Is S21 a voltage gain or power gain ??

Hi all,

This question might be too easy for you But, I am so confusing, since from the definition of S parameter, it is defined as a ratio of voltage (or current) signal. So, it should be a voltage gain. However, I have seen in several papers mentioning it as a power gain ??? How come ? Please suggest ....

Thank you,

DYL

S21 is similar to a voltage gain. Technically, it is the ratio of transmitted/incident "wave amplitudes".

Since on a transmission line, you can have forward and reverse travelling "wave amplitudes", you can not simply call them "voltages" since you can not measure them at a point with something like a pyhsical voltmeter. If you did have a "microwave voltmeter" and stuck it on a transmission line, at that one point it would measure the superposition of both forward and travelling wave amplitudes.

Think of looking out at the ocean. There can be waves coming into shore, and other waves bouncing off of piers, rocks...the height of the water is a superposition of all those waves.

If you wanted the power gain, you would measure S21 and square it [S21²]. For example, if you had a "3 dB attenuator pad", you would measure its S21 magnitude to be approximately 0.707. If you wanted to know how much it attenuated power, you would then use Pout/Pin=(.707)²=0.5. In other words, a 3 dB pad drops the power by half.

Oh, thank you very much for this quick and clear answer. However, I still have a confusion, by just squaring the ratio of magnitude, how do you get power ??? How about the resistance of interest, since power is somehow related to resistance ?

Thank you very much again,

DYL

You may want to consult the S parameter definition to answer the question yourself. S parameters are based
on a characteristic impedance (e.g. 50 ohm), for this reason you can always convert S21 into a power gain.

A relationship between input & output, similar as dB, what you can then apply in voltages or powers (..20log/10log..)...
K.

Not POWER, but POWER RATIO...a dimensionless quantity. Like Pout/Pin =
5 watts/1 watts=5, or 7 dB.

I had this issue too.

The trick is that Power or Voltage Gain can be in dB...

The main caveat is S-Parameters are used mainly in 50Ω systems (RF/Microwave).

So P = V²/Z !

ratio = P1/P2==> {V1²/Z1}/ {V2²/Z2} !
Note that if we are in a 50Ω system Z1≡Z2=50 !
So:
ratio = P1/P2 ≡ V1²/V2² ! (50 Ω / 50 Ω = 1).

So to answer your question S21 is BOTH voltage gain & power gain .

Cheers

Hi Element_115,

Thank you very much for your explanation. However, is it exactly the same that S21 is both power gain and voltage gain ?? By definition, S21 is a ratio of voltage wave, not a ratio of power quantity. Is it correct that we need to square magnitude of S21 to get a power gain ?

Best regards

DYL

DoYouLinux said:

Hi Element_115,

Thank you very much for your explanation. However, is it exactly the same that S21 is both power gain and voltage gain ?? By definition, S21 is a ratio of voltage wave, not a ratio of power quantity. Is it correct that we need to square magnitude of S21 to get a power gain ?

Best regards

DYL

Click to expand...

Yes and no....

"Ratio of Voltage" = v1/v2 !
(Note Px=Vx^2/Zx !)
v1= √(P1*Z1)
v2= √(P2*Z2)

==> ratio of voltage = v1/v2 = √[{P1*Z1}/{P2*Z2}] ! If Z1=Z2 (50 Ω)
==> ratio of voltage = v1/v2 = √[P1 /P2] ....

If Z1 ≠ Z2 then it would not be true.

You know how some times you see EQ's with 10*Log(...) and other times
20*Log(...)? Well the 20 is from (10*2):

A*Log(B^2)==> (A*2)*Log(B).
It's related.


Cheers

Hi Element_115,

Thank you for the explanation again. Yes, it might be confusing that [S21]^2 is power, and Small-signal power gain (dB) =10*log[S21]^2 = 20*log[S21]
which is S21 in dB

DYL

hi all, i got some question on antenna gain measurement with network analyzer.
I got three antenna, two dipole and one tested antenna.
First , i connect dipole antennas to both port 1 and port 2 of network analyzer and then measure the S21 (dipole-dipole). The gain of dipole antenna is known
After that, i change the receive antenna to the tested antenna and then measured the S21(dipole-tested antenna)again.
S21(dipole-tested antenna)-S21 (dipole-dipole) = G relative
G tested antenna= G relative + G dipole

Am my concept or methods correct? I am urgently need some advice on this issue. Anyone please share your idea with me.
Thank you and best regards
long88

Antennas are a different story. Scope this out: