A pair of terminals at which a signal (voltage or current) may enter or leave is called a port.

Here all four parameters

Here

where

Here

For more details on this topic visit the following links :

http://fourier.eng.hmc.edu/e84/lectures/ch3/node11.html

http://en.wikipedia.org/wiki/Two-port_network

http://web.cecs.pdx.edu/~ece2xx/ECE222/Slides/TwoPortsx4.pdf

A network having only one such pair of terminals is called a one 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 "black box" with a set of distinctive properties, enabling us to abstract away its specific physical buildup, thus simplifying analysis. Any circuit can be transformed into a two-port network provided that it does not contain an independent source.

A two-port network is represented by four external variables: voltage and current at the input port, and voltage and current at the output port, so that the two-port network can be treated as a black box modeled by the the relationships between the four variables , , and . There exist six different ways to describe the relationships between these variables, depending on which two of the four variables are given, while the other two can always be derived.

**Note**: All voltages and currents below are complex variables and represented by phasors containing both magnitude and phase angle. However, for convenience the phasor notation and are replaced by

*V*and

*I*respectively.

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

Input voltage V1

Output voltage V2

Input current I1

Output current I2

Input voltage V1

Output voltage V2

Input current I1

Output current I2

**Z-model**: In the Z-model or impedance model, the two currents

*I*1 and

*I*2 are assumed to be known, and the voltages

*V*1and

*V*2can be found by:

where

Here all four parameters

*Z*11,*Z*12 ,*Z*21 , and*Z*22 represent impedance. In particular,*Z*21 and Z12 are transfer impedances, defined as the ratio of a voltage*V*1(or*V*2) in one part of a network to a current*I*2(or*I*1 ) in another part .*Z*12 =*V*1 /*I*2 .**Z**is a 2 by 2 matrix containing all four parameters.**Y-model**: In the Y-model or admittance model, the two voltages

*V*1 and

*V*2 are assumed to be known, and the currents

*I*1 and

*I*2 can be found by:

where

Here all four parameters

*Y*11,

*Y*12 ,

*Y*21 , and

*Y*22 represent admittance. In particular,

*Y*21 and

*Y*12 are transfer admittances.

**Y**is the corresponding parameter matrix.

**ABCD -model**: In the A-model or transmission model, we assume

*V*1 and

*I*1 are known, and find

*V*2 and

*I*2 by:

where

Here

*A*and*D*are dimensionless coefficients,*B*is impedance and*C*is admittance. A negative sign is added to the output current*I*2 in the model, so that the direction of the current is out-ward, for easy analysis of a cascade of multiple network models.**H-model**: In the H-model or hybrid model, we assume

*V*2 and

*I*1 are known, and find

*V*1 and

*I*2 by:

where

Here

*h*12 and*h*21 are dimensionless coefficients,*h*11 is impedance and*h*22 is admittance.**g model :**In g model or inverse hybrid model, we assume*V*1 and*I*2 are known, and find*V*2 and*I*1 by :where

Here

*g*12 and*g*21 are dimensionless coefficients,*g*22 is impedance and*g*11 is admittance.For more details on this topic visit the following links :

http://fourier.eng.hmc.edu/e84/lectures/ch3/node11.html

http://en.wikipedia.org/wiki/Two-port_network

http://web.cecs.pdx.edu/~ece2xx/ECE222/Slides/TwoPortsx4.pdf

## 2 comments:

Can you tell me what applications that use this two-port method? Please, It's my homework.

Given ABCD parameters for a n/w how do i calculate the following

1)i/p impedance

2)o/p Impedance

3)charecteristic impedance of a n/w?

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