Scattering Parameters - Higher-order S-parameter Matrices

Higher-order S-parameter Matrices

Higher order S-parameters for pairs of dissimilar ports, where may be deduced similarly to those for 2-port networks by considering pairs of ports in turn, in each case ensuring that all of the remaining (unused) ports are loaded with an impedance identical to the system impedance. In this way the incident power wave for each of the unused ports becomes zero yielding similar expressions to those obtained for the 2-port case. S-parameters relating to single ports only require all of the remaining ports to be loaded with an impedance identical to the system impedance therefore making all of the incident power waves zero except that for the port under consideration. In general therefore we have:

and

For example, a 3-port network such as a 2-way splitter would have the following S-parameter definitions