Connecting a 3D Electromagnetic Wave Model to an Electrical Circuit

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Connecting a 3D Electromagnetic Wave Model to an Electrical Circuit

An application built with the RF Module can be connected to an electrical circuit equivalent, if there is some structure outside of the model space that you want to approximate as a circuit equivalent. An example is shown in Figure 1, the 3D model of a coaxial cable is connected to a voltage source, in series with a matched impedance, and sees a load, also of matched impedance.

Figure 1: Schematic of a section of a coaxial transmission line connected to a voltage source, source impedance, and load.

Model Definition

The geometry in this example is a short section of a air-filled coaxial transmission line, shown schematically in Figure 1. A 3D modeling space is used to model the coaxial cable. The walls of the coax are treated as perfect electric conductors. This is appropriate when the skin depth, and the losses in the conductors, are insignificant.

At one end of the coaxial cable, Lumped Port boundary condition is used to connect the model to nodes 0 and 2 of the Electrical Circuit. A Voltage Source between circuit nodes 0 and 1 excites the system, and a Resistor representing the source impedance is added between nodes 1 and 2. Node 0 is specified as the Ground Node by default, which fixes the absolute voltage. The connection from the Electrical Circuit model to the Electromagnetic Waves interface is via the External I Vs. U features.

At the other end of the coaxial cable, another Lumped Port boundary condition is used to connect the model to nodes 3 and 0 of the Electrical Circuit. A Resistor which works as a matched load is added between nodes 3 and 0. At any nonzero frequency, the absolute voltage has no well-defined meaning, voltage only has a meaning as the path integral of electric field between two points, so any arbitrary point in the model can be chosen to have zero voltage. If you are working with a purely RF model, without an electrical circuit, it is not even possible to fix the absolute voltage. However, when using the Electrical Circuit interface, it requires that the absolute voltage be fixed at one node (Node 0) in the model.

Results and Discussion

Figure 2 is a combined plot of the default electric field norm, magnetic field, and power flow.

Figure 2: Electric field norm (multislices) and electric field, magnetic field, and power flow (red, green, and blue arrows) inside the coaxial cable.

The fields and power flow plot shows the TEM wave propagation inside the coaxial cable, which is excited by the Electrical Circuit interface.

Notes About the COMSOL Implementation

The Electrical Circuit interface is located under the AD/DC Module branch, but it is included with the RF Module.

RF_Module/Transmission_Lines_and_Waveguides/coaxial_cable_circuit

Modeling Instructions

From the menu, choose .

In the window, click

.

1

In the window, click

.

2

In the tree, select .

3

4

In the tree, select .

5

6

7

In the tree, select .

8

Step 1: Frequency Domain

1

In the window, under click .

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In the window for , locate the section.

3

In the text field, type 10[GHz].

Global Definitions

1

In the window, under click .

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In the window for , locate the section.

3

In the table, enter the following settings:


Name	Expression	Value	Description
r_coax	1[mm]	0.001 m	Coax inner radius
R_coax	2[mm]	0.002 m	Coax outer radius
L_coax	20[mm]	0.02 m	Length of coax core into cavity
Z_coax	Z0_const/(2pi)log(R_coax/r_coax)	41.56 Ω	Analytical impedance

Here, Z0_const is a predefined COMSOL constant for the speed of the light and the wave impedance in vacuum, respectively.

Create the geometry of the coaxial cable using two cylinders.

1

In the toolbar, click

.

2

In the window for , type Coax outer in the text field.

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Locate the section. In the text field, type R_coax.

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In the text field, type L_coax.

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Locate the section. From the list, choose .

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In the toolbar, click

.

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In the window for , type Coax inner in the text field.

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Locate the section. In the text field, type r_coax.

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In the text field, type L_coax.

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Locate the section. From the list, choose .

Difference 1 (dif1)

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In the toolbar, click

and choose .

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Select the object only.

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In the window for , locate the section.

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Find the subsection. Click to select the

toggle button.

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Select the object only.

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.

7

button in the toolbar.

Electromagnetic Waves, Frequency Domain (emw)

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In the window, under right-click and choose .

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Select Boundary 1 only.

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In the window for , locate the section.

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From the list, choose .

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From the list, choose .

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In the toolbar, click

and choose .

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Select Boundary 10 only.

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In the window for , locate the section.

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From the list, choose .

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From the list, choose .

Electrical Circuit (cir)

In the window, under click .

Voltage Source 1 (V1)

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In the toolbar, click

.

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In the window for , locate the section.

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In the table, enter the following settings:


Label	Node names
p	1
n	0

4

Locate the section. From the list, choose .

Resistor 1 (R1)

1

In the toolbar, click

.

2

In the window for , locate the section.

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In the table, enter the following settings:


Label	Node names
p	1
n	2

4

Locate the section. In the R text field, type Z_coax.

Resistor 2 (R2)

1

In the toolbar, click

.

2

In the window for , locate the section.

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In the table, enter the following settings:


Label	Node names
p	3
n	0

4

Locate the section. In the R text field, type Z_coax.

External I vs. U 1 (IvsU1)

1

In the toolbar, click

.

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In the window for , locate the section.

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In the table, enter the following settings:


Label	Node names
p	2
n	0

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Locate the section. From the V list, choose .

External I vs. U 2 (IvsU2)

1

In the toolbar, click

.

2

In the window for , locate the section.

3

In the table, enter the following settings:


Label	Node names
p	3
n	0

4

Locate the section. From the V list, choose .

Next, assign material properties on the model. Specify air for the coaxial cable.

1

In the toolbar, click

to open the window.

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Go to the window.

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In the tree, select .

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Click in the window toolbar.

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In the toolbar, click

to close the window.

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In the window, under click .

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In the window for , locate the section.

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From the list, choose .

4

.

In the toolbar, click

.

Electric Field (emw)

The default plot shows the E-field norm inside the coaxial cable. Add arrow plots for the electric field, magnetic field, and power flow.

Right-click and choose .

1

Right-click and choose .

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In the window for , click in the upper-right corner of the section. From the menu, choose .

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Locate the section. From the list, choose .

1

Right-click and choose .

2

In the window for , click in the upper-right corner of the section. From the menu, choose .

3

Locate the section. From the list, choose .

4

In the toolbar, click

.

Compare the resulting plot with that shown in Figure 2.