The Designer's Guide Community Forum

The Designer's Guide Community Forum
https://designers-guide.org/forum/YaBB.pl
Simulators >> RF Simulators >> s-parameter calculation using ac analysis
https://designers-guide.org/forum/YaBB.pl?num=1266168115

Message started by R. Zakai on Feb 14^th, 2010, 9:21am

Title: s-parameter calculation using ac analysis
Post by R. Zakai on Feb 14^th, 2010, 9:21am

Hello,
Just wondering if anyone knows where I can find formulas to manually compute s-parameters using nodal voltages from ac analysis. I have taken a shot at calculating these formulas myself but I have run into some ambiguities with s21 and Ap. If someone already has those formulas and has used them with confidence, I'll greatly appreciate if you can share them with me.
Rehan

Title: Re: s-parameter calculation using ac analysis
Post by pancho_hideboo on Feb 14^th, 2010, 9:39am

R. Zakai wrote on Feb 14^th, 2010, 9:21am:

Just wondering if anyone knows where I can find formulas to manually compute s-parameters using nodal voltages from ac analysis.

It is very easy. You can find such formula in any basic circuit or filter theory text book.
See http://www.designers-guide.org/Forum/YaBB.pl?num=1215827287/3#3

As direct method, assume port impedances(=reference impedances), R₀₁ and R₀₂ are all real.
Available power of port1 is Pa=(|E|/2)²/R₀₁
Power delivered to port2 is Pload=|V₂|²/R₀₂

|S₂₁|²=Pload/Pa=(2*|V₂/E|)²*R₀₁/R₀₂

S₂₁=(2*V₂/E)*sqrt(R₀₁/R₀₂)=(V₂/(E/2))*sqrt(R₀₁/R₀₂)

Here "E" is an open circuit voltage of port1. And E/2 is not equal to V₁ generally.

S₂₁ is different from conventional voltage gain V₂/V₁ even if R₀₁ is equal to R₀₂.
Also |S₂₁|² is different from conventional power gain Pload/Pin.

About meaning of "E", see the following and my related previous posts.
http://www.designers-guide.org/Forum/YaBB.pl?num=1237656418/3#3

As another method, evaluate Y or Z parameters by AC analysis.
Then convert them to S parameters.
See http://www.rfcafe.com/references/electrical/s-h-y-z.htm

Title: Re: s-parameter calculation using ac analysis
Post by Frank Wiedmann on Feb 15^th, 2010, 12:57am

See http://w7zoi.net/S-param%20extraction.pdf and the last paragraph of http://www.designers-guide.org/Forum/YaBB.pl?num=1251245633/3#3.