RF and Microwave Engineering: Fundamentals of Wireless Communications

Chapter 5

Scattering Parameters

The electrical behaviour of linear multi-port networks is generally described by matrix equations. Different matrices like the impedance matrix Z or admittance matrix Y are commonly used. The voltages and currents of the different network terminals are then related by a linear system of equations.

In the RF and microwave frequency range we most often use the scattering matrix S that follows a slightly different approach. At higher frequencies network ports are generally connected to transmission lines that bridge distances between the multi-port network under consideration and other circuits. From our discussion in Chapter 3 we know that forward and backward propagating voltage and current waves can exist on such lines. By means of a suitable normalization of the voltage waves we finally arrive at power waves. Scattering parameters now relate these incoming and reflected waves at the ports of the terminal.

Scattering parameters bring practical benefits: in order to determine the elements of the S-matrix we connect the ports to transmission lines and measure incoming and reflected power waves. A vector network analyser (VNA) can perform this task up to very high frequencies. Direct measurement of voltages and currents at the terminals of a network becomes more and more difficult with increasing frequency. Furthermore, the voltage is not uniquely defined for non-TEM wave modes. By connecting the multi-port network to transmission lines the network ...