Admittance parameters

Admittance parameters or Y-parameters (the elements of an admittance matrix or Y-matrix) are properties used in many areas of electrical engineering, such as power, electronics, and telecommunications.

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] Z-parameters,[2] H-parameters, T-parameters or ABCD-parameters.

[3][4] A Y-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 Y-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 Y-parameter matrix are complex numbers and functions of frequency.

For a one-port network, the Y-matrix reduces to a single element, being the ordinary admittance measured between the two terminals.

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

The Y-parameters of a network are related to its S-parameters by[5] and[5] where IN is the identity matrix,

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

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 and real characteristic admittance

The following expressions show the applicable relations: where In this case

Vice versa the Y-parameters can be used to determine the Z-parameters, essentially using the same expressions since and