Extraction of Effective Dielectric constant.
Actually, i simulated a coplanar stripline structure and retrieved s-parameter,gamma values as matrix data and exported that file to matlab (.m file). Now i want to extract and plot effetive dilelctric constant using the above values. can somebody help me with such formulas or its matlab file.
Thanks in advance
Hi Ashish
i am not sure how you would get effective dielectric value from simulation.but the equations for calculating the effective dielectric constant are as below.
epsiloneff=1+(epsiolonr-1)(K(k')K(k1))/2*K(k)K(K1')
Where K=a/b
K'=sqrt(1-k^2)
K'=sqrt(1-k1^2)
K1=sinh((pi*a)/4h))/sinh((pi*b)/4h)
Hope you will find it useful in calculating your simulated value of epsilon effective.
Regards
Rotmanlens
Hi ashish,
you should find the wavelength in the line. It should be possible from you data, for example from the phase of s21 and the line length.
Then, considering that the wavelength in the line is the wavelength in free space multiplied by sqrt(epsilon_eff), you can get epsilon_eff.
Regards
Z
Thank you Zorro for your reply. But can give me some more detailed explanation considering i have a matrix data of phase of s21 and dimensions as w=0.025 in, s=0.004, t=0.003 in, h=0.01 in epsilonr=10.2, length=1 in (as it is a propagating structure and not radiating, length is unconstrained) with frequency range being 2ghz to 12ghz and solution frequency=9ghz.
---------- Post added at 12:45 ---------- Previous post was at 12:35 ----------
Thank you Rotmanlens for your reply. I have already gone through these formulas in one of the books. But to much concern is that mine is a case of artificial dielectric substrate which changes in s parameter curves according to different types of discontinuities that i place inside host substrate RT/Duroid. So effectively s parameter curves are the ones which are of my help and recently I heard someone talking about NRW Approach regarding this but i am still confused. Please help me.
Hi Ashish,
In order to be clear, please let's take the actual data.
Can you give values of s12 ?
Regards
Z
How have you done your simulation?
Was the transmission line terminated?
The transmission line needed not to be terminated. You can rely on the 2-port S parameters to extract the effective permittivity. The detailed equations should be available in classical textbooks talking about transmission lines. BTW, IE3D has a build-in function to extract the effective permittivity and characteristic impedance etc based on the simulated S-parameters.
Actually i have simulation results in HFSS 12, don't know much about IE3D. There is one more thing tn ask in hfss12, it has option for plot of "epsilon" v/s frequency; what this plot is? Is it the effective dielectric constant or something else. Please help in suggesting the "classical books" that you mentioned also please help me on NRW approach.
Thank you.
To zorro, i will soon upload the matlab file of phase of s parameters.
Thank you.
HFSS is fine. I mentioned IE3D just because its built-in function of permittivity extraction is easier to use.
You can refer to Pozar's classical book "Microwave engineering, 3rd ed". On page 208, there is a table telling how to relate the ABCD matrix (which can be deduced based on the S matrix simulated) with the transmission line parameters.