Filter Design Blog


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41 thoughts on “Filter Design Blog

  1. Hi,
    I came across your blog today. You’re doing a very good job at educating people in this interesting topic, filters are not boring 🙂 I recently started my own blog for coupling-matrix based filter design mostly using my own software, Couplings Designer. I’m planning on adding lots of tutorials covering basic stuff and the newest approaches to modern advanced filter designs. As this is more of a hobby to me and since I love to learn new stuff maybe we could work on some interesting articles together? You seem to have LOTS of experience in this subject! Go to and have a look!

    By the way, if you have an iPhone and want to try my software I could give you the full version for free. Feedback from actual filter experts is always welcome!

    1. Hi Göran,
      Thanks for dropping by. I am trying to add new content, but writing something meaningful always takes time.
      Great on the Couplings designer. Filter design on an iPhone sounds like fun!
      I have done some work on CAT – computer aided filter tuning recently. Unfortunately, it cannot be made public.
      Will check out your website and contact you.

      take care and keep up the good work


  2. Hello everybody,

    I’m a student from Germany and was developing a waveguide filter for a student project. The whole filter and waveguide theory can be somehow hard and complicated which needs some time to understand, but after making some progress I got stuck because the solution for tuning a filter cannot be found directly via Google. I knew that the problem had to do something with the concept of coupling and that’s how I landed on

    I wrote an Email to Dieter who immediately answered and was able to identify the problem very quickly, which lead me to taking the development on a very huge step further. I profited a lot from Dieter’s expertise regarding to simulation technique, mathematical and physical insight of filter and waveguide theory and of course because of his general system overview. Furthermore, it is very pleasant corresponding with him because he is not just a great engineer but a good person as well.

    From a technical point of view, I don’t think I could have found out the important key knowledge he taught me or maybe it would have taken a huge period of time. Finally, I just want to thank you Dieter for your excellent work and help which, was a great benefit for me and hopefully for more people.

    Keep up the good work 😉

    1. Hi Daniel
      Glad to have been able to help a little.
      best wishes for your future

  3. hello every body.
    im a student.and my project is combline filter with(bandwidth1-2 Ghz).
    I want design combline filter with hfss of this project.can help me?please anybody has this file,sent it to my email.

    1. Have you considered reading the relevant literature ?

  4. This site is a gem!

    I had a nagging doubt on the filter synthesis using the coupling matrix method. I’d be honest here : one month of pondering and search did not lead me to the right result. Then, yesterday I came across this blog. If the quality of the material doesn’t impress then hold on, I mailed Dieter my question. I got my reply the same night. Fast, precise , in-depth with few presentation slides. Thank you so much, Dieter. Keep up the good work.

    1. Hi Kirti
      Glad to have been able to help a little.
      Good luck

  5. Hello everybody,
    I have a question about cavity filter design, I’m new in the RF Filters,
    while finding the coupling coefficient between two resonators I’m using eigenmode solver but I dont know what does the modes mean? which mode should I choose in eigenmode solver ? and my cavity filter design consists of 6 cavities how to calculate the rest of coupling coefficients between cavities (3th,4th,5th,6th cavities)

    Thank you for your help…

    1. Hello Ferit
      I suggest you first study the Eigenmodes of two coupled cavities. The theory is covered in many books and publications. If you have access to IEEE MTT, then just search for “filter resonators, eigenmodes”. The papers by Prof. K. Zaki are very good.
      The Eigenmodes are the natural resonances of a coupled resonator structure. Whereas both resonators by themselves resonate on the same frequency, the coupling between the resonators creates two resonances or “modes”. These resonances are symmetrical about the resonant frequency of the individual resonator.
      Fundamentally, the first two Eigenmodes of a symmetrical structure with two resonators directly provide the coupling bandwidth. CBW = |mode(1) – mode(2)| is the simplified relationship. CST has a CBW calculation in the template based post-processing. You need to calculate 2 modes. There may also be examples on the CST website.
      For your 6-pole filter you can simulate all couplings in isolation by creating 2-resonator models for each coupling, ignoring the other couplings. This may not be 100% accurate, but it will give you a good starting value for the dimensions of the coupling. I assume that your filter is a narrowband filter with a small relative bandwidth (BW/fc <= 10%). Good luck Dieter

      PS: If you have access to “Microwave Filters for Communication Systems” by Cameron, Kudsia, Mansour, please read pages: 507 – 511.

      1. Dear Mr Dieter,
        Thank you very much for your detailed information. I’ll take into consideration your valuable advices.

  6. Dear Dieter,
    I have question again about the cavity filter, I designed a six-pole cavity BPF(in CST), but I need to insert two cross coupling inside that. One of them is L and the other C. How should I proceed to do this and what is the methods?

    1. Dear Ferit,

      The mainline couplings in a combline filter are inductive. So the “L” cross-coupling is an iris. The “C” cross-coupling will be a capacitive probe. If you Google pictures of combline filters you can see examples of probes. You design the cross-couplings just like you do the mainline couplings. Build a two cavity model in CST and measure the resulting coupling. Vary the dimensions of the probe or iris until you get into the right region. Then plot a coupling curve around the desired region.


  7. Hi, I’m a EE/Phy Phd student trying to model some special cases of transmission lines containing FSS.

    I have tried to apply HFSS eigenmode solver to a transmission line problem in a fashion very similar to what you have described in “Other Eigenmode analysis applications” section of your site. (I found your site while locking for an answer to this problem)

    In my particular case modal driven HFSS solver is out of a question since HFSS doesn’t support wave-ports touching master-slave boundary or a rationally periodic floquet-port.

    The problem manifests when I’m trying to find propagation constant of a lossy line via eigen frequency of its section.

    I think that relation (beta = f/c) between eigen frequencies and propagation constant breaks down for complex values of both (gamma=s/c), due to ill defined wave-speed in lossy non-TEM line. Should c be complex too, since wave is losing energy, and am i left with enough information form complex f (s) to solve for gamma, or is the problem ill defined without additional field information dependent on a loss distribution (conductor/dielectric).

    Does this question even sound coherent enough for you, or have I jumbled some concepts in my head?

  8. Hallo everybody,
    I am a student from Germany. Over the last couple of weeks I have had to design a dielectric triple mode filter. I designed the filter but unfortunately it is not producing the correct S-Parameters.
    I wrote to Mr. Dieter Pelz an email. I was very amazed to have received a quick reply with the necessary corrections in my design and explanation as to why my design was not functioning rightly. Mr. Pelz is not only an experienced and great engineer but also a kind and nice person. Thank you very much indeed for your help. I will recommend this site to all my fellow students.

  9. Hello,

    I enjoy this site—thank you.

    Hey, with regard to your textbook list, and Daniels’ text, there is the comment “Contains many listings of FORTRAN code.” It is more obscure than that; it is a language called Telcomp II. Appendix A has everything one needs to understand the listings in Telcomp II. It is a very simple language. It is one of my favorite textbooks on filters.


    1. Hi Gregory
      I finally got to correcting the Daniels book description. I am grateful for your correction.

  10. For those of you in Europe, there will be a class on cavity filter design in Dresden, Germany, June 3-5. A lot of practical content.

  11. hello
    I am a student from Algeria, how can I calculate the coupling coefficient between two waveguide resonator, I am beginner in CST.
    Is this coupling coefficient the same one of the coupling matrix M.

    1. Hi
      The coupling coefficients for realising a particular filter response are quite independent of the physical filter structure. Yes, the couplings are the same as those in the coupling matrix. In CST you can use Eigenmode simulation of a 2-resonator model. There is a post-processor that directly calculates the coupling bandwidth or the relative coupling. Read the chapter on Eigenmode analysis:
      good luck

  12. Hi Dieter,
    Thank you every much for sharing the information. There is so much to learn at your website make me feel like a student again and again.
    Long Bui

  13. Dear Dieter,

    First of all I would like to congratulate you with your beautiful site and helpful blog. I am currently a PhD student working on the extraction of the coupling matrix from measured or simulated scattering data (especially in the case where multiple solutions exist).

    I am however less specialized in the physical implementation of the filter structures. I have a question concerning the feeding structures in the case of microstrip line technologies. I currently have a design that works fine for 1 GHz. The design consists of so called ‘square open loop’ resonators. I would however like to increase the the central frequency to 2 GHz while maintaining the same fractional bandwidth, as a consequence I scale the resonators (divide their length by approximately 2) . Now I also decrease the width of the resonators lines, because otherwise the resonators start looking like full metal squares. I design the filter for 50 Ohm loads, therefore I choose the widths of the feeding lines such that they have a characteristic impedance of 50 Ohms as well. This makes that the feeding lines are much wider than resonators (almost 2 times as wide), such that I can no longer use a tapped-feed-line structure. Therefore I would like to use a coupled-feed-line structure. In literature (Hong), I have found some examples of such structures. There is however something that I do not understand: where the feeding line couples with the resonator it becomes much more narrow. I do not understand why and also I do not understand how much narrower it should become. Do you know why they do this and whether there are some design rules to choose how much narrower the line should become?

    Kind regards,


    1. Hi Matthias
      Thanks for dropping by. I’ll try and help.
      You say you scaled the physical resonators by approx. 1/2 to move fc from 1GHz to 2GHz. Given that this is a microstrip filter, the scaling must be done on the electrical length, taking into account the effective permittivity of the structure. That would lead to a physical length reduction of less than 1/2.
      On your other question, I would need to see the filter layout before I can answer. For the end-resonators you can simulate these alone and adjust the coupling structure for the nominal end-loaded Q values. covers this subject as well. If you are using CST then this is very easy to do using the appropriate template based post-processing.

      good luck


  14. The approach one uses to realized an RF filter that meets design targets can be critical to a successful design. However, determining which methods are most applicable to the type of filtering you are trying to put together can be a navigation leading to many dead ends if these methods aren’t well categorized and explained. The ‘Filter design by synthesis’ section does a very good job in covering these different methods and helped me a lot with this overwhelming navigational task for my filter application. Also, I found the ‘Key papers & books on LC filter synthesis’ extremely useful in honing in my approach to realizing my LC filter networks. The resources in that section were very helpful, more so that any other references I’ve come across.

    Great site!


  15. Hi Dieter
    Your description on microwave iris filter design routine and your help with coping with challenges such as de-embedding waveport to measure external quality factor and the effect of loading of inductive irises on resonance frequency of resonators was really effective.
    Your step by step supervising guided me to finish my simulation of microwave iris filter and your never-expected manner shows your professionalism.
    Thank you very much

  16. Hello Dieter

    This site is very useful.Thanks a lot for your effort,Sir.

    I came across a specification like:

    Group Delay Variation:

    1)Can you please explain parabolic group delay and how is it measured?

    2)How are these interrelated?

    3)What is the significance of these parameters in communication systems, espicially parabolic group delay?

    Thanks & Regards

    1. Hi Sreejith
      Group delay variation is a measure for signal distortion often found in filter specifications. For the definition of GD please see my website. One can distinguish between linear GD variation and other variations. Linear denotes the unsymmetry of GD with reference to a center frequency. Parabolic GD is an approximation of the GD response versus frequency using a parabolic function. As such, parabolic GD variation does not exist in practice but is instead a reduction of the actual GD to its parabolic portion. I am not aware of the possibility of measuring parabolic GD separately. What exists is the GD response versus frequency. GD ripple is usually a +/- variation of GD with reference to a mean value. Modern data transmission modes are relatively immune to GD distortion.

  17. Hi Dieter

    Thank You very much for sharing the information.


  18. Hi Dieter,

    The web site is looking great!
    I am teaching in Europe in Sept 2017 for those who are interested.

    Best regards,


  19. I followed the paper by Cameron and could find the polynomials except E(s). I would be grateful if someone could tell me how to arrive the the characteristic Hurwitz polymial.

    1. Answered by direct e-mail.

  20. Hi, I am working on arriving at the coupling matrix for a filter. But I am getting negative values for the self coupling elements in the matrix. Is this wrong. Can anyone tell me if there is any mistake in my approach.

    Thanks and regards.

    1. Sorry for delay. In principle, negative coupling values are valid. The sign denotes the nature of the coupling: capacitive or inductive. If by self-coupling you mean the input and output couplings, then a negative value is probably incorrect.

  21. Hi. Is there anyone who could help me with the reduction of a coupling matrix so as to make it a realizable one. Lots of doubts arise as on how to choose the pivot etc.

    Thanks in advance.

    1. I suggest you study the various examples provided in Richard Cameron’s IEEE MTT papers.

  22. Hi,
    how to do the optimization of a coupling matrix using gradient based approach. Can anyone send supporting materials for the same.

    Thanks in advance.

    1. There are various approaches for this. Generally, you can chose starting values for the couplings on the basis of a monotonic Chebyshev response filter. Thereafter, you add weak cross-couplings and restore the passband return loss while leaving the cross-coupling constant. You may find the recent work by Daniel Swanson helpful.

  23. Hi all,
    I am working on elliptic filter. I want to find the prototype element values for an elliptic filter. I could find the element values for 0.1 dB insertion loss in Book by Hong and lancaster. My requirement is 0.25dB pass band insertion loss. How to find the element values for this specification. i could find the filter order to be 5. For this filter order how to proceed to the element values.

  24. I think you mean 0.1 dB and 0.25 dB passband ripple (due to reflective loss). Insertion loss is always due to dissipation in the filter resonators. 0.25 dB is a very high value for a passband ripple. Maybe you are mixing up two things. 0.25dB might indeed be the insertion loss at fc and that is determined by the unloaded Q of the resonators (also by filter degree, bandwidth and filter response).
    If you are designing a bandpass filter, there is a design process which you can find in R. Cameron’s papers. Alternatively, you can use an optimisation based approach using a circuit simulator. Tables for elliptic filter prototype elements usually relate to those with fixed transmission zeroes.

  25. I am trying to reproduce results given in the paper:
    I can easily obtain results for 2.45 GHz on the substrate with height 1.27 mm, dielectric constant 10.8 in HFSS 13.

    I would like to get same design curves for another substrate for example: height 0.508 mm and dielectric constant 6.15. For square open loop resoantor with 1 mm gap it yields for the same frequency size a = lamda/2 * 1/8 + 2*w = 11.3 mm where w is the width od the 50 ohm microstrip.

    But unfortunately I can’t get any resonant peaks (like in that case near resonance so I can’t figure out coupling coefficient like in the previous. What I am doing wrong?

    1. Did you consider the effect of the change of dielectric constant on the overall length of the resonators ?

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