Impedance 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 behavior of linear electrical networks.

They are also used to 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,[1] Y-parameters,[2] H-parameters, T-parameters or ABCD-parameters.

[3][4] 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.

A Z-parameter matrix describes the behaviour of any linear electrical network that can be regarded as a black box with a number of ports.

A port in this context is a pair of electrical terminals carrying equal and opposite currents into and out-of the network, and having a particular voltage between them.

The Z-matrix gives no information about the behaviour of the network when the currents at any port are not balanced in this way (should this be possible), nor does it give any information about the voltage between terminals not belonging to the same port.

Typically, it is intended that each external connection to the network is between the terminals of just one port, so that these limitations are appropriate.

In general 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.

In this case the relationship between the port currents, port voltages and the Z-parameter matrix is given by: where For the general case of an N-port network, The input impedance of a two-port network is given by: where ZL is the impedance of the load connected to port two.

is a diagonal matrix having the square root of the characteristic impedance at each port as its non-zero elements,

is the corresponding diagonal matrix of square roots of characteristic admittances.

In these expressions the matrices represented by the bracketed factors commute and so, as shown above, may be written in either order.

[5][note 1] In the special case of a two-port network, with the same characteristic impedance