How to export the imaginary part ereff'' from propagation constant gamma?

Hallo,

i measured the propagation constant gamma of an embedded microstrip line.
With v= c/sqrt(ereff) und b=2 pi/v
i get ereff. Only the real part ereff'.
But how can i also export the imaginary part ereff''.

Thanks

If you know complex gamma, use the formula gamma = sqrt(epsr_eff)*k0. Assuming all permeabilities are unity.

If you don't know complex gamma, we need more information. Are your data from simulation or measurement? If the latter, what type of measurement? How accurate do you need alpha?

@Wiley.

Thanks for your answer.

The complex gamma is from onwafer measurement with Thru-Reflect-Line Calibration.

Do you mean k0^2=w^2 mu epsilon - j w kappa mu ?

This way, i need epsilon_r and kappa values from the substrate.
Is there no way to get e=e'-je'' without this information ?

electr0

electr0,

Nope, I mean k0 = 2*pi*f/c0 where c0 is the speed of light in free space. In free space gamma and k0 should be equal. The ratio between gamma and k0 is the effective relative permittivity (assuming mu_r = 1).

For TRL, the error in gamma is second order, so it should be quite accurate.

-Wiley

@ Wiley.

Ok thanks, it works.

But it is the same relation i already used to get real(ereff) from imag(gamma)=beta.


velocity = c/ sqrt( ereff) und imag(gamma) beta = omega / velocity.

Your suggestion is: using the complex gamma, instead of the real part = beta.


Thanks.

@ Wiley.

As I already said last time, there is a straightforward relation between beta = imag(gamma) and the real ereff (permittivity).

Your suggestion was to use the complex gamma in this relation instead of beta.
It gave good looking results, but if I think about it gives me a headache.

If I extract G and C from gamma and Zc (characteristic impedance) we get quite different values for tangent delta or imaginary part of er.

tanD=G/wC

tanD= - Im( ereff ) / Re ( ereff )

Any ideas ?

to all others:

how can i get the complex ereff from measured propagation constant gamma (embedded microstrip line).

er = er' - j er''

tanD = er''/er'

thanks.