Help needed on defniition of S12 vs S21

A colleage and I are having a discussion about the meaning of the scattering parameters S12 and S21.

My belief is that if the system is perfectly matched (S11=S22=0), then the ratio of the signals at port 1 to port 2 are given by S21. So if the input to port 1 is 1 V, the output from port 2 is 10 V, then S21 is 10.

My colleage believes the opposite, in other words S12 would be 10. Reading

https://www.antenna-theory.com/definitions/sparameters.php

where it says:


S-parameters describe the input-output relationship between ports (or terminals) in an electrical system. For instance, if we have 2 ports (intelligently called Port 1 and Port 2), then S12 represents the power transferred from Port 1 to Port 2. S21 represents the power transferred from Port 2 to Port 1. In general, SNM represents the power transferred from Port N to Port M in a multi-port network.


My belief is the information at https://www.antenna-theory.com/definitions/sparameters.php is wrong, so I'm intersted in the views of others.

I must admit, I tend to trust https://www.antenna-theory.com/ far more than Wikipedia, but in this case, I think Wikipedia

https://en.wikipedia.org/wiki/Scattering_parameters#Two-Port_S-Parameters

is right.

Dave

Hi,

The S21 is the S transmit parameter from the port 1 to the port 2 and the ratio of a2/a1.
a1 is the complex electrical field 'measured on port 1' and a2 is the complex electrical field 'measured on port 2' .

The Sij parameters are the complex value type with two components : amplitude and phase or, real and imaginary.

If the modulus of S21=0 (-inf in dB) => not energy transmitted.
If the modulus of S21=1 (0 dB) => all energy transmitted, zero loss !! from port 1 to port 2 : a1=a2 and log(1)=0dB :-D

I hope to be clear...

BR

The first paragraph on the antenna theory page has multiple errors. Interestingly though the paragraph right below figure 1 does get the relationship right.

In the above Figure, S21 represents the power received at antenna 2 relative to the power input to antenna 1. For instance, S21=0 dB implies that all the power delivered to antenna 1 ends up at the terminals of antenna 2 (which isn't physically possible). If S21=-10 dB, this implies that 1 Watt delivered to antenna 1 (or 0 dB), ends up as -10 dB at antenna 2, or 0.1 Watts.

pstuckey said:

The first paragraph on the antenna theory page has multiple errors. Interestingly though the paragraph right below figure 1 does get the relationship right.

In the above Figure, S21 represents the power received at antenna 2 relative to the power input to antenna 1. For instance, S21=0 dB implies that all the power delivered to antenna 1 ends up at the terminals of antenna 2 (which isn't physically possible). If S21=-10 dB, this implies that 1 Watt delivered to antenna 1 (or 0 dB), ends up as -10 dB at antenna 2, or 0.1 Watts.

Click to expand...

I agree, there are multiple errors. Most obviously a confusion between power and voltage.

- - - Updated - - -

pstuckey said:

The first paragraph on the antenna theory page has multiple errors. Interestingly though the paragraph right below figure 1 does get the relationship right.

In the above Figure, S21 represents the power received at antenna 2 relative to the power input to antenna 1. For instance, S21=0 dB implies that all the power delivered to antenna 1 ends up at the terminals of antenna 2 (which isn't physically possible). If S21=-10 dB, this implies that 1 Watt delivered to antenna 1 (or 0 dB), ends up as -10 dB at antenna 2, or 0.1 Watts.

Click to expand...

I agree, there are multiple errors. Most obviously a confusion between power and voltage.

Had higher hopes for that website when first encountering it sometime back, but, sad to say it looks almost like a simple 'industry front' website ... this (these errors) only go to underscore or reinforce that thought.

Compare that website with:

. . https://www.microwaves101.com/

run by somebody with I would judge to have actually worked in the field with his subject.


_Jim