lossy circular waveguide

7/21/2019 Lossy Circular Waveguide

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Solved with COMSOL Multiphysics 4.2

2 0 1 1 C O M S O L 1 | L O S S Y C I R C U L A R W A VE G U I D E

L o s s y C i r c u l a r Wav e gu i d e

Introduction

In mode analysis it is usually the primary goal to find apropagation constant. This

quantity is often, but not always, real valued; if the analysis involves some lossy part,

such as a nonzero conductivity or an open boundary, the eigenvalue is complex. In

such situations, the real and imaginary parts have separate interpretations:

The real part is the propagation constant

The imaginary part is the attenuation constant, measuring the damping in space

Model Definition

The mode analysis study for electromagnetic waves solves the eigenvalue problem

where

is the eigenvalue. For time-harmonic problems, the electric field for out-of-plane

propagation can be written as

where zis the known out-of-plane direction.

The spatial parameter, z j , can have a real part and an imaginary part. The

propagation constant is equal to the imaginary part, and the real part, z, represents

the damping along the propagation direction.

V A R I A B L E S I N F L U E N C E D B Y M O D E A N A L Y S I S

The following table lists the variables that are influenced by the mode analysis in termsof the eigenvalue lambda:

NAME EXPRESSION CAN BE COMPLEX DESCRIPTION

beta imag(-lambda) No Propagation constant

dampz real(-lambda) No Attenuation constant

1

E E 0=

k02

rj-----

=

E r t Re E r ejt z

=


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2 | L O S S Y C I R C U L A R W A V E G U I D E 2 0 1 1 C O M S O L

This two-dimensional model finds the modes of a circular waveguide with walls made

of a nonperfect conductor, which is copper in this case. The losses in the walls lead to

attenuation of the propagating wave. The propagation constant is obtained as the

imaginary part of and the damping zis obtained as the real part. Since the

wave in the waveguide is attenuated in the zdirection as ezz, the attenuation in dB

scale is calculated using the formula

Results and Discussion

The eigenvalue solver returns six eigenvalues. Table 1shows the six effective mode

indices, neff, closest to 1, where

and k0is the wavenumber in vacuum. The table also lists the propagation constant and

damping in dB/m for each eigenmode.

dampzdB 20*log10(exp(1))*

dampz

No Attenuation per meter in dB

neff j*lambda/k0 Yes Effective mode index

TABLE 1: EFFECTIVE MODE INDICES, PROPAGATION CONSTANTS, AND ATTENUATION.

EFFECTIVE MODE INDEX PROPAGATION CONSTANT (1/M) ATTENUATION (DB/M)

0.9308 - 2.2082e-6i 19.5071 4.0199e-4

0.9733 - 2.1116e-6i 20.3992 3.844e-4

0.9566 - 1.7954e-6i 20.0486 3.2684e-4

0.9566 - 1.7954e-6i 20.0486 3.2684e-4

0.9844 - 9.38e-7i 20.6324 1.7076e-4

0.9844 - 9.38e-7i 20.6324 1.7076e-4

NAME EXPRESSION CAN BE COMPLEX DESCRIPTION

dB 20z elog=

nef f jk0------=


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The default surface plot shows the norm of the electric field for the effective mode

index 0.9308 2.208106j. This plot is shown in Figure 1.

Figure 1: The surface plot visualizes the norm of the electric field for the effective modeindex 0.9308 - 2.20810-6j.

Model Library path: RF_Module/Tutorial_Models/

lossy_circular_waveguide

Modeling Instructions

M O D E L W I Z A R D

1 Go to the Model Wizardwindow.

2 Click the 2Dbutton.

3 Click Next.

4 In the Add physicstree, select Radio Frequency>Electromagnetic Waves (emw).

5 Click Next.


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6 In the Studiestree, select Preset Studies>Mode Analysis.

7 Click Finish.

G E O M E T R Y 1

Circle 1

1 In the Model Builderwindow, right-click Model 1>Geometry 1and choose Circle.

2 Go to the Settingswindow for Circle.

3 Locate the Size and Shapesection. In the Radiusedit field, type 0.5.

4 Click the Build Allbutton.

M A T E R I A L S

1 In the Model Builderwindow, right-click Model 1>Materialsand choose Open Material

Browser.

2 Go to the Material Browserwindow.

3 Locate the Materialssection. In the Materialstree, select Built-In>Air.

4 Right-click and choose Add Material to Modelfrom the menu.

Air

By default the first material you add apply for all domains.

Next, specify copper as the material on the boundaries.

1 In the Model Builderwindow, right-click Materialsand choose Open Material Browser.

2 Go to the Material Browserwindow.3 Locate the Materialssection. In the Materialstree, select Built-In>Copper.

4 Right-click and choose Add Material to Modelfrom the menu.

Copper

1 In the Model Builderwindow, click Copper.

2 Go to the Settingswindow for Material.

3 Locate the Geometric Entity Selectionsection. From the Geometric entity levellist,select Boundary.

4 From the Selectionlist, select All boundaries.


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E L E C T R O M A G N E T I C W A VE S

Impedance Boundary Condition 1

1 In the Model Builderwindow, right-click Model 1>Electromagnetic Wavesand choose

Impedance Boundary Condition.

2 Go to the Settingswindow for Impedance Boundary Condition.

3 Locate the Boundary Selectionsection. From the Selectionlist, select All boundaries.

S T U D Y 1

Solve for the 6 effective mode indices closest to 1.Step 1: Mode Analysis

1 In the Model Builderwindow, expand the Study 1node, then click Step 1: Mode

Analysis.

2 Go to the Settingswindow for Mode Analysis.

3 Locate the Study Settingssection. In the Desired number of modesedit field, type 6.

4 In the Model Builderwindow, right-click Study 1and choose Compute.

R E S U L T S

Electric Field (emw)

The default plot shows the electric field norm for the lowest mode found; compare

with Figure 1.

Derived Values

Calculate the propagation constant and the attenuation constant (in dB) for each

effective mode index.

1 In the Model Builderwindow, right-click Results>Derived Valuesand choose Global

Evaluation.

2 Go to the Settingswindow for Global Evaluation.

3 In the upper-right corner of the Expressionsection, click Replace Expression.

4 From the menu, choose Electromagnetic Waves>Propagation constant (emw.beta).

5 Click the Evaluatebutton.

Compare the results with those in the second column of Table 1.

6 Go to the Settingswindow for Global Evaluation.

7 In the upper-right corner of the Expressionsection, click Replace Expression.


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8 From the menu, choose Electromagnetic Waves>Attenuation constant, dB

(emw.dampzdB).

9 Click the Evaluatebutton.

Compare with with the third column of Table 1.

lossy circular waveguide

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