# Circuit Theory : Two Port Networks

By Yash Bansal|Updated : November 16th, 2021

In this article, you will find the study notes on Two Port Network which will cover the topics such as Z-parameter, Y-parameter, h-parameter, g-parameter, T-parameter, Interrelationship between different types of parameter & Series, Parallel and Cascade connection of Two Port networks.

TWO PORT NETWORK

• A pair of terminals through which a current may enter or leave a network is known as a port.
• Two-terminal devices or elements (such as resistors, capacitors, and inductors) result in one-port networks.
• The four-terminal or two-port circuits are used in op-amps, transistors, and transformers.
• Two Port Network circuit is shown below.

• The current entering one terminal leaves through the other terminal so that the net current entering the port equals zero.
• A two-port network consists of two pairs of terminals in which one pair of terminals is designated as input and other pair being output.
• Two port networks are useful in communications, control systems, power systems, and electronics.
• To characterise a two-port network requires that we relate the terminal quantities V1, V2, I1, and I2. The various terms that relate these voltages and currents are called parameters.
• When the voltage or current are compared at same port then the term defined the Driving Imminence Function,while on the other hand when the comparison is done at different port then the function will defined as Transfer Imminence Function.

### 1. (Z-parameters) Open circuit Impedance Parameters

Here, The voltages at input and output are expressed in the terms of input and output currents. The equations are given below.

V1 = Z11I1 + Z12I2

V2 = Z21I1 + Z22I2

where, Z11, Z12, Z21 and Z22 are called the Z-parameters

The Z-Parameter are found as follow:

The z-parameters are also called as open-circuit impedance parameters because  they are obtained as the ratio of voltage and current when it is open-circuiting port 2 ( I2 = 0) or port 1 ( I1 = 0).

• Z11 is the driving Point impedance when output is open circuited.
• Z12 is the reverse transfer impedance when input is open-circuited.
• Z21 is the forward transfer impedance when output is open-circuit.
• Z22 is the driving Point impedance when input is open-circuited.

### 2. (Y-parameters) Short Circuit Admittance parameters

Y parameters are achieved by representing the currents at the two ports of the network in terms of voltages at two ports. Thus, voltages V1 and V2 are independent variables, while I1 and I2 are dependent variables.

The equations are given below.

I1 = Y11V1 + Y12V2

I2 = Y21V1 + Y22V2

Where, Y11, Y12, Y21, Y22 are called the Y-parameters.

The y-parameters are also called short-circuit admittance parameters. These are obtained as a  ratio of current and voltage. The parameters are calculated by short-circuiting port 2 (V2 = 0) or port 1 (V1 = 0).

So the Y-Parameter can be found as follow:

• Y11 Short-circuit driving point input admittance
• Y12 Short-circuit reverse transfer admittance
• Y21 Short-circuit forward transfer admittance
• Y22 Short-circuit driving point output admittance

### 3. h-parameters: Hybrid Parameters

• These parameters are By expressing voltage at input port and the current at the output port, the h-parameters are obtained.
• Two-port network variables  are selected as independent of the input current (I1 )and the output voltage(V2).
• Here, the input voltage and the output current are the dependent variables of this model.

Equations for voltage at input port and current at the output port are given below.

V1 = h11I1 + h12V2

I2 = h21I1 + h22V2

The h-Parameter can be found as follow:

• h11 Short-circuit input impedance:
• h21 Forward short-circuit current gain it is dimensionless .
• h12 Reverse open-circuit voltage gain it is dimensionless :

The h-parameters are also called hybrid parameters since they consist of both open-circuit parameters (I1 ) and short-circuit parameters (V2 )

### 4. ( g-parameters ) Inverse hybrid parameters

• These parameters are obtained by expressing voltage at output port and the current at the input port.
• Off-diagonal g-parameters are dimensionless, while diagonal members have dimensions the reciprocal of one another.

I1 = g11V1 + g12I2

V2 = g21V1 + g22I2

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

### 5.(T-Parameters) or ABCD parametersTransmission Parameters

These parameters are generally used in the analysis of power transmission in which the input port is considered as the sending side while the output port is considered as receiving side. These parameters are calculated by expressing voltage and current at the output port.

ABCD parameters can be defined as following:

• A is the reverse voltage ratio with open output.
• B is the reverse transfer impedance with shorted output.
• C is the  reverse transfer admittance with open output.
• D is the reverse current ratio with shorted output.

V1 = AV2 + B(–I2)

I1 = CV2 + D(–I2)

The transmission parameters express the primary (sending end) variables V1 and I1 by dependence of the secondary variables i.e., V2  (receiving end)  and '-I2' . The negative sign of I2 is used to mention that the current to enter the load at the receiving end.

• Symmetry Condition: if input impedance seen through both the port is same then both port are known as symmetric port.If port are symmetric then both port can be interchanged.
• Reciprocity Condition: If only single source is acting in the circuit then “By changing the position of response and excitation if ratio of response to excitation is constant then circuit is reciprocal”.

### 6.Conversion of Z-parameter in term of Y-parameter

• In the similar fashion we can obtain the other relationship

### 7.INTERCONNECTION OF TWO-PORT NETWORKS

The two-port networks can be connected in many ways such as series, parallel or cascade. the configuration listed below:

• Series Connection: When two 2-port network are connected in series configuration the z- parameter of each port will be directly added in the result of equivalent 2-port network.

This can be concluded  that if two-port networks with Z-parameters [Z]1,[Z]2,[Z]3,[Z]n , are connected in series, then the equivalent two port-parameters are given as

[Z]eq = [Z]1+ [Z]2+ [Z]3+ [Z]

• Parallel-connected Two-port Network  When two 2-port network are connected in Parallel configuration the Y- parameter of each port will be directly added in the result of equivalent 2-port network.

This can be concluded  that if two-port networks with Y-parameters [Y]1,[Y]2,[Y]3,[Y]n , are connected in Parallel, then the equivalent two port-parameters are given as

[Y]eq = [Y]1+ [Y]2+ [Y]3+ [Y]

• Cascade Connection of Two-port Network:

When two 2-port network are connected in cascaded configuration then the T-parameter of equivalent two port network will be the Product of T-parameter of individual network.

networks have transmission parameters [A]1,[A]2,[A]3,[A]n, then the equivalent two-port parameter will have a transmission parameter given as

[A]eq = [A]1*[A]2*[A]3*[A]n

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