement - Bondwires, described in the


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schematic window of ADS, are mapped to the ADS layout and incorporated into theoverall FEM design for simulation. Dielectric bricks are defined as part of thesubstrate definition. Since these portions of the design are difficult to see in layout,the visualizer can be used to validate their location and design.

Setting Up the Advanced Visualization on External X WindowDisplays

On Unix/Linux Systems, it is common practice to use a local machine as a display and dothe actual processing on another machine. The display from the original machine istypically mapped back to the local display using the following command:

export DISPLAY=machine:0.0

For using the Advanced Visualizer feature, you need to need to set an additionalenvironment variable, HOOPS_PICTURE. This environment variable is set to the samevalue as the display variable with the addition of X11/ prior to the machine name. Usingthe above example, the HOOPS_PICTURE variable would be set to

export HOOPS_PICTURE=X11/machine:0.0

Validating Your Geometry Visually

You can invoke the Advanced Visualization feature by clicking the AdvancedVisualization button in the Results window. The following figure highlights this button:

The Advanced Visualizer needs to be started each and every time that you want to reviewyour design as it does not remain synchronized with the current design. It isrecommended that you do not keep one instance of the visualizer open while an olderinstance is present. It will not interfere with the data; however, it might be confusing andcause an unnecessary error.


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Identifying and Highlighting Individual Objects

Individual objects can be selected and highlighted in two ways:

Picking on the Screen - Objects can be selected graphically using the mouse. If thevisualizer is in Query mode, an object can be selected by clicking on any line orvertex of the object. Once selected, the object's lines are highlighted, the object isselected in the material and object list and the coordinates of the selection point aredisplayed in the lower right area of the status bar.

Selection from the Material or Object List - Objects can be selected from eitherthe material or object list box. Once selected, the object's lines become highlighted.

Identifying and Highlighting Materials

The material selection is located in the docking widget. It has the same controls forindividual objects as the Object Tab. In addition, each material's visibility and shading canbe controlled using check boxes associated with the material itself.

Controlling the Visibility and Translucency of Selected Objects and Materials

Once an object has been selected, its visibility and translucency can be controlled usingthe Object Information control located at the bottom of the docking widget. This optionenables you to control the translucency and visibility of an object.


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It is also possible to control the visibility and shading for the substrate and mask layers.Within the Material portion of the docking widget, each material and object has separatetoggles for visibility and shading. By setting these controls appropriately, you can controlthe visibility and shading for all the objects that share this substrate or mask. However,the translucency can only be controlled at the object level.

Navigating in the 3D Environment

The Advanced Visualizer operates in several different modes. The current mode isdisplayed in the lower left portion of the status bar. Regardless of the mode, the mousewheel will enable you to zoom in and out of the design at the location of the mouse cursoron the screen.

Zoom Box - You can select a region on the design by selecting a rectangle aroundthe area of interest. Once selected, the visualizer will zoom into this area and updatethe local rotation origin.Zoom - You can zoom in or out on the design by moving the mouse up or down onthe image respectively.Rotate - The rotation mode is the default start up mode for the visualizer. You canrotate the design around its current origin by holding down the main mouse buttonand moving it around the screen.Pan - You can move the design around on the screen by holding down the mainmouse button and moving it around the screen.Query - You can query your model using this command. When you click on anobject's edge or vertex, the location and object name are displayed in the status bar.In addition, the object is highlighted and the object is automatically selected in theObject and Material tabs in the Docking widget. Visually, a solid dot is placed if theselected location is on a vertex and a hollow dot is placed if the selected location ison an edge.

Measuring Distances in the Advanced Visualizer

The measure dialog is activated from the Window/Measure command. Once activated, themeasure dialog is displayed.


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Measurement is done between a reference point and the current query point . The querypoint is updated after every mouse selection using the query command. The referencepoint remains fixed until it is explicitly updated using the Move Current Point to Reference.

Note: For more information on Advanced visualizer, refer to Using the Advanced Visualization Feature(fem).

january 2010 empro 2009 - keysight

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