s1p manipulation - how to implement a quarterwave impedance transform for all freqs?

Hello

Short version: Please could someone explain how would I implement a phase offset to an existing s1p data file I have captured in order to effect a lambda/4 transformation for every data point? Do I just add "90" to the "degrees" column?

background: I've measured the input Z of a resonator - it's a fairly high impedance (not matched to the usual system Zo) and hence the reflection coefficient approaches unity at all frequencies. The Smith chart trace is in the "detuned open" position and, for the measurements I want to do, I need to transform it to the "detuned short" position.

Normally I would use the "phase offset" control on the VNA to rotate the position of the resonant point (X=0) so that it ends up positioned on the real axis, but now at the low impedance end. However, for various reasons I have had to record the s1p data without that transform being applied.

I'm left with an s1p data set of the form

GHz MA

1.100000 1.000 -0.408
1.200089 0.999 -0.406
1.300179 0.998 -0.380
...
...
...
2.249777 0.999 0.561
2.49888 1.000 0.582
2.50000 1.000 0.584

and I want to transform it numerically (using Octave for example) to it's phase shifted equivalent. I modelled a quarterwave line with zero loss in order to apply the impedance transform I wanted, but of course, that's only valid at one frequency - in my case, the resonant point of the resonator - so outlying points don't receive the correct phase shift.

Please can someone put me on the right track? I've confused myself.

Thanks

Roger Freeman

Well, think about it. Lets say you have an S11 measurement of a pure open circuit, i.e. |1| angle 0 degrees. Lets say you add 10 degrees of line length between that S11 measurement and the new port. So the new incident wave would go down the line 10 degrees, and the reflected wave would go down the line another 10 degrees. So the New S11' measurement will be rotated by 20 degrees.

so IF the transmission line you are adding is 50 ohm line, and if it is 90 degrees long, then the S11' data is shifted 180 degrees.


If you only want to rotate phase by 90 degrees, just either add or subtrace 90 degrees from the angle of S11

Biff44 - thanks. It makes sense; I'm not sure why I couldn't understand my own thoughts, but I did indeed muddle myself up. Yes, considering the "journey" which a wavefront has to make from a source to a load then back again, it's a two-way transit time so the round-trip is two lots of electrical length.

Time to do some simple maths - thanks biff44

edit - yes, a bit of AWK script to add 180 to the <angle> column and the new rotation now looks correct.