# Group delay calculation through S-parameters extracted from a touchstone file

1. Aug 16, 2012

### rizias

Hello everyone,
I am working on the group delay of the front end filter of a GPS system. I am given the measurements of the S parameters of the filter in a touchstone file (s2p) in the following format.
! S-Parameter for B3521 in Touchstone format with Magnitude (lin) and Phase
! Normalised impedance: 50 Ohm. Measurement system: 50 Ohm. Ta=25°C
! B3521_SB.S2P not matched. Measurement full 2-port calibrated incl. Port.Ext.
! Start: 1.3GHz, Stop: 1.8GHz, Span 500MHz 801 Pts., Step 312kHz.
! Date: 21/03/07 - EPCOS SAW COM WT AE PD; AB !

MHZ S MA R 50

! freq magS11 angS11 magS21 angS21 magS12 angS12 magS22 angS22 1.300000E+03 9.676685E-01 -7.491579E+01 2.369824E-04 1.706093E+02 2.323036E-04 1.696126E+02 9.564306E-01 -8.052716E+01…..
That I want to do is to model the group delay of the particular filter in matlab, pass through it a signal and comment on the introduced distortion. I can understand that I can calculate the group delay through the angle of the transmission coefficient (S21).But I cannot understand how,while I have only numbers,I don’t know how to take the derivative needed for calculating it (if it is the only way of finding it) .
Isn’t it that the tg=(-1/360)*dfi/df,if it is how do I take the derivative of a number while it is zero?

2. Aug 16, 2012

### yungman

I am no expert in the group delay this way, I just join in and talk. So don't take me too serious.

I look at the definition of group delay, it defines the delay of the signal from input to output, which also implies delay of each of the frequency component of the signal. from input to output. If this is true, can this be done frequency by frequency of the input signal? You have the S21 in magnitude and phase, so you know the amplitude and phase change of each of the frequency component of the signal. So by knowing the period (T) of each of the frequency component and knowing the phase shift from S21, you can calculate the time delay of each of the component.

So if you know the frequency components of the input signal, you calculate the delay of each and then recombine them after passing through the DUT. Just make sure the S parameters cover the whole frequency range.

I know nothing about Mathlab, so I won't even try. Again, this is interesting, I am just joining in.

One concern any mismatch will add components into the output, This will complicate the situation as the reflection mixes in with the forward signal and you get the sum. So unless you have perfect matching of all the frequency components, you have to take into consideration of the input and output reflection coef $\Gamma$. But you should still be able to calculate. If you dig up RF book, you get the equation and just change from phase to time delay. You just do this on every frequency component. Again, I am just talking out loud with you.

Last edited: Aug 16, 2012