06 March, 2007

Two Port Networks - Z , Y , h , g , ABCD Parameters

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

Z-model : In the Z-model or impedance model, the two currents I1 and I2 are assumed to be known, and the voltages V1and V2can be found by:

where


Here all four parameters Z11,Z12 ,Z21 , and Z22 represent impedance. In particular, Z21 and Z12 are transfer impedances, defined as the ratio of a voltage V1(or V2) in one part of a network to a current I2(or I1 ) in another part . Z12 = V1 / I2 . Z is a 2 by 2 matrix containing all four parameters.
Y-model : In the Y-model or admittance model, the two voltages V1 and V2 are assumed to be known, and the currents I1 and I2 can be found by:

where



Here all four parameters Y11,Y12 ,Y21 , and Y22 represent admittance. In particular, Y21 and Y12 are transfer admittances. Y is the corresponding parameter matrix.

ABCD -model : In the A-model or transmission model, we assume V1 and I1 are known, and find V2 and I2 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 I2 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 V2 and I1 are known, and find V1 and I2 by:

where



Here h12 and h21 are dimensionless coefficients, h11 is impedance and h22 is admittance.

g model :In g model or inverse hybrid model, we assume V1 and I2 are known, and find V2 and I1 by :


where



Here g12 and g21 are dimensionless coefficients, g22 is impedance and g11 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:

Anonymous said...

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

Arun said...

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?