How to get this transfer function?

Hi,
When I read the online tutorial, it gives this transfer function. I wonder where the '2' in the denominator comes from. In elsewhere I see a matched condition would result S21/2, but it doesn't mention a matched condition here.

Can you tell me something about the '2'?

Best Regards,

Robert

Gamma_in is not the transfer function. It actually stands for the reflection at port 1 when port 2 has the reflection coefficient gamma_l. When port 2 is perfectly terminated, gamma_l = 0, then gamma_in = S11 as expected.



I would think the factor 2 comes from the definition of the transfer function. It is the voltage ratio between load and source. The source impedance will lower down the voltage on the load. When both Gamma_l and Gamma_s equal to 0, S21 = 1, the transfer function = 1/2 as expected.

I knew Sin is not a transfer function.
Transfer function was shown in the first attached picture. I upload it again here:

It doesn't say S11=0. How do you get S21=1?

Thanks for your reply.

I just assume the simplest case to check if the formula is correct. If you would like to derive the formula yourself, one method is to convert the S-parameter matrix to Z-parameter matrix, then you will get the voltage transfer function.