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For one of the four S-parameters - the S21 - why is that S21 can be translated as 2Vout/Vgen?

Is there a simple explanation for it?

JRE
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kintaro
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    Because that's the definition of S21. – SteveSh Oct 31 '21 at 11:40
  • Have you read: https://en.wikipedia.org/wiki/Scattering_parameters ? The definition there: \$s_{21} = \frac{V_{out}}{V_{in}} \$ doesn't match your formula: \$s_{21} = 2 \frac{V_{out}}{V_{gen}} \$. Yours could still be correct depending on what \$V_{gen}\$ is and what the source/load impedances are. You should draw the circuit for which your formula applies. – Bimpelrekkie Oct 31 '21 at 11:43

1 Answers1

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S21 is the output voltage divided by the input voltage when the "circuit being measured" is properly impedance matched to the source and correctly impedance loaded on the output.

So, the act of applying an ideal voltage source (\$V_{GEN}\$) via a matching impedance to the "circuit being measured" is to reduce the actual input voltage to the "circuit being measured" by 2. Hence, with respect to the ideal voltage source (\$V_{GEN}\$), S21 has to be: -

$$\dfrac{V_{OUT}}{V_{GEN}/2} = \dfrac{2\cdot V_{OUT}}{V_{GEN}}$$

Andy aka
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