Coaxial to Waveguide Coupling

Feeding a waveguide from a coaxial cable is a straightforward way to get electromagnetic waves inside the waveguide. This example shows how to compute the reflection and transmission in a coupling from a coaxial cable to a rectangular waveguide.

Model Definition

As seen in the results plot in Figure 1, the coaxial cable is attached to an opening in the bottom of the rectangular waveguide. The inner conductor of the cable continues into the waveguide in order to transmit the waves. The model is run at a frequency of 6 GHz.

The wave coming in through the coaxial cable is set up using a Port boundary condition, with a 1 W coaxial feed selected. At the passive output port, the fundamental rectangular TE10 mode is assumed. The interpretation of the port conditions is that the coaxial cable and the rectangular waveguide continue indefinitely outside the model. The model therefore isolates the properties of the coupling from the properties of any outside circuit connecting to the other end of the waveguide or the cable.

The port boundary conditions are perfectly transparent only to their own specified mode. These same modes are also used in the automatic S-parameter analysis. For these reasons, it is important that the modeled sections are long enough that any evanescent waves have almost completely died out before they reach the ports. This leaves only the propagating modes - at 6 GHz, the only supported propagating modes are the specified, fundamental modes.

An impedance boundary condition with material properties for copper is used for the coaxial conductors and the metal surfaces of the waveguide. At the considered frequency, copper is such a good conductor that a perfect electric conductor condition would be a reasonable alternative. However, the impedance condition also helps to accommodate the port boundaries, by smoothing out any numerical inconsistencies at the edges where they meet.

Results and Discussion

For cable feeds it is interesting to compare the reflected wave going back into the coaxial cable with the wave propagating in the rectangular waveguide. You can make such a comparison by evaluating the S-parameter on the coaxial port and compare it with the S-parameter on the rectangular port. The following table shows the result for a frequency of 6 GHz in dB scale:


Parameter	Value	Description
S11	-8.4 dB	Reflected wave into the coaxial cable
S21	-0.7 dB	Wave exiting the rectangular waveguide

The following plot shows the electric field distribution. The z-component is shown in the rectangular waveguide and the y-component on a vertical slice through the coaxial cable and into the waveguide. Except for just at the end of the inner coaxial conductor, the x- and y-components of the field are negligible in the waveguide. Likewise, the z-component is barely present in the coaxial cable.

Figure 1: Horizontal slice through the rectangular waveguide showing the z-component of the field, and vertical slice through the coaxial cable showing the y-component.

RF_Module/Transmission_Lines_and_Waveguides/coaxial_waveguide_coupling

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

Click

In the tree, select .

Click

Study 1

Step 1: Frequency Domain

In the window, under click .

In the window for , locate the section.

In the text field, type 6[GHz].

Global Definitions

To help in creating the geometry, define some parameters defining its dimensions.

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
H	17.5[mm]	0.0175 m	Height, waveguide
L	100[mm]	0.1 m	Length, waveguide
l	20[mm]	0.02 m	Length, coaxial cable
R	5[mm]	0.005 m	Outer radius, coaxial cable
r	1[mm]	0.001 m	Inner radius, coaxial cable

The width of the waveguide is taken to be twice the height.

Geometry 1

Block 1 (blk1)

In the toolbar, click

In the window for , locate the section.

In the text field, type L.

In the text field, type 2*H.

In the text field, type H.

Cylinder 1 (cyl1)

In the toolbar, click

In the window for , locate the section.

In the text field, type R.

In the text field, type l.

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

In the text field, type H.

In the text field, type -l.

Click

Cylinder 2 (cyl2)

In the toolbar, click

In the window for , locate the section.

In the text field, type r.

In the text field, type l+H/2.

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

In the text field, type H.

In the text field, type -l.

Click

As you are going to represent all conductors as boundaries, you will now create a hole in the geometry replacing the inner conductor of the coaxial cable.

Click the

button in the toolbar.

Difference 1 (dif1)

In the toolbar, click

and choose .

Click in the geometry to select and add the outer cylinder of the coaxial cable and the box representing the waveguide.

Select the objects and only.

In the window for , locate the section.

Find the subsection. Select the

toggle button.

Select and add the inner cylinder of the coaxial cable.

Select the object only.

Click

Definitions

With the geometry set up, define a couple of boundary selections to allow for quick access to some commonly used boundaries.

Metal Boundaries

In the toolbar, click

In the window for , type Metal Boundaries in the text field.

Locate the section. From the list, choose .

Select the check box.

Select Boundaries 1–7 and 9–20 only.

Remove Boundaries 8 and 21 from the selection. These are the boundaries where the wave will enter and leave your waveguide coupling.

Input Port

In the toolbar, click

In the window for , type Input Port in the text field.

Locate the section. From the list, choose .

Select Boundary 8 only.

Boundary 8 is the outer face of the coaxial cable.

Output Port

In the toolbar, click

In the window for , type Output Port in the text field.

Locate the section. From the list, choose .

Select Boundary 21 only.

Boundary 21 is the boundary on the far end of the rectangular waveguide section.

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select .

Click in the window toolbar.

Materials

Air (mat1)

Select Domain 1 only.

Dielectric

In the window, right-click and choose .

In the window for , type Dielectric in the text field.

Select Domain 2 only.

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Relative permittivity	epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0	2	1	Basic
Relative permeability	mur_iso ; murii = mur_iso, murij = 0	1	1	Basic
Electrical conductivity	sigma_iso ; sigmaii = sigma_iso, sigmaij = 0	0	S/m	Basic

Add Material

Go to the window.

In the tree, select .

Click in the window toolbar.

In the toolbar, click

to close the window.

Materials

Copper (mat3)

In the window for , locate the section.

From the list, choose .

Electromagnetic Waves, Frequency Domain (emw)

Impedance Boundary Condition 1

In the window, under right-click and choose .

In the window for , locate the section.

From the list, choose .

Port 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

For the first port, wave excitation is by default.

Port 2

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

Mesh 1

In the window, under right-click and choose .

Study 1

In the toolbar, click

Results

Multislice

In the window, expand the node, then click .

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

Locate the section. Find the subsection. In the text field, type 0.

Find the subsection. In the text field, type 0.

Find the subsection. From the list, choose .

In the text field, type H/4.

In the toolbar, click

Slice 1

In the window, right-click and choose .

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

Locate the section. From the list, choose .

In the text field, type H.

Click to expand the section. Locate the section. From the list, choose .

In the toolbar, click

In the coaxial cable, the field is largely radial, meaning the y component dominates. The other slice shows the field in the rectangular waveguide, where the z component takes over.

The port conditions automatically compute and supply the S-parameters.