Polynomial synthesis in coupling matrix technique
Get the following book from the library and read chapter 8.
Microstrip Filters
for RF/Microwave
Applications
JIA-SHENG HONG
M. J. LANCASTER
....
8. Coupled Resonator Circuits
8.1 General Coupling Matrix for Coupled-Resonator Filters
8.1.1 Loop Equation Formulation
8.1.2 Node Equation Formulation
8.1.3 General Coupling Matrix
8.2 General Theory of Couplings
....
Without cross-coupling, the synthesis is still easy. With cross-coupled resonators it becomes demanding.
If it helps, i can generate the polynomials for you. But i need a specification (passband(s), stopband(s), ripple, transmission zeros, etc.)
Thanks for the guidance niki.......
I have gone through the relevent content of the book, but its totally about the coupling technique, although its required but as a startup for this tech., I need polynomials for the synthesis of which I've faced several problems. The required specs are passband (5.5 to 5.85 GHz) i.e. 2 Tx zeros at these frequency points.The resonant frequency of the filter, fo=5.8GHz with 190MHz bandwith. while return loss/equiripple loss is 20-22 dB.
Moreover, I also need a systematic explanation to implement filter synthesis by this technique. Till now, I have inferred that,
1) first we need polynomials S11 and S21 etc containing filter requirements (Tx zeros, ripples etc).
2). Make a coupling matrix using these polynomials.
3). now, Convert the coupling matrix coefficients into physical values of the elements (C or L) whic will be used in a physical structure of filter.
4). Thus design of a filter, completed.
Kindly make it confirm to me, is this understanding of mine is true or not?
Please check/correct the specifications:
passband from 5.5 to 5.85 gives a bandwidth of 350 MHz
center frequency f0=5.8GHz with 190 MHz leads to a passband from 5.705 to 5.895 GHz
Are the transmission zeros correct with 5.5 Ghz and 5.85 GHz ?
Possibly a typo somewhere...
These para. are wrt the S parameter graph you can find in the attachment.
Moreover, I also need a systematic explanation to implement filter synthesis by this technique. Till now, I have inferred that,
1) first we need polynomials S11 and S21 etc containing filter requirements (Tx zeros, ripples etc).
2). Make a coupling matrix using these polynomials.
3). now, Convert the coupling matrix coefficients into physical values of the elements (C or L) whic will be used in a physical structure of filter.
4). Thus design of a filter, completed.
Kindly make it confirm to me, is this understanding of mine is true or not?
For filter approximation, it is better to work with the so-called characteristic function K.
There you can directly tune the reflection and transmission zeros (see attachement).
To understand this, you need to completely solve a "simple example" by hand.
Afterwards you can use a good software tool for it. This topic is a bit tricky and takes some time to get started.
I am unable to find the attachment from your previous reply..... would you please suggest me some material to do simple examples from there. I also think, rather than to post questions repetitively, some by-hand examples will clear my concepts well. In lancaster's book, there are no as such examples to be done.
Moreover was that K in ur previous reply a "coupling coefficient"?
I will prepare an example, but I need some time.
Important: The theory is not easy to understand, it took me almost a year to study the relevant literature.
Regards
Peter
You can refer the website: www.synmatrix360.com to see the synthesis case. It also includes the computer aided tuning function to assist you simulation.
okay .... i'm waiting for that.
Hi,
I need this response if filter. Would you please suggest me how to start from the very base to synthesis a filter with such a response using coupling matrix tech. How can I make proper polynomials from the given specs (fo=5.8 G BW=150 M giving more than 20 db of return loss, equiripple is obvious from the attached figure.) and then how to
1.evaluate order?
2.draw/ design a prototype?
3.draw a coupling matrix from that?
4.optimize the matrix?
5.extract physical dimensions?
Current method for the synthesis is as follows:
1. Direct synthesis of the coupling matrix.
2. Transformation of the coupling matrix to get different topologies.
3. Extract physical dimensions.
For step 1 and 2 read the IEEE-papers
"General coupling matrix synthesis methods for Chebyshev filtering functions"
Richard J. Cameron.
"An analytical technique for the synthesis of cascaded N-tuplets cross-coupled resonators microwave filters using matrix rotations"
S. Tamiazzo; G. Macchiarella
In the appendix I have given a few examples. But I need more informations about the specs of the stopband(s).
For step 3 you need a software tool.
@@@I am working on the directions mention in your most last reply.
Side by side I also want to know about the aattached image. What is its usage? I have just saw it from a literature but could'nt findout any further info. about it. It seem ias some matlab toolbox which can help us in doing the mathematics, in generating polynomials and matrices, without doing it manually with hands.
Some people have written algorithms and programs that replace handwork. But this requires deep understanding and a lot of effort.
You are a lucky guy if someone provides you with such a tool for free.
Questions:
Do you know the meaning of the polynomials F, P and E?
Have you already determined a transfer function yourself (using the characteristic function K=F/P)?
If not, then take a simple example in a book and trying to understand the example.
Without this knowledge, it is difficult to discuss the synthesis of a coupling matrix.
I can only help if I know what you know.
I can give you a simple example of a classic LC network, where you can see the use of the polynomials P, F and E.
What kind of info do you need?
Well, I am following the referred papers and cameron book, and till now I have the knowledge about:
1. Basics of P E F,
2. how to generate P and F (unfortunately, not E at this time....for this I am further doing the literature review)
I have done this following steps given in an Cameron's example(last pages of chap6)(But interestingly I have'nt found the K=F/P factor throughout these examples.....Is that an easy way to do the Poly. synthesis?.....)
Overall, At this time I am following your 8th December reply....?
Should I continue with that in the same flow as described in that reply? Is there any need for the example which u may provide to me on request.
Thank you so much for rapidly-responding to my queries.
Things I Know:
"poly. generations"
Things I want:
point A:"First of all, I want the confirmation; This work is totally by-hand based or whether there are tools to done the stuff quickly. This manual work is taking too much ofmy time."
point B: "a sequential, short n brief, ellabortion to obtain prototype physical filter which I can use in my Simulation work to confirm its response. As far as my understandings are concern, I think this is the flow.....
.............evaluate order>>evaluate polynomials>>draw a coupling matrix from that>>optimize the matrix>>extract physical dimensions of required filter"
point C: "optimization steps of coupling matrix to acheive desired results."
Information regarding point A and B is urgent...
I don't think you have time to understand everything. You need a tool for the synthesis of the coupling matrix. I can deliver certain data, but I can't explain everything (it takes too much time).
Questions:
Which simulation software do you use?
Can you analyze a coupling matrix (frequency response)?
Do you understand the difference between a normalized and an unnormalized coupling matrix?
What concrete data should I provide to help you?
(frequencies, coupling factors, LC-values...)
Answers:
I have no tool at this time, for CM synthesis.
For simulation, I use HFSS.
No I cant analyze its spectrum
No, I cant understand the difference very well.
if have foundout this tool @Dedale@ https://www-sop.inria.fr/apics/Dedale/
it can be used to findout coupling matrix from order, polynomials etc info. Any suggestions from your side.
I have'nt try this, but , want to confirm whether this coupling matrix can be later on translated to some physical structre RLC
I think you can use this tool, but it does not replace the user's experience. You have to evaluate the many structures (topologies) and choose the "best" ones.
Look at the example in the attachement: Try to analyze the coupling matrix (frequency response). Try to analyze the LC-network.
In this simple example, there are not many topologies. Later I will show an example with a lot of possibilities for the topologies.
simply.pdf