Two-port network

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Example two-port network

A two-port network (or four-terminal network, or quadripole) is an electrical circuit or device with two pairs of terminals. Examples include transistors, filters and matching networks. The analysis of two-port networks was pioneered in the 1920s by Franz Breisig, a German mathematician.

A two-port network basically consists in isolating either a complete circuit or part of it and finding its characteristic parameters. Once this is done, the isolated part of the circuit becomes a blackbox with a set of distinctive properties, enabling us to forget about its specific physical buildup, thus simplifying analysis. Any circuit can be transformed into a two-port network provided that it doesn't contain an independent source.

The parameters used in order to describe a two-port network are the following: Z, Y, h, g, T. They are usually expressed in matrix notation and they establish relations between the following parameters:

V 1

Input voltage

V 2

Output voltage

I 1

Input current

I 2

Output current

1 Z-Parameters (or Impedance Parameters)
2 Y-Parameters (or Admittance parameters)
3 h-Parameter (or Hybrid parameters)
4 g-Parameters (or Inverse Hybrid Parameters)
5 Transmission Parameters

[edit] Z-Parameters (or Impedance Parameters)

${V_1 \choose V_2} = \begin{pmatrix} Z_{11} & Z_{12} \\ Z_{21} & Z_{22} \end{pmatrix}{I_1 \choose I_2}$ .

where

$Z_{11} = {V_1 \over I_1 } \bigg|_{I_2 = 0} \qquad Z_{12} = {V_1 \over I_2 } \bigg|_{I_1 = 0}$

$Z_{21} = {V_2 \over I_1 } \bigg|_{I_2 = 0} \qquad Z_{22} = {V_2 \over I_2 } \bigg|_{I_1 = 0}$

[edit] Y-Parameters (or Admittance parameters)

${I_1 \choose I_2} = \begin{pmatrix} Y_{11} & Y_{12} \\ Y_{21} & Y_{22} \end{pmatrix}{V_1 \choose V_2}$ .

where

$Y_{11} = {I_1 \over V_1 } \bigg|_{V_2 = 0} \qquad Y_{12} = {I_1 \over V_2 } \bigg|_{V_1 = 0}$

$Y_{21} = {I_2 \over V_1 } \bigg|_{V_2 = 0} \qquad Y_{22} = {I_2 \over V_2 } \bigg|_{V_1 = 0}$

[edit] h-Parameter (or Hybrid parameters)

${V_1 \choose I_2} = \begin{pmatrix} h_{11} & h_{12} \\ h_{21} & h_{22} \end{pmatrix}{I_1 \choose V_2}$ .

where

$h_{11} = {V_1 \over I_1 } \bigg|_{V_2 = 0} \qquad h_{12} = {V_1 \over V_2 } \bigg|_{I_1 = 0}$

$h_{21} = {I_2 \over I_1 } \bigg|_{V_2 = 0} \qquad h_{22} = {I_2 \over V_2 } \bigg|_{I_1 = 0}$

[edit] g-Parameters (or Inverse Hybrid Parameters)

${I_1 \choose V_2} = \begin{pmatrix} g_{11} & g_{12} \\ g_{21} & g_{22} \end{pmatrix}{V_1 \choose I_2}$ .

where

$g_{11} = {I_1 \over V_1 } \bigg|_{I_2 = 0} \qquad g_{12} = {I_1 \over I_2 } \bigg|_{V_1 = 0}$

$g_{21} = {V_2 \over V_1 } \bigg|_{I_2 = 0} \qquad g_{22} = {V_2 \over I_2 } \bigg|_{V_1 = 0}$

[edit] Transmission Parameters

${V_2 \choose I_2} = \begin{pmatrix} A & B \\ C & D \end{pmatrix}{V_1 \choose I_1}$ .

where

$A = {V_2 \over V_1 } \bigg|_{I_1 = 0} \qquad B = {V_2 \over I_1 } \bigg|_{V_1 = 0}$

$C = {I_2 \over V_1 } \bigg|_{I_1 = 0} \qquad D = {I_2 \over I_1 } \bigg|_{V_1 = 0}$

This technique is exactly analogous to the use of ABCD matrices for ray tracing in the science of optics. See also ray transfer matrix.

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