Admittance parameters

Admittance parameters or Y-parameters are properties used in electrical engineering, electronics engineering, and communication systems engineering describe the electrical behavior of linear electrical networks when undergoing various steady state stimuli by small signals. They are members of a family of similar parameters used in electronics engineering, other examples being: S-parameters, Z-parameters, H-parameters, T-parameters or ABCD-parameters.

The General Y-Parameter Matrix

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 Y-parameter definition is in terms of input voltages and output currents, $V_{n}\,$ and $I_{n}\,$ respectively.

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

$I=YV\,$

where Y is an N x N matrix the elements of which can be indexed using conventional matrix(mathematics) notation. In general the elements of the Y-parameter matrix are complex numbers.

The phase part of an Y-parameter is the spatial phase at the test frequency, not the temporal (time-related) phase.

Two-Port Networks

The Y-parameter matrix for the 2-port network is probably the most common. In this case the relationship between the input voltages, output currents and the Y-parameter matrix is given by:

${I_{1} \choose I_{2}}={\begin{pmatrix}Y_{11}&Y_{12}\\Y_{21}&Y_{22}\end{pmatrix}}{V_{1} \choose V_{2}}$.

where

$Y_{11}={I_{1} \over V_{1}}{\bigg |}_{V_{2}=0}\qquad Y_{12}={I_{1} \over V_{2}}{\bigg |}_{V_{1}=0}$

$Y_{21}={I_{2} \over V_{1}}{\bigg |}_{V_{2}=0}\qquad Y_{22}={I_{2} \over V_{2}}{\bigg |}_{V_{1}=0}$