s parameter to capacitance

I've saw many article discuss inductor measurement and modeling.

Recently I meet problem to get a capacitance from 2-port S parameter measurement of a interdigital capacitor.

Thanks for discuss and reply.

use TRL calibration and make the full 2-port calibrate, then do test on VNA.Save the measurement result in Touchstone formats and use circuit simulator to extract the equivalent parameter.

you can use circuit fit to the S parameter.
to do this,many tool can be use,such as MWO...

Hi
just use some formulas that relate the the Sij parameters to the measured or simulated line structure:

- ch(g.l)=((1+S11)*(1-S22)+(S12*S21))/(S12+S21)

- Zc=
Zr*sqrt(((1+S11)*(1+S22)-(S12*S21))/((1-S11)*(1-S22)-(S12*S21)))

- R = Real(g*Zc)
- L = (Imag(g*Zc))/w
- C = (Imag(g/Zc))/w
- G = Real(g/Zc)

g: is the propagation constant =a+jb (a: attenuation, b=2*pi/wavelenght)
R: resistance
L: self induction
C: capacitance
G: admittance
Zc: Characteristic impedance
l: length of the line
ch: hyperbolic cosine
Zr: Characteristic impedance of the measurement system: usually 50Ohm

A less formal method (compared to the proposed by elek_fyc), is put the 2port s matrix into a linear simulator (ADS, Harmonica, MWO Genesys, etc), then short port 2 to GND, now you have an 1 port circuit. analyze and plot s11 in R+jX. format.
The imag. part is the reactance.

Give me the possibility to add a short note about real part: The equivalent Series Resistance. For my opinion, the typical accuracy of VNA measurement is not sufficient to get accurate knowledge of tand (or Q or ESR)

use the network analyazer to measurement

I agreed with pewang. TRL is an accurate way to measure the inductance and perform deembedding for capacitance extraction.

Hallo Everyone,

elek_fyc, where did you get all this formulas from...... do you have the references where I can go and look them up....?

You can measure the 2 port Y parameter, or convert the S parameter to Y parameter, or simulate with a tool to get the Y parameter from S parameter file. After you get the 2 port Y parameter, you can get the capacitance with this:
C = -1/(imag(1/Y11)*2*pi*freq)
where, freq is the frequency correspinding to the S parameter data.

Here, elek_fyc posted how to get capacitance in terms of s parameters. But if i want to get the capacitances of a parallel coupled line (microstrip), then there is two types of capacitances involved, gap capacitance (cg) and parallel capacitance (cp)...how can i get the specific capacitance values from the s parameters? Can anyone please tell me ....