Measurement of S-Parameters

[Electro11]

In the measurement setup , I was going through the theory and I don't understand where the 2 comes from in the equation to find the S parameter S21. ( ie. S21 = 2V2/VG1) Why is it there??

 

[GOTWW]

If your reference impedance is normallized to 1 ohm the s21
is (v2/vg1)^2 as I recall. Maybe you have a misprint.

 

[GOTWW]

The above answer was not correct, This would represent the "power". The formal definition for S21 is b2/a1 when a2=0 (ie. the output port is connected to the reference impedance). Therefore, If the device is matched at input and output, VG1=a1, and V2=b2, so S21=V2/VG1.

 

[S21]

My point is that this is because of normalization of amplitude. From book:
Reinhold ludwig & Pavel Bretchko
"RF Circuit Design Theory and Applications"
Page 171-172
You can find solution there.
By the way, I have a question here,too. Does somebody know why we should normalize here? I feel confuing for the normalization factor in those formulas.

 

[GOTWW]

When you perform calcualtions based on voltage & currents such as when using ABCD parameters, normallizing to 1 ohms really cleans up the equations. You can renormilize to the real port impedances when you are finished.