H-Bend Waveguide 3D

This example shows how to model a rectangular waveguide for microwaves. A single hollow waveguide can conduct two kinds of electromagnetic waves: transversal magnetic (TM) or transversal electric (TE) waves. This example examines a TE wave, one that has no electric field component in the direction of propagation. More specifically, for this example you select the frequency and waveguide dimension so that TE10 is the single propagating mode. In that mode the electric field has only one nonzero component — a sinusoidal with two nodes, one at each of the walls of the waveguide. This makes it possible to set up and solve the model in 2D, which is done in a separate version; see H-Bend Waveguide 2D.

One important design aspect is how to shape a waveguide to go around a corner without incurring unnecessary losses in signal power. Unlike in wires, these losses usually do not result from ohmic resistance but instead arise from unwanted reflections. You can minimize these reflections by keeping the bend smooth with a large enough radius. In the range of operation the transmission characteristics (the ability of the waveguide to transmit the signal) must be reasonably uniform for avoiding signal distortions.

With air as the inside medium of the waveguide, the transmission is nearly perfect throughout the range of operation. In this example, to make the simulation and the results more interesting, the bend is filled with silica glass, a dielectric medium.

The model also shows how to systematically compute and export all S-parameters to a Touchstone file.

Model Definition

This example illustrates how to create a model that computes the electromagnetic fields and transmission characteristics of a 90° bend for a given radius. This type of waveguide bends changes the direction of the H field components and leaves the direction of the E field unchanged. The waveguide is therefore called an H-bend. The H-bend design used in this example is well-proven in real-world applications and you can buy similar waveguide bends online from a number of manufacturers. This particular bend performs optimally in the ideal case of perfectly conducting walls.

The waveguide walls are typically plated with a very good conductor, such as silver. In this example the walls are considered to be made of a perfect conductor, which means that the tangential component of the electric field is zero, or that n × E = 0 on the boundaries. This boundary condition is referred to as a perfect electric conductor (PEC) boundary condition.

The geometry is as follows:

The waveguide is considered to continue indefinitely before and after the bend. This means that the input wave needs to have the form of a wave that has been traveling through a straight waveguide. The shape of such a wave is determined by the boundary conditions of Maxwell’s equations on the sides of the metallic boundaries, that is, the PEC boundary condition. If polarized according to a TE10 mode, the shape is known analytically to be E = (0, 0, sin(π (a − y)/(2 a))) cos(ωt) given that the entrance boundary is centered around the y = 0 axis, and that the width of the waveguide, in the y direction, is 2a.

The model is set up using the time-harmonic Electromagnetic Waves interface. This means that only the phasor component of the field is modeled. The incident field then has the form E = (0, 0, E0z) = (0, 0, sin(π (a − y)/(2 a))), and is considered as part of the expression E = Re{(0, 0, sin(π (a − y)/(2 a))ejωt)} = Re{Eejωt}, where complex-valued arithmetic has been used (also referred to as the jω method).

The width of the waveguide is chosen so that it has a cutoff frequency of 3.7 GHz. This makes the waveguide operational up to 7.5 GHz. At higher frequencies other modes than the TE10 appear, causing a “dirty” signal. The input wave then splits into several modes that are hard to control without having large power losses. Below the cutoff frequency, no waves can propagate through the waveguide. This is an intrinsic property of microwave waveguides.

The cutoff frequency of different modes in a straight waveguide is given by the relation

where m and n are the mode numbers (m = 1, n = 0 for the TE10 mode), a and b are the lengths of the sides of the waveguide cross-section, and c is the speed of light.

For this waveguide, a = 2b and b = 2 cm.

The first few cutoff frequencies are (νc)10 = 3.7 GHz, (νc)01 = 7.5 GHz, (νc)11 = 8.4 GHz. The frequencies used in this example are from 4.0 GHz to 5.2 GHz, and hence entirely within the single-mode range.

On the input boundary, the Port boundary condition lets you choose which mode to send in. Any reflected waves having the same shape are transmitted back through this same boundary. The output boundary also uses a Port condition, but without field excitation, to specify the shape of the wave that it lets pass through. Using port boundary conditions means that you automatically gain access to postprocessing variables for the S-parameters.

Results and Discussion

The wave is found to propagate through the bend with a varying amount of reflection depending on the frequency.

Figure 1: The z-component of the electric field for a frequency of 5.1 GHz.

The S-parameters are shown as functions of the frequency in Figure 2.

Figure 2: The S-parameters, on a dB scale, as a function of the frequency.

The two dips in S21 closely correspond to cavity resonances of the dielectric region in the bend. At these frequencies, the transmission is almost perfect. (Without the dielectric, the transmission would be nearly as good throughout the frequency range.)

RF_Module/Transmission_Lines_and_Waveguides/h_bend_waveguide_3d

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 range(4[GHz],25[MHz],5.2[GHz]).

Global Definitions

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
l_wg	10[cm]	0.1 m	Waveguide length
w_wg	4[cm]	0.04 m	Waveguide width
h_wg	2[cm]	0.02 m	Waveguide height

Geometry 1

Work Plane 1 (wp1)

In the toolbar, click

In the window for , click

Work Plane 1 (wp1)>Plane Geometry

In the window, click .

Work Plane 1 (wp1)>Circle 1 (c1)

In the toolbar, click

In the window for , locate the section.

In the text field, type w_wg.

Work Plane 1 (wp1)>Circle 2 (c2)

In the toolbar, click

In the window for , locate the section.

In the text field, type 2*w_wg.

In the text field, type 90.

Locate the section. In the text field, type -90.

Work Plane 1 (wp1)>Difference 1 (dif1)

In the toolbar, click

and choose .

Select the object only.

In the window for , locate the section.

Find the subsection. Click to select the

toggle button.

Select the object only.

Work Plane 1 (wp1)>Rectangle 1 (r1)

In the toolbar, click

In the window for , locate the section.

In the text field, type w_wg.

In the text field, type l_wg.

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

Work Plane 1 (wp1)>Rectangle 2 (r2)

In the toolbar, click

In the window for , locate the section.

In the text field, type l_wg.

In the text field, type w_wg.

Locate the section. In the text field, type -l_wg.

In the text field, type -2*w_wg.

In the toolbar, click

Extrude 1 (ext1)

In the window, under right-click and choose .

In the window for , locate the section.

In the table, enter the following settings:


Distances (m)
h_wg

Click

Click the

button in the toolbar.

Electromagnetic Waves, Frequency Domain (emw)

Wave Equation, Electric 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

Port 1

In the toolbar, click

and choose .

Select Boundary 1 only.

In the window for , locate the section.

From the list, choose .

For the first port, wave excitation is by default.

Port 2

In the toolbar, click

and choose .

Select Boundary 15 only.

In the window for , locate the section.

From the list, choose .

The default boundary condition is perfect electric conductor, which is fine for all exterior boundaries except the ports. The software automatically imposes continuity on interior boundaries.

Materials

Air

In the window, under right-click and choose .

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

Select Domains 1 and 3 only.

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


Property	Variable	Value	Unit	Property group
Refractive index, real part	n_iso ; nii = n_iso, nij = 0	1	1	Refractive index

Silica Glass

Right-click and choose .

In the window for , type Silica Glass in the text field.

Select Domain 2 only.

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


Property	Variable	Value	Unit	Property group
Refractive index, real part	n_iso ; nii = n_iso, nij = 0	1.44	1	Refractive index

Mesh 1

In the window, under right-click and choose .

If you look closely at the mesh, you can see that it is indeed a bit finer in the bend than elsewhere.

Study 1

In the toolbar, click

Results

Electric Field (emw)

The default plot shows the distribution of the electric field norm on slices of the waveguide, for the highest frequency in the sweep. Note the wave pattern in the bend and the rectangular input section. This indicates standing waves caused by reflections in the bend. In contrast, the pattern beyond the bend is independent of the y-coordinate, showing that the output port does a good job of transmitting the wave.

An S-parameter plot gives you a quantitative measure of how much of the wave is transmitted and reflected at different frequencies.

Global 1

In the window, expand the node, then click .

In the window for , click to expand the section.

Find the subsection. From the list, choose .

In the toolbar, click

The result, which should look like Figure 2, shows that the transmission varies throughout the frequency range. Note in particular that S21 has two deep dips, corresponding to almost perfect transmission. This is the result of resonances in the bend. To confirm this, try looking at the field distribution for the frequency where the upper peak is located, 5.1 GHz.

Smith Plot (emw)

Electric Field (emw)

In the window, click .

In the window for , locate the section.

From the list, choose .

In the toolbar, click

The standing wave pattern still remains in the bend, but at this frequency it is almost completely gone in the input section.

For an alternative view, you can plot the instantaneous value of the electric field inside the waveguide. Only the z component will be substantially nonzero. For a better view, add also deformation. Replace the Multislice with a single horizontal slice plot.

Multislice

In the window, expand the node.

Right-click and choose .

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 .

From the list, choose .

Locate the section. From the list, choose .

In the toolbar, click

The Wave color table looks its best using a symmetric range. You can also play with a deformed shape plot to make the waves appear more clearly.

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

Deformation 1

Right-click and choose .

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

In the toolbar, click

The remaining instructions show you how to systematically solve with one port active at a time, and save the results in the Touchstone format.

Electromagnetic Waves, Frequency Domain (emw)

In the window, under click .

In the window for , locate the section.

Select the check box.

Click . By clicking the button, all necessary port sweep settings such as sweep parameter and parametric study step will be automatically added. It is necessary to run the parametric sweep with port names to get a full S-parameter matrix.

Select the check box.

Click the button and select a file to which you want to export the results in the Touchstone format. If the file does not exist, it will be created.

Study 1

In the toolbar, click