Scattering (S−) Parameters

Abstract

S-parameters are another means for describing multi-port networks. The scattering matrix ties port reflected/transmitted waves to incident ones. The waves have units of square root of power and have direct relations to terminal voltages and current. Calculations of S-parameters amount to selectively terminating ports, exciting a single port and measuring reflected/transmitted waves across all ports. We illustrate this process on many examples, culminating in a T-branch RC network. Scattering parameters, like their Z- and Y -sisters, are generally frequency dependent and complex. They are viewed by plotting magnitude/phase or real/imaginary versus frequency. S-parameters were invented in the RF world to deal with high-frequency issues that are difficult to deal with using other parameters. They form a complete description of networks and can be used virtually anywhere; for example they are the tool of choice for modeling packages and printed circuit boards. Lastly we wrap the chapter by deriving a direct relation between the S- and Z-matrices. Since S-parameters are yet another form of transfer functions, they lend themselves nicely to all of our spectral and convolution techniques.