How to Generatethe Coupling Matrix

Getting Started

How to Generate the Coupling Matrix

This start-up tutorial will guide you on how to generate the coupling matrix. We will be using an example set of customer requirements for a band pass filter (BPF) –input your own specifications for your project.

Specifications Requirements

Frequency Range (MHz) 3300 ~ 3400

Insertion Loss (dB) < 1.5

Rejection (MHz)

0.09 ~ 3190 > 100 dB

3190~3280 > 40 dB

3420~3460 > 40 dB

3460~6800 > 80 dB

Return Loss (dB) > 17

Peak Power (Watts) 100

Operating Temperature (ºC) -30~80

Connector Type SMA

Example Requirements – BPF Case

Picture caption for these models.

Under the specification panel, click on the “ON” button to activate the specification analysis.

1A

Step 1: Input the customer specification to generate the specification “mask”

1AActivate the specification analysis

To the right of the panel, click on the “Add” button to add a new specification.

1B

1BAdd a new specification

In the first column of the newly added row, click on the drop-down menu and select the specification you want to add (RL, IL, ISO, GD). Input the frequency range and specification values to complete the row.

1C

Tip: You do not need to input a wideband rejection specification; it will squeeze the overall filter performance and result in inaccurate results.

S-Parameter graph with wideband rejection specification added, the display range is too wide.

Wideband rejection omitted.

1CSelect specification (RL, IL, ISO, GD)

Step 2: Input the frequency specification and the Return Loss (RL)

Under the Input Parameters panel, you can continue to input your specifications. Filter Order and Unloaded Q are experience-based parameters. You may optimize these parameters until the specifications can be achieved. Initially, we can set the Unloaded Q value as infinite.

2A

2A

Input Filter Order

2ASet as infinite initially, to be changed later

The RL is usually set 3dB lower than the customer specification for design margin purposes.

2B

2BSet RL usually 3dB lower than spec

Specifications Requirements

Frequency Range (MHz)

3300 ~ 3400

Insertion Loss (dB) < 1.5

Return Loss (dB) > 16

Recall the customer specifications.

The “Shift” function is also called fine-tune function. It is used for fine-tuning the filter performance when users incorporate the temperature drift analysis. Initially we can set these values to 0.

2C

2CSet as 0 initially, to be changed later

Tip: Click the blue radio button to switch different frequency input formats.

Tip: The first value indicates the frequency shift and the second is BW tuning; all units for both parameters are in “MHz”

Freq Shift BW tuning

Step 3: Design the transmission zeros to meet the specification

Initially the transmission zero (TZ) value can start with the rejection frequency either at the beginning or end of the rejection specification.

All TZ values need to be tuned and optimized, step by step, based on the customer’s specification. Sometimes more TZs need to be added to provide sharp isolation performance to satisfy the rejection requirement.

TZ1 TZ2

TZ3

Rejection

3190~3280 > 40 dB

3420~3460 > 40 dB

3460~6800 > 80 dB(3280) (3420)

(3460)

Tip: Click “NOR” or “GHZ” to switch Frequency input formats.

Normal Frequency. Real Frequency.

How TZ affects a S-Parameter graph.

F(s) is a polynomial with real coefficients, and its roots lie along the imaginary axis as conjugate pairs; P(s) is a pure even polynomial with real coefficients. Its roots lie on the imaginary axis in conjugate pairs.

Filter requirements call for low loss in the passband and high loss in other frequency bands. Such a requirement can best be achieved by assigning all the zeros of F(s) to the j𝜔 axis in the passband region and all zeros of P(s) to the j𝜔axis in the high loss frequency bands.

For some applications, the zeros of P(s) have a non-j𝜔-axis location. This results in an improved phase and group delay response in the passband at the expense of attenuation in the stopband. Such a trade-off is sometimes beneficial for the overall system requirements.

**References: Cameron, R. J., Kudsia, C. M., & Mansour, R. R. (2007). Microwave filters for communication systems: Fundamentals, design, and applications

𝑆21(𝑠) =𝑃(𝑠)

𝜀𝐸(𝑠)𝑆11(𝑠) =

𝐹(𝑠)

𝜀𝑟𝐸(𝑠) and

Transmission zeros knowledge — The Filter Transfer Function

Root of F: Transmission Poles

Root of P: Reflection Poles

In the normalized format, the “Complex Pair Zero” transmission zeros is always in pairs. This is true with symmetric and asymmetric filter responses. Therefore, the number of real zeros and the number of complex zeros must be even numbers.

For “Pure Finite Zeros” transmission zeros, the number of transmission zeros is even for symmetric responses or odd for asymmetric responses.

Transmission zeros knowledge (cont.)

𝑆21(𝑠) =𝑃(𝑠)

𝜀𝐸(𝑠)𝑆11(𝑠) =

𝐹(𝑠)

𝜀𝑟𝐸(𝑠)&

jω

σ

Position of roots of P(s)

+j

-j

Case1: Complex Pair

Transmission zeros knowledge (cont.)

jω

σ

Position of roots of P(s)

+j

-j

Position of roots of P(s)

jω

σ

+j

-j

Case2: Complex Pair

Case3: Pure Imaginary

Step 4: Define the physical topology (if necessary)

SynMatrix defaults to the folded-type topology. If the user-defined topology is not synthesizable, SynMatrix will either return the optimized result or an error message. SynMatrix now supports up to 90% of all topologies which can be used for a wide variety of engineering applications.

4AModify topology

Click on the “Edit Topology” button to enter the topology modification interface.

4A

Edit the checkboxes to modify the topology.

4B

4BEdit checkboxes

Topology setup.

Types of Topology Setups

Cascade Triplet(CT) CT+ Cascade Quadruplet(CQ)

Extend Box + CQ

CT+CQ Triple Mode + CT

Step 5: Click the “Calculate All” button to start the synthesis process

5AClick “Calculate All”

Step 5 (cont.)

After adjusting the filter order and TZs position, the final filter order is 9 and the TZ number is 4.

The unloaded Q value can be based on experience or the simulation.

To mitigate the risks from structural design and post-tuning workflow issues, the margin rules need to be applied as follows:• Set RL to be less than 3dB from the customer’s specification• The rejection level needs to be at least 3dB less than the customer specification

A lower RL level requires higher coupling energy, which may result in impractical coupling coefficients (ex. Planar and co-planar structures). Likewise, the lower rejection level may result in a small coupling coefficient value that can not be realized in real life.

Additionally, lower RL and transmission zeros levels may cause difficulties during test and tuning.

>7dB >7dB

>10dB

Supplementary Notes

Under Thermal Settings, choose the material. The corresponding coefficient of thermal expansion (CTE) will be automatically selected.

6A

6ASelect material

Input the specification environment requirement, then click the “Calculate” button. The thermal drift value will be returned.

6AEnter env. requirement

6ACalculate

6AEnter env. requirement

By considering the thermal drift value, the margins will be shown in the table below.

Step 6: Fine-tune the matrix and keep the proper design margins

The red square box means the current design fails to meet the thermal drift variation during ambient change.

6A (cont.)

Recall in Step 2C that the fine-tune (Shift) function is used to either expand/narrow the BW or shift up/down the frequency to balance the right/left frequency margins.

Fine-Tune (Shift) Function: The first value indicates the frequency shift and the second is BW tuning; all units for both parameters are in “MHz”

Freq Shift BW tuning

6A (cont.)

Left Margin RightMargin

Frequency Margin: The distance between the S parameter (S11/S21) and the specification line.

Group Delay and Power Analysis Tabs

Group Delay and Power Analysis tabs

Group Delay Curves from Group Delay tab

Stored Energy Curves from Power Analysis tab

Additional Features

Matrix Modifications

Matrix Modifications

Edit and load the matrix, export the matrix and S2P file, and change the signs