Two-port network

 Two-port network

A two-port network (a kind of four-terminal network or quadripole) is an 

electrical network (circuit) or device with two pairs of terminals to connect to 

external circuits. Two terminals constitute a port if the currents applied to them 

satisfy the essential requirement known as the port condition: the electric current 

entering one terminal must equal the current emerging from the other terminal on 

the same port. The ports constitute interfaces where the network connects to other 

networks, the points where signals are applied or outputs are taken. In a two-port 

network, often port 1 is considered the input port, and port 2 is considered the 

output port.

The two-port network model is used in mathematical circuit analysis techniques 

to isolate portions of larger circuits. A two-port network is regarded as a "black 

box" with its properties specified by a matrix of numbers. This allows the response 

of the network to signals applied to the ports to be calculated easily, without solving for all the internal voltages 

and currents in the network. It also allows similar circuits or devices to be compared easily. For example, transistors 

are often regarded as two-ports, characterized by their h-parameters (see below) which are listed by the 

manufacturer. Any linear circuit with four terminals can be regarded as a two-port network provided that it does not 

contain an independent source and satisfies the port conditions.

Examples of circuits analyzed as two-ports are filters, matching networks, transmission lines, transformers, and 

small-signal models for transistors (such as the hybrid-pi model). The analysis of passive two-port networks is an 

outgrowth of reciprocity theorems first derived by Lorentz.

In two-port mathematical models, the network is described by a 2 by 2 square matrix of complex numbers. The 

common models that are used are referred to as z-parameters, y-parameters, h-parameters, g-parameters, and 

ABCD-parameters, each described individually below. These are all limited to linear networks since an underlying 

assumption of their derivation is that any given circuit condition is a linear superposition of various short-circuit 

and open-circuit conditions. They are usually expressed in matrix notation, and they establish relations between the 

variables

 V1 , voltage across port 1

 I1, current into port 1

 V2 , voltage across port 2

 I2, current into port 2

which are shown in figure 1. The difference between the various models lies in which of these variables are regarded 

as the independent variables. These current and voltage variables are most useful at low-to-moderate frequencies. 

At high frequencies (e.g., microwave frequencies), the use of power and energy variables is more appropriate, and 

the two-port current-voltage approach is replaced by an approach based upon scattering parameters.

The port conditions

The port condition is that a pair of poles of a circuit is considered a port if and only if the current flowing into one 

pole from outside the circuit is equal to the current flowing out of the other pole into the external circuit. 

Equivalently, the algebraic sum of the currents flowing into the two poles from the external circuit must be zero