# Theory behind S parameters

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#### tronixbug

##### Newbie level 6
can s12 be used as a parameter which specifies the transmission coefficient?
can this formula be used for the gain
gain=20logl(s12)l
and
insertion loss=-20logls12l

with input VSWR as high as 30:1 can the device operate efficiently

#### boy

s parameters

There are 3 sections of gain. S11, S21 and S22 (assume that S12 = 0). For the detail, you can look at Gonzalez's book. generally, S21 will be the gain if both S11 and S21 are matched for maximum gain. Also it depends on where do you measured.

#### pit

##### Full Member level 4
Re: s parameters

tronixbug said:
can s12 be used as a parameter which specifies the transmission coefficient?

Forward transmission coefficient is S21, not S12! Only on a fully passive two-port device with only isotropic materials S21 and S12 are reciprocal (theoretically). For example if you have ferrite beads S21 and S12 are not reciprocal any longer.

In general:

S11: input port voltage reflection coefficient
S21: forward voltage gain
S12: reverse voltage gain
S22: output port voltage reflection coefficient

You may have a look here:

https://en.wikipedia.org/wiki/Scattering_parameters

with input VSWR as high as 30:1 can the device operate efficiently

This is awfully bad, matching should not exceed 1.5:1, depending on application. You should do something about matching here. Of course 30:1 is far far away from being efficient.

CU

#### DDavid

##### Full Member level 5
Re: s parameters

Next articel will answer to you question

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