capacitance, inductances at high frequencies

[mfarhan1]

fastmodel fasthenry

Dear all
I know the question I am putting is asked many times with different context but I couldn’t find a straight forward response to it, so I seek your advice.

Let say I have modelled a capacitor (or inductor) in EM simulation tool, now the most common method to measure capacitance (or inductance) is measuring the imaginary part of Y11. Now this makes sense but as we go higher in frequency the imaginary part doesn’t represent only capacitance (or inductance) but parasitic inductances as well, so to measure imaginary part is not a valid approximation anymore.

How to find capacitance or inductance now?

One solution that comes to my mind is to use the lump equivalent model of inductor or capacitor. Let say I know the capacitor equivalent lump model (shown in figure) now again how do I find the values of all components which gives the same final reactive component. People say use SPICE model now I am new to it, as far as i know it has few predefined models like Pi ledder rational polynomial etc which gives equavalent values but can i somehow put my capacitor model in SPICE and get the lumped components values?

Many thanks looking forward to your responces

 

[Abhishekabs]

Hi mfarhan1
I have 1 suggestion.
Say You have simulated, designed and made a microstrip or lumped capacitor/inductor.
Try measuring Capacitance & Inductance using LCR meter.
and cross check.

 

[mfarhan1]

@Abhishekabs
Thanks for your reply.
I want simulated results because i want to make a design kit for helical inductor and MIM capacitor so measuring is not a feasible option,
Any other suggestion

 

[bala_uzzal]

Hi mfarhan1,
If you know the geomtery then you can compute capacitance and inductance at high frequency using FastCap and FastHenry (with the help of FastModel editor). It is free, you will find it https://www.fastfieldsolvers.com/

Best regards,
Uzzal

 

[Idan]

Hi, if I understand your question correctly you may be able to get approximate results for a capacitor by assuming Z = SQRT(ESR^2+(Xl-Xc)^2). While Xl = ωL and Xc = 1/ωC. If you can have the Z(f) versus frequancy function data from your simulation tool then the lower point will represnt the ESR and by deriving the function far enough from the turning point you can calculate the inductance.

 

[madengr]

The capacitance is dominant at low frequencies and minimal transmission line effects. So measure S11 with the other DUT terminal open and you are measuring C11||(C12+C22); "+" means in series, "||" means in parallel. Now short the terminal to measure C11||C12. If you assume C22=C11 you can compute C12, or reverse the DUT to obtain a 2nd measurement to solve for all three unknowns.

Now you need to find the 1st resonant frequency (series resonance). You can do this from S21 of a series measurement, but better to put the DUT in shunt and measure the frequency and depth of the notch. From the resonant frequency you can determine L11+L22, and from the depth of the notch you can determine R11+R22. Of course technically the R and G can be obtained from a DC measurement, but they are a function of frequency so you could get different results, and G is so small you could not measure R.

Then you would compare the lumped model response to measurements and tweak it more.

So really it's a matter of measuring at low, high, and resonant frequencies, and terminating the output with opens and shorts. From this you can extract values for the lumped elements. You can even lift the DUT away from the ground plane to minimize C11 and C22.

If you read up on small signal model extraction they will detail some of the methods.