# S-Parameters of lossy two-port network

I have a lossy passive two-port network with some input mismatch, so, $$S_{11} \neq 0$$ By simulation, I find the S11 and S21 parameters. What I would like to know is the losses within the network, when a wave is incident at port 1. I first thought it should be $$1 - |S_{11}|^2 - |S_{21}|^2$$ because what is not reflected and not transmitted must be lost within the network. However, a discussion with a colleague gave rise to the idea that $$S_{21}$$ is somehow contained within $$S_{11}$$... So, is it possible to find the losses from S-Parameters?

• Are you willing to assume all the non-reflected input energy is usefully put to work? in wiggling a gate or base, to generate some transconductance. Cgs or Cbc provide direct paths from input to output, and vice versa. StabilityFactors have to take the combined FORWARD/BACKWARD energy movements into account. – analogsystemsrf Apr 10 '17 at 8:56

How is $S_{21}$ contained in $S_{11}$? By the definition of S-parameters, $S_{11}$ is the amount of wave leaving the two-port from port 1 when all other ports are terminated in a matched load, and a wave is incident on port 1. $S_{21}$ is the wave energy leaving port 2 due to an incident wave on port 1. Therefore, your original statement is correct, in that the power lost (assuming all energy absorbed in the two port is loss) is:
$$1 - |S_{11}|^2 - |S_{21}|^2$$
$$|S_{11}|^2 + |S_{21}|^2 = 1$$ $$|S_{22}|^2 + |S_{12}|^2 = 1$$