This blog is about using SynMatrix software to design a filter. SynMatrix software is a powerful tool for designing cavity filters, as well as diplexers and multiplexers. The purpose of today's project is to design a coaxial cavity filter. However, we will use that as a basis for explaining how the tool works.

The following flowchart shows a few of the options available in SynMatrix. We will go through them one by one.

Phase 1: Filter Synthesis

When you open Synmatrix, the Synthesis mode will be activated. Users have the option of designing a filter or a diplexer, a BPF/BSF/LPF or MultiBand filter, and need to specify the topology. Let's take a look at that. SynMatrix's interface can be viewed here. Choose a single filter, a BPF, and the topology. There is a wide variety of topologies available. In our case, we will assume a simple straight topology. Therefore, there is no change.

Specify the band of the filter. It is possible to specify Fo and the 3dB bandwidth or to switch to the start/end 3dB frequencies instead.

The order of the filters will affect the rate at which the insertion curve drops. Provide the required RL for the band of interest. The dF and dB values are used when using a multi-band option. Specify each resonator's unloaded Q in the last option. An unloaded Q is the maximum Q-factor of the cavity when it is not connected to any load. When a load is applied, the Q will decrease. The unloaded Q of a lossless cavity is infinite.  The user will notice a decrease in insertion rate if Q does not equal infinity.

Press Calculate All. This plot shows the S-parameters, the group delay, and the stored energy in each resonator. You may activate or hide any curve by clicking on its name in the table below.

It is also possible for the user to add zeros. These are frequencies outside the band of interest, where the insertion should be very low. Add a zero at 0.95GHz and 1.05GHz. After that, click Calculate all again.

Specify the frequency range of the plots at the top of this page. We are interested in plotting the response from 0.875GHz to 1.125GHz in this case.

The dispersion is shown on the left. It is possible for the user to specify the dispersion correction to be applied. We will talk about the dispersion at the end of the video.

The dispersion occurs as a result of the symmetrical filter. The insertion curve drop faster on one side comparing to the other side.

The normalized coupling parameter calculated by the software can be seen on the right. The coupling between S, the source, and the first cavity is shown here. The value is 1.0873. Between 1 and 2, it is 0.9103. You may also change the display to show coupling bandwidth values instead, of course in MHz.

dF is calculated from the following driven model:

You may modify these values by editing the matrix. Changing them will alter the shape of the response. It is also possible to change the sign. It is possible to export the S-matrix or the coupling matrix.

Add markers. Select the location and click to place the marker. Here is a list of all the markers that have been added. You may delete or modify any of them.

The last panel is the Specification panel. The purpose of this is for thermal considerations. The thermal settings will be discussed in special sessions.

Then click Calculate All to upgrade the design and move on to the next phase, 3D modeling. Cavity.

Phase 2: Filter Design

Step1: Cavity Dimensions

The following options are available: coaxial, rectangular waveguide, circular waveguide, SIW, or planar coupled resonator. Choose coaxial cable. Confirm and begin a new design.

Based on the specifications, SynMatrix calculates the dimensions of the cavity. The following choices can be made: the shape of the inner resonator: square or round, the shape of the cavity: square, round, or hexagonal, and lastly, the type of tuning: Flat on Top, Bowl on Top, and Disk on Top. There are advantages to each type. The flat on top is simple to implement, however the resonant frequency changes in a quadratic manner with the gap. Changes rapidly with small gaps, then very slowly with large gaps. Due to this behavior, tuning by hand is very difficult. The resonant frequency of a bowl on top, on the other hand, changes linearly as the gap widens.

The ranges you see here are for the purpose of verification. On the right, if I select fixed diameter, it means I am changing the height from 4.288 to 5.513. Let us calculate this. SynMatrix selected this point at 1.16GHz. Consider the case in which I change the radius with a fixed height. As we can see, the Q changes in relation to the diameter. It is now clear why SynMatrix selected a diameter of 0.788 cm.

The next step is to set up the single cavity in its final configuration. We have already decided on the shape and dimensions. The user has the option of adding drafty to the inner and outer radius. A round fillet or a segment fillet can be selected at the bottom of the resonator.

Select "Apply and next step": The tuning scheme. Please confirm the entries once again. You can also select whether the resonator should be uniform (the same material) or non-uniform - partial.

The next step is to apply:

In the HFSS step, specify whether the eigen solver or the driven solver should be used. At this stage, select the eigen solver. Then construct the model. Start the simulation. Come to HFSS. It is currently running. As can be seen, the model is fully parameterized. HFSS calculates the resonant frequency as 1.157 and the Q as 7113.5. Provided that the value is greater than the end of the band, the design is acceptable.

The reduction of the gap of the screw should also be tested to ensure that it produces a frequency lower than the lower band of interest. The cavity height is 7, and the resonator height is 5.25. Adjust the screw to a height of 1.7 cm. There is a resonant frequency of 0.892GHz, which is smaller than the band's start frequency of 0.975GHz. As a result, this design is capable of accommodating the entire band.

We choose to use 1.632cm screw length, gives a resonant at 1GHz, with Q = 6551

Step 2: Coupling Section

We now proceed to the next step, the "Coupling Scheme." Any type selected here changes the entries. Selecting the first option. We need to specify the Iris width, the step width, the step height, the cavity distance, and finally the screw diameter and depth.

Apply and proceed to the next step: HFSS. The purpose of this study is to investigate the eigen modes of two resonators using HFSS. The coupling is derived from the first two modes. The same applies: "construct and run". According to HFSS, the coupling coefficient is 0.0474. When viewing the results in HFSS, display the eigenmodes.

The dF_coupling of the model is 1.00119GHz-1.00356GHz=2.37MHz. So, the coupling coefficient is 1.87MHz/50MHz=0.0473. Similar to what was reported by SynMatrix.

The cavity distance must be such that we can meet all the coupling values or dF in the table. Using the eigensolver, solve two cavities and then extract the delta between the first two modes in order to meet the coupling bandwidth requirements. 

M12 = dF / BW            (BW is the bandwidth of the filter 58MHz)

In SynMatrix activates the Parametric study, and change cavity distance:

For 0.9738, the cavity distance between 1 and 2 is 4.85cm, and for 0.6825, the cavity distance between 2 and 3 is 5.2cm.

Step 3: Input Section

 Next, we will discuss the input/output scheme. SynMatrix offers a number of options, including Tap (LPF/BPF), Disk (BPF), Loop (BPF), and Tap-Through. For our BPF, select tab one. The goal is to reach the coupling number 1.1208. This is a loaded coupling. It cannot be unloaded.

https://www.microwavejournal.com/ext/resources/pdf-downloads/Hagensen3.pdf

We obtain around 9ns from port height 2.625. 10.136 ns is what we are looking for. Tune the port height using the parametric study option in SynMatrix. The port height appears to be 2.425.

Step 4: Full Model

The final stage is the full 3D Model. Check the entries of each cavity, that they match what you selected.

The response is not as we expected. We need to optimize the structure.

Phase 3: Manual Optimization

The next step is to extract the s-parameters from HFSS and import them into SynMatrix. In HFSS>Results>Export>Export Matrix Data> Do Not Override solution renormalization.

Back to SynMatrix. Activate the CAT Computer Aided Tuning option:

Click on "Load the data" and select the S-parameter file. As shown in the figure, the red line represents the expected S21 values, while the dotted line represents the obtained S21 from HFSS.

It is evident that there is a difference between what we wanted and what we received. Reverse engineering is performed by pressing Extract Matrix, which extracts the matrix obtained from HFSS.

As we see the Matrix is totally different. How to tell, select the Error Levels panel.

You will notice that the M11 and M55 are large, this is due to the input rod changing the cavity resonance a great deal. Positive values indicate that the screw length needs to be increased. From SynMatrix, select Cavity > Main Body Design

Select Cavities 1 and 5, and change the tuning screw depth to 1.7cm. Aggressive change.

Go to Modeling>Update Model>Run Simulation. When you solve, export the s-parameters same way we did before. Back, to SynMatrix, turn on the Track Mode, and import the s-parameters. Select Extract Matrix, again. What you see are the old and new values. The 1.7 was too aggressive. We need to go back and try new values.

Repeat this procedure for all coupling values until all differences are minimized to near zero.

The dotted curve is shifted in this diagram. This is known as the dispersion effect. The dispersion effect occurs in symmetrical filters when the insertion curve drops faster on the high band side and slower on the low band side. To make the dotted curve match the solid curves (especially the red one), we must add dispersion during the Synthesis stage. Select the dispersion that corresponds to the shape we observed in the previous graph under Synthesis> Single.

If you change the dispersion number to 3, the filter matrix will change to be a symmetrical filter.

5 Cavities Coaxial Filter @ 1GHz

References:

https://tektelic.com/expertise/cavity-filter/

https://www.youtube.com/watch?v=oWezN5bNDdA

https://storage.googleapis.com/jst-journals/articles/ssad/155/21026_1.3m.pdf

https://www.microwavejournal.com/ext/resources/pdf-downloads/Hagensen3.pdf