Cascaded Rectangular Cavity Filter

A cascaded cavity filter provides much better bandpass filter performance compared to a single cavity filter. Here, three rectangular cavity filters are coupled via slots and provide excellent out-of-band rejection.

Figure 1: A cascaded rectangular cavity filter consisting of three cavities, coupling slots, and microstrip lines feeds.

Model Definition

The resonant frequencies of a rectangular cavity are given by

where a and b are the dimension of the aperture of a waveguide and d is the length of the waveguide cavity. The size of a single cavity used in this example is 50 mm, 50 mm, 100 mm in depth, height, and width, respectively. The resonant frequency at the dominant mode TE101 is 3.354 GHz. In this example, three such cavities are coupled through slots. The dimensions and locations of the slots can be adjusted to improve input matching properties as well as power transfer between in and output ports. Two shorted microstrip lines, fed by a lumped port, couple into the first and last cavities of the structure. The air box around the microstrip lines is enclosed by metallic walls, representing the packaging.

Results and Discussion

Solving the model over a range of frequencies reveals that the resonant frequency of the cascaded filter is 3.354 GHz, as expected. The out-of-band rejection at ±90 MHz is better than -60 dB.

Figure 2: A plot of the electric field shows the dominant TE101 mode in each cavity.

Figure 3: Frequency response of the cascaded rectangular cavity filter shows good bandpass characteristics.

Notes About the COMSOL Implementation

This example also uses the Frequency Domain Modal study step combined with an Eigenfrequency analysis to evaluate the frequency response of the filter circuit. This approach is faster than a regular frequency sweep performed in a Frequency Domain study, but its usage is limited to only high-Q devices or circuits presenting bandpass frequency properties excited by lumped ports. Since an Eigenfrequency analysis is computationally intensive, it may require more than 8 GB of RAM.

Reference

1. D.M. Pozar, Microwave Engineering, John Wiley & Sons, 1998.

RF_Module/Filters/cascaded_cavity_filter

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(3.3[GHz],2.5[MHz],3.38[GHz]).

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file cascaded_cavity_filter_parameters.txt.

Here mil refers to the unit milliinch, that is 1 mil = 0.0254 mm.

Geometry 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

Create a cavity at the input port.

Cavity1

In the toolbar, click

In the window for , type Cavity1 in the text field.

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

In the text field, type d_cavity.

Locate the section. From the list, choose .

In the text field, type -w_cavity/2-w_cavity/8.

In the text field, type d_cavity.

Click

Create a substrate at the input port.

Substrate

In the toolbar, click

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

Locate the section. In the text field, type w_cavity/3.

In the text field, type d_cavity.

In the text field, type d.

Locate the section. In the text field, type -w_cavity-w_cavity/8.

In the text field, type -w_cavity/4.

In the text field, type d_cavity*1.5.

Click

Create a microstrip line at the input port.

Feed

In the toolbar, click

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

Locate the section. In the text field, type l_feed+w_slot.

In the text field, type 3.2[mm].

In the text field, type d.

Locate the section. From the list, choose .

In the text field, type -w_cavity/2-w_cavity/8-x_slot-l_feed/2.

In the text field, type d_cavity*1.5+d/2.

Click

To see the interior, you can choose wireframe rendering:

Click the

button in the toolbar.

Create a box enclosing the input port.

FeedBoxBlock

In the toolbar, click

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

Locate the section. In the text field, type w_cavity/3.

In the text field, type d_cavity.

In the text field, type h_feed.

Locate the section. From the list, choose .

In the text field, type -w_cavity-w_cavity/8+w_cavity/6.

In the text field, type d_cavity*1.5+h_feed/2.

Click

Create coupling slots between the cavities.

Work Plane 1 (wp1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 25[mm].

Click

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

In the toolbar, click

In the window for , locate the section.

In the text field, type 3.5[mm].

In the text field, type 26.4[mm].

Locate the section. From the list, choose .

In the text field, type -28.5[mm].

Click

Create coupling slots between the microstrip line feed and the cavity linked to the feed as well.

Work Plane 2 (wp2)

In the window, right-click and choose .

In the window for , locate the section.

In the text field, type 75[mm].

Click

Work Plane 2 (wp2)>Rectangle 1 (r1)

In the toolbar, click

In the window for , locate the section.

In the text field, type w_slot.

In the text field, type 45[mm].

Locate the section. From the list, choose .

In the text field, type -w_cavity/2-w_cavity/8-x_slot.

Right-click and choose .

Generate the second cavity by mirroring the first one.

Mirror 1 (mir1)

In the toolbar, click

and choose .

Click in the window and then press Ctrl+A to select all objects.

In the window for , locate the section.

In the text field, type 1.

In the text field, type 0.

Locate the section. Select the check box.

Click

Click the

button in the toolbar.

Cavity1.1 (blk5)

In the window, under right-click and choose .

In the window for , locate the section.

In the text field, type 0.

Click

Electromagnetic Waves, Frequency Domain (emw)

The default boundary condition is perfect electric conductor, which is applied to all exterior boundaries. Assign perfect electric conductor to interior boundaries on the cavity walls and microstrip lines.

Perfect Electric Conductor 2

In the window, under right-click and choose the boundary condition .

Select Boundaries 6, 16, 17, 22, 29, 36, 44, 52, 55, and 58 only.

Assign a lumped port with port excitation at the end of one microstrip line.

Lumped Port 1

In the toolbar, click

and choose .

Select Boundary 14 only.

For the first port, wave excitation is by default.

Assign a lumped port at the end of the other microstrip line.

Lumped Port 2

In the toolbar, click

and choose .

Select Boundary 59 only.

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select .

Click in the window toolbar.

In the toolbar, click

to close the window.

Materials

Create a dielectric material for the substrates.

Material 2 (mat2)

In the window, under right-click and choose .

Select Domains 2, 4, 7, and 9 only.

In the window for , 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	3.38	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

Mesh 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

Click

Study 1

In the toolbar, click

Results

Electric Field (emw)

The default plot shows the norm of the electric field for the highest frequency. Follow the instructions to reproduce Figure 2.

In the window for , locate the section.

From the list, choose .

Multislice

In the window, expand the node, then click .

In the window for , locate the section.

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

Find the subsection. From the list, choose .

In the text field, type -d_cavity/2+0.1,d_cavity/2+0.1,d_cavity/2*3-0.1.

Click to expand the section. Select the check box.

In the text field, type 800.

In the toolbar, click

S-parameter (emw)

In the window, under click .

In the window for , locate the section.

From the list, choose .

Smith Plot (emw)

3D Plot Group 4

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Isosurface 1

Right-click and choose .

In the window for , locate the section.

In the text field, type 20.

Locate the section. Click

In the dialog box, select in the tree.

Click .

Filter 1

Right-click and choose .

In the window for , locate the section.

In the text field, type y>0.

In the toolbar, click

Analyze the same model with a Frequency Domain Modal method. When a device presents resonances, the Frequency Domain Modal method combined with an Eigenfrequency analysis provides a faster solution time.

Electromagnetic Waves, Frequency Domain (emw)

Lumped Port 1

In the window, under click .

In the window for , locate the section.

Click

In the dialog box, Create a set of selections for use in the study settings.

type Lumped port 1 in the text field.

Click .

Lumped Port 2

In the window, click .

In the window for , locate the section.

Click

In the dialog box, type Lumped port 2 in the text field.

Click .

Add Study

In the toolbar, click

to open the window.

Go to the window.

Find the subsection. In the tree, select .

Click in the window toolbar.

In the toolbar, click

to close the window.

Study 2

Step 1: Eigenfrequency

In the window for , locate the section.

In the text field, type 3.3[GHz].

Step 2: Frequency Domain, Modal

In the window, click .

In the window for , locate the section.

In the text field, type range(3.3[GHz],2.5[MHz]/50,3.38[GHz]).

With a 50 times finer frequency step, the solutions will increase the file size tremendously when it is saved. When only S-parameters are of interest, a common theme in most passive RF and microwave device designs, it is not necessary to store all of the field solutions. By selecting the check box in the section, we can control the part of the model on which the computed solution is saved. We only add the selection containing these boundaries where the S-parameters are calculated. The lumped port size is typically very small compared to the entire modeling domain, and the saved file size with the finer frequency step is more or less that of the regular discrete frequency sweep model when only the solutions on the port boundaries are stored.

Click to expand the section. Find the subsection. From the list, choose .

Under , click

In the dialog box, in the list, choose and .

Click .

In the toolbar, click

Results

Electric Field (emw) 1

Since the results are stored only on the lumped port boundaries, this default E-field norm plot does not provide useful information.

Right-click and choose .

Generate all S-parameters from each analysis on the same plot and compare them to each other.

S-parameter (emw) 1

In the window, under click .

In the window for , click to expand the section.

From the list, choose .

In the text area, type S-parameter Comparison between Frequency Domain Modal and Discrete Sweep.

Locate the section. From the list, choose .

Global 2

In the window, expand the node.

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Click to expand the section. Find the subsection. From the list, choose .

Find the subsection. From the list, choose .

Global 1

In the window, click .

In the window for , locate the section.

In the table, enter the following settings:


Expression	Unit	Description
emw.S11dB	1	S11, FD Modal
emw.S21dB	1	S21, FD Modal

In the toolbar, click

See Figure 3 for S-parameter plot.

Smith Plot (emw) 1

Compare the solution time between two studies.

The following instruction shows how to use the subfeature to analyze 1D plots. When plotting S11 of a bandpass filter, poles are of interest and a graph marker captures the local minima. For analyzing the insertion loss such as S21, the -3dB bandwidth of the passband can be computed through an additional graph marker.

S-parameter with Graph Markers

In the toolbar, click