Implementing Kramers–Kronig causality check on real VNA s-params

[yefj]

Hello , Kramers–Kronig need infinite BW but I measure s-params from 0 to 70GHZ.
how do you reccomend to deal with the missing data?
Thanks.

 

[Baluncore]

To work perfectly, Kramers-Kronig requires a bandwidth from DC to daylight, but perfection is impossible, so you must settle for less.

The same is true in time domain reflectometry, TDR, where the incident step must be instant and the sampling rate infinite. For that you must buy a more expensive storage oscilloscope, say, with a BW of 100 GHz and a sampling rate of 240 Gss.

The advantage of time domain reflectometry, is that you do not need an IFFT or an integration, but TDR still has the bandwidth problem of Gibb's Effect, which breaks causality by appearing before the step.

 

[yefj]

Hello Baluncore,what is the proper way to implement Kramers-Kronig on my s-params which has only 10MHz-67GHz? for causality checking.

 

[Baluncore]

It will depend on the format of the data available.
Google AI to find papers and code.

 

[yefj]

Hello Baluncore, first I need to do the extrapolation .
In the article they say that they use the polinomial but they dont say how they got the polinomial coeffients.
Is there a manual that explains better the polinomial extrapolation methedfology in the Kramer -Kronig method?