Tunable Evanescent Mode Cavity Filter Using a Piezo Actuator

An evanescent mode cavity filter can be realized by adding a structure inside of the cavity. This structure changes the resonant frequency below that of the dominant mode of the unfilled cavity. A piezo actuator is used to control the size of a small air gap which provides the tunability of the resonant frequency.

Figure 1: A tunable evanescent mode cavity filter is composed of a rectangular cavity with a metallic post, a piezo actuator disk, and slot-coupled microstrip lines. There is a small gap between the top of the post and the bottom side of the piezo actuator. The front part of the cavity wall is removed for visualization purposes.

In addition to the RF Module, this example requires one of the Acoustics Module, the MEMS Module, or the Structural Mechanics Module.

Model Definition

This example starts from a basic rectangular cavity filter, whose resonant frequencies are given by

where a and b are the waveguide aperture dimensions and d is the length of the waveguide cavity. In this example, the cavity width, height, and length are a = 100 mm, b = 50 mm, and d = 50 mm, respectively. The resulting resonant frequency of the dominant mode, TE101, is 3.354 GHz.

By adding a metallic post and creating reactance inside the cavity, the resonance frequency can be lowered. The cavity is air filled and the height of the post is slightly smaller than b, which creates a small gap between the top of the post and the cavity where the electric fields are confined. Two shorted 50 Ω microstrip lines on a dielectric substrate, fed by a lumped port, are coupled into the cavity. The dimensions and locations of the slots can be adjusted to improve input matching properties and power transfer between input and output ports. The air box around the microstrip lines are enclosed by a scattering boundary condition representing the infinite air space. A circular aperture at the top of the cavity is closed with a piezo actuator and the bottom surface of the disk is finished with a layer of a highly conductive material that is several skin depths in thickness.

Model all metal parts — the cavity walls, post, substrate ground planes, microstrip lines, and the bottom surface of the piezo device — as perfect electric conductors (PECs). The material for the piezo actuator is Lead Zirconate Titanate (PZT-5H). It is z-polarized and generates mainly z-directional deflection of the device.

Mesh the model using a tetrahedral mesh with approximately five elements per wavelength in each material at the highest simulation frequency. When the piezo device deforms due to the input bias, the Moving Mesh interface is used to deform the mesh for the Electromagnetic Waves physics.

Results and Discussion

A +300 V potential is applied across the piezo actuator, which causes the device to deflect ~90 μm toward the bottom; see Figure 2. This makes the reactance stronger and shifts the resonant frequency lower than the negative bias case. Figure 3 plots the electric field norm at the resonance. At the center of the cavity as well as in the gap between the top of the post and the bottom of the piezo device, strong electric fields are observed.

Figure 2: This plot shows the total piezo displacement when 300 V is applied on the actuator. The visualization is exaggerated to emphasize the deflection.

The S-parameters plotted in Figure 4 show the effect of the piezo device deflection on the filter’s resonant frequency. The tunable frequency range of this example is ~40MHz. This range can be adjusted by different choices of the piezo disk size and the input bias voltage.

Figure 3: The dominant mode inside the cavity is observed from the electric field distribution plot.

Figure 4: The deflection for the piezo device controlled by the input bias can shift the resonance frequency of the filter.

Notes About the COMSOL Implementation

This example uses the built-in Piezoelectricity multiphysics interface which couples the Solid Mechanics and Electrostatics interfaces through the Piezoelectric Effect node located under the Multiphysics branch. Other physics interfaces used are Moving Mesh and Electromagnetic Waves, Frequency Domain. A Stationary study is used for the Solid Mechanics, Electrostatics and Moving Mesh interfaces, and a Frequency Domain study is used for the Electromagnetic Waves interface.

RF_Module/Filters/tunable_cavity_filter

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

In the tree, select .

Click .

Click

In the tree, select .

Click

Study 1

Stationary

In the toolbar, click

and choose .

Frequency Domain

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type range(3[GHz],2.5[MHz],3.06[GHz]).

Geometry 1

The model geometry is available as a parameterized geometry sequence in a separate MPH-file. If you want to build it from scratch, follow the instructions in the section Appendix: Geometry Modeling Instructions. Otherwise load it from file with the following steps.

In the toolbar, click

Browse to the model’s Application Libraries folder and double-click the file tunable_cavity_filter_geom_sequence.mph.

In the toolbar, click

Click the

button in the toolbar.

Click the

button in the toolbar.

Global Definitions

Parameters 1

Add parameters that are not related to geometry.

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
V0	300[V]	300 V	Piezo actuator bias

Here, c_const is a predefined COMSOL constant for the speed of light in vacuum.

Definitions

Create a set of selections for use when setting up the physics. First, create a selection for the microstrip feed line.

Feed line

In the toolbar, click

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

Locate the section. From the list, choose .

Select Boundaries 17, 22, 47, and 50 only.

Add a selection for the ground.

Ground

In the toolbar, click

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

Locate the section. From the list, choose .

Select Boundaries 6, 16, 28, 39, and 53 only.

Add a selection for the substrate.

Substrate

In the toolbar, click

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

Select Domains 2, 4, 6, and 8 only.

Add a selection for the piezo actuator disk.

Piezo actuator

In the toolbar, click

In the window for , type Piezo actuator in the text field.

Select Domain 5 only.

Add a selection for fixed edges of the piezo disk.

Piezo fixed edges

In the toolbar, click

In the window for , type Piezo fixed edges in the text field.

Locate the section. From the list, choose .

Select Edges 50, 51, 63, and 66 only.

Add a selection for the open boundaries of RF domain.

Open boundaries

In the toolbar, click

In the window for , type Open boundaries in the text field.

Locate the section. From the list, choose .

Select Boundaries 4, 5, 7, 8, 10, 12, 13, 23, 25, 37, 38, 40, 41, 43–45, 56, and 57 only.

Set up the Moving Mesh. Because the substrate and top air domains are deflection free regions, do not include them.

Deforming Domain 1

In the toolbar, click

and choose .

Select Domain 1 only.

Prescribed Mesh Displacement 1

In the toolbar, click

and choose .

Select Boundary 28 only.

In the window for , locate the section.

Specify the dx vector as


u	X
v	Y
w	Z

Before defining materials, specify domains for each physics.

Solid Mechanics (solid)

In the window, under click .

In the window for , locate the section.

From the list, choose .

Electrostatics (es)

In the window, under click .

In the window for , locate the section.

From the list, choose .

Electromagnetic Waves, Frequency Domain (emw)

In the window, under click .

Select Domains 1–4 and 6–8 only.

Assign material properties. Use three materials for this model: PZT-5H, air, and a user-defined substrate.

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 tree, select .

Click in the window toolbar.

In the toolbar, click

to close the window.

Materials

Lead Zirconate Titanate (PZT-5H) (mat1)

In the window, under click .

In the window for , locate the section.

From the list, choose .

Air (mat2)

In the window, click .

Select Domains 1, 3, and 7 only.

Material 3 (mat3)

In the window, right-click and choose .

In the window for , locate the section.

From the list, choose .

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

Solid Mechanics (solid)

Now, set up the physics constraints. Start by assuming the bottom rim of piezo actuator part is attached on the same size circular aperture of the cavity top and no deflection is expected.

In the window, under click .

Fixed Constraint 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Electrostatics (es)

Next, define the Electrostatics constraints.

In the window, under click .

Electric Potential 1

In the toolbar, click

and choose .

Select Boundary 29 only.

In the window for , locate the section.

In the V0 text field, type -V0.

Ground 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Electromagnetic Waves, Frequency Domain (emw)

In the window, under click .

Perfect Electric Conductor 2

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Perfect Electric Conductor 3

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Scattering Boundary Condition 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Lumped Port 1

In the toolbar, click

and choose .

Select Boundary 14 only.

For the first port, wave excitation is by default.

Lumped Port 2

In the toolbar, click

and choose .

Select Boundary 54 only.

Mesh 1

Adjust the maximum and minimum element size manually on the piezo actuator to reduce the memory cost of running the study without compromising the accuracy. Then, use swept mesh for the piezo actuator to handle the structural deformation more efficiently.

In the window, under click .

In the window for , locate the section.

From the list, choose .

Size 1

In the window, under click .

In the window for , locate the section.

In the text field, type 10.

In the text field, type 1.

Free Tetrahedral 1

In the window, click .

In the window for , locate the section.

From the list, choose .

Select Domains 1–4 and 6–8 only.

Select all domains except for the piezo actuator.

Swept 1

In the toolbar, click

Distribution 1

Right-click and choose .

In the window for , locate the section.

In the text field, type 2.

Click

Study 1

Parametric Sweep

In the toolbar, click

In the window for , locate the section.

Click

In the table, enter the following settings:


Parameter name	Parameter value list	Parameter unit
V0 (Piezo actuator bias)	-300,300	V

Step 1: Stationary

In the window, click .

In the window for , locate the section.

In the table, clear the check box for .

Step 2: Frequency Domain

In the window, click .

In the window for , locate the section.

In the table, clear the check boxes for , , and .

In the table, clear the check box for .

In the toolbar, click

Results

Displacement

Replace the default stress plot by displacement plot.

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

Surface 1

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 .

In the toolbar, click

Click the

button in the toolbar.

This plot shows the deflected piezo actuator disk; compare with Figure 2.

Electric Potential (es)

The electric potential inside the piezo actuator disk.

Electric Field (emw)

In the window, click .

In the window for , locate the section.

From the list, choose .

In the toolbar, click

Multislice

In the window, expand the node, then click .

In the window for , click to expand the section.

Select the check box.

In the text field, type 1000.

In the toolbar, click

The resulting plot shows strong electric fields resulting from the dominant resonance at the center of the cavity as well as in the gap between the metallic post and the ceiling of the cavity.Compare the plot with that shown in Figure 3.

S-parameter (emw)

In the window for , locate the section.

From the list, choose .

Global 1

In the window, expand the node, then click .

In the window for , locate the section.

From the list, choose .

In the toolbar, click

The plotted S-parameters show the frequency shift as a function of the input bias on the piezo actuator; compare with Figure 4.

Smith Plot (emw)

Analyze the same model with a much finer frequency resolution using based on asymptotic waveform evaluation (AWE). When a device presents a slowly varying frequency response, the AWE provides a faster solution time when running the simulation on many frequency points. The following example with the AWE can be computed 10 times faster than regular Frequency Domain sweepswith a same finer frequency resolution.

Electromagnetic Waves, Frequency Domain (emw)

Lumped Port 1

In the window, expand the node, then click .

In the window for , locate the section.

Click

In the dialog box, 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

In the window for , locate the section.

Clear the check box.

Parametric Sweep

In the toolbar, click

In the window for , locate the section.

Click

In the table, enter the following settings:


Parameter name	Parameter value list	Parameter unit
V0 (Piezo actuator bias)	-300 300	V

Stationary

In the toolbar, click

and choose .

In the window for , locate the section.

In the table, clear the check box for .

Adaptive Frequency Sweep

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type range(3[GHz],0.25[MHz],3.06[GHz]).

Use a 10 times finer frequency resolution.

A slowly varying scalar value curve works well for AWE expressions. When is set to in the study settings, abs(comp1.emw.S21) is used automatically for two-port devices.

In the text field, type 0.001.

Use a smaller value for the to get more accurate results.

Locate the section. In the table, clear the check boxes for , , and .

In the table, clear the check box for .

Because such a fine frequency step generates a memory-intensive solution, the model file size will increase tremendously when it is saved. When only the frequency response of port related variables are of interest, 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 port variables are calculated. The lumped port size is typically very small compared to the entire modeling domain, and the saved file size with the fine frequency step is more or less that of the regular discrete frequency sweep model when only the solutions on the lumped port boundaries are stored.