Admittance (Y) and Impedance (Z) Parameters
Consider the modeling of an n-port device. The relation between voltage v and current i at the ports is in the s-domain, given via the admittance matrix Y by:
Y is a symmetrical, complex-valued matrix of dimension n × n. Alternatively, the port behavior may be characterized by the impedance matrix Z, which is the inverse of Y:
An n-port device, with port voltages and currents, can be visualized as follows:
S-parameters characterize the relation between incident and reflected waves at the device ports when terminated by reference impedances.
Typically, a 50 Ω or 75 Ω reference impedance is used, matching the characteristic impedance of common measurement cables. At the ports we have the following relations:
Where subscripts i and r denote incident and reflected wave, respectively. Z0 is a diagonal matrix whose jth entry holds the reference impedance at the jth port. The s-parameter is defined as:
Finally the EMT-type, time-domain Norton equivalent circuit is:
