Electronic – S21 parameters multiplication

S-parameters can be used at any range of frequencies that's the first point. The second point is understanding what a simple matrix of s parameters represents because two of the parameters are reflection coefficients and although they are of interest (generalism alert!) at any frequency, they tend to be ignored (because they don't offer any significant benefit) at (say) audio frequencies. The reason is because in audio, outputs tend to be low impedance whilst inputs tend to be high impedance. This kind of makes s-parameters to unwieldy for any circuit analysis other than when matched impedances are used. That leaves RF generally.

The long answer is set up the problem like this:

^{simulate this circuit – Schematic created using CircuitLab}

Now calculate the forward and reverse-travelling waves at each of the ports. This gives you \$S_{11}\$ and \$S_{21}\$.

Then hook up the generator on the other side of the device and calculate the forward and reverse travelling waves again to get \$S_{12}\$ and \$S_{22}\$.

But since you are already using ADS, there is an easier way: Hook up your device model between S parameter ports and simulate it. This will also make it easier to make ADS draw a graph comparing the simple model with the more complex model.

If your "theoretical" model is a simple combination of R, L, and C elements, you could even use the ADS optimizer to tune the theoretical model to match the phenomenological model (or vice versa), or to match some measurement data.