Z-parameters

Impedance parameters or Z-parameters (the elements of an impedance matrix or Z-matrix) are properties used in electrical engineering, electronic engineering, and communication systems engineering to describe the electrical behaviour of linear electrical networks that can be regarded as black boxes with several ports. They also describe the small-signal (linearized) response of non-linear networks. They are members of a family of similar parameters used in electronic engineering, other examples being: S-parameters, Y-parameters, H-parameters, T-parameters or ABCD-parameters.

Z-parameters are also known as open-circuit impedance parameters as they are calculated under open circuit conditions. i.e., Ix=0, where x=1,2 refer to input and output currents flowing through the ports (of a two-port network in this case) respectively. For a generic multi-port network definition, it is assumed that each of the ports is allocated an integer n ranging from 1 to N, where N is the total number of ports. For port n, the associated Z-parameter definition is in terms of the port current and port voltage, In and Vn respectively.

For all ports the voltages may be defined in terms of the Z-parameter matrix and the currents by the following matrix equation:

Where Z is an N × N matrix whose elements can be indexed using conventional matrix notation. Generally, the elements of the Z-parameter matrix are complex numbers and functions of frequency. For a one-port network, the Z-matrix reduces to a single element, being the ordinary impedance measured between the two terminals. The Z-parameters are also known as the open circuit parameters because they are measured or calculated by applying current to one port and determining the resulting voltages at all the ports while the undriven ports are terminated into an open circuit.