getting Zc from measured gamma

Hallo,

i measured the complex propagation constant gamma from MSL with Thru-Reflect-Line Calibration.
Papers from Dylan and Marks (NIST) explain how to calculate the complex characteristic impedance from the measured gamma.

gamma / Z = jwC + G
gamma * Z = R + jwL

RC+LG = Im (gamma * gamma) / jw

If we neglect G and use Rdc (measured) as R, we can solve for the capacitance
per unit length.

Then it is possible to obtain Z in magnitude and phase from gamma / Z = jwC.


The calculated phase looks good compared to HFSS calculation, but
there is an offset in the calculated magnitude of Z.
The frequency dependency seems good, but agreement to the HFSS simulation is only given, if I add a value of about 55 to it.

Can anybody see the mistake.....


elektr0

Hi, elektr0:

I have not read teh paper. However, I don't think you can find Zc from Gamma only. You can have different kinds of TLN with the same Gamma while the Zc can be quite different. There must be some other available parameters. Otherwise, you should not be able to solve for the Zc.

Best regards,

Same gamma but different Zc is possible. This is right.

The line specific parameters, which are used in addition are the line capactitance C and the dielectric resistance 1/G.
The method is based on the assumptions G=0 and C is determined from Rdc.
Rdc depends on the line geometry.

Hi, elektr0:

I assume Rdc is the R at DC. It is dependent upon the cross-section area of the strip and the ground. It does not seem to me we can find C from the R at DC because C is dependent upon the width of the strip and the distance of the strip to the ground and the permittivity of the substrate, while Rdc is kind of independent of the strip to ground distance.

Regards.

electr0,

I have never used that particular method. I never trusted our measurements for R, and the requirement G = 0 does not hold for FR4.

I've use another Williams and Marks method for Zo. See Williams, Marks, and Davidson, "Comparison of on wafer calibrations", ARFTG Conference Digest, Dec. 1991. This paper can be downloaded from Dylan's (via NIST) website. The idea is that the probe from TRL calibration can be written as a section of transmission line and an impedance transformer. From the probe's cascade matrix you can calculate the Zo of the line, and as a bonus, it works well for lossy lines.

-Wiley

Ok..I read an Ieee about measuring TL cap , and I try the method in the lab, the method will give good agrement till 1 Ghz , if u measure the capacitance
via the Rdc, also Rdc must be measured using the 4-point method.
On the other hand u must keep in mind that HFSS will give u a non trusted result for low frequency and try to model your structure correctly , by consider the wave port and not the discrete port , because the if u placed arbitrarly u may have excess curent.
Hope that will help a little ...