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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.

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

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