Group delay calculation through S-parameters extracted from a touchstone file 2

[rizias]

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?
Thank you in advance for your reply.

 

[biff44]

Attached find and .xlx example of how to manually calculate group delay from phase measurements. It is a simple calculation, but you need to get the units right.

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Maguffin Microwave wireless design consulting

 

[rizias]

Thank you very much!

 

[hacksaw]

nice summary

 

[biff44]

No problem. I had to do that manual calculation for a project because, even though I have used Group Delay's hundreds of times before, when I actually tried to manually calculate it out I was way off until I hunted down the right units.

I did just see one small error in the nomenclature. Where there is a column named "delta frequency [GHz}" it really should say "delta frequency [GRad/Sec]".

http://www.MaguffinMicrowave.com

Maguffin Microwave wireless design consulting