How to obtain coupling coefficient between resonators?

how to find coupling coefficient

I will make a Hairpin-line Bandpass Filters which is made up of some coupling 1/2 wavelength resonators .Now I wonder how to get the external quality factor which change with the taped line position at the start and end resonator and the coupling coefficients between middle resonators.
I was told by full-wave simulator the data can be extracted.I wonder whether some people know the way.I will be grateful if someone tell you. TKS.

i HAVE the same problem too.
do you have the answer now?

Hi

I guess you have calculated your coupling coefficients and the Q-factors from the normalized filter-coefficients(g1, g2, g3.....).
The way to find the coupling coefficients, is to take lets say two resonators in the middle of the filter structure, this would be k12 or k23, between resonator 1 & 2 and between resonator 3 & 4.
Now as you say you can find these from simulation in ADS of some other CAD. The coupling coefficint between resonators are controlled by two parameters: width of the coupled line section and the gap between them.

The coupling coefficient can be expressed as Kij =±(f²b-f²a)/(f²b+f²a), where fa is the lower of the two resonant frequencies and fb is the higher one.

So by changing the width and gab between resonators and simulating S21, you will see two peaks at two frequencies. If you insert these into the above equation, you can calculate the coupling coefficients. If you do not see two peaks, then you should apply looser coupling at the input and output, which means you should change the port impedance.

It is the placement of the input port and ouput port, that determine your quality factors.

But this can become quite lengthy, so i can give you some good book about this:

Microwave resonators and filters for wireless communication: Theory, Design and Application by Makimoto and Yamashita.

Microstrip-line split-ring resonators and their application to bandpass filters by Mitsuo Makimoto. Electronics and communications in Japan, Vol. 72, 1989.

Microstrip Filters for RF/Microwave Applications by Jia-Sheng Hong &M. J. Lancaster.

Hope this helps or at least to give you some good references.

Regards

thanks for you help .
I'll try again.

hi thank you
bcas i too need this information

Problem!: How to obtain coupling coefficient between resonators?

I simulate two triangle using HFSS for calculate electric coupling coefficient. I dont see any two peak in S21!!! I loose coupling in feeds, but I dont see any two peak again! please help me.

---------- Post added at 14:21 ---------- Previous post was at 14:10 ----------

I simulate two triangle using HFSS for calculate electric coupling coefficient. I dont see any two peak in S21!!! I loose coupling in feeds, but I dont see any two peak again!
Resonators that I want to calculate their coupling coefficient, is in below URL.
https://obrazki.elektroda.pl/1_1322476950.png
How I must feed it???
please help me.