**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 V
_{1}, V_{2}, I_{1}, and I_{2}. 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.

V_{1} = Z_{11}I_{1} + Z_{12}I_{2}

V_{2} = Z_{21}I_{1} + Z_{22}I_{2}

where, Z_{11}, Z_{12}, Z_{21} and Z_{22} 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 ( I_{2} = 0) or port 1 ( I_{1} = 0).

- Z
_{11}is the driving Point impedance when output is open circuited. - Z
_{12}is the reverse transfer impedance when input is open-circuited. - Z
_{21}is the forward transfer impedance when output is open-circuit. - Z
_{22}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 V_{1 }and V_{2} are independent variables, while I_{1} and I_{2} are dependent variables.

The equations are given below.

I_{1} = Y_{11}V_{1} + Y_{12}V_{2}

I_{2} = Y_{21}V_{1} + Y_{22}V_{2}

Where, Y_{11}, Y_{12}, Y_{21}, Y_{22} 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 (V_{2} = 0) or port 1 (V_{1} = 0).

So the Y-Parameter can be found as follow:

- Y
_{11 }Short-circuit driving point input admittance - Y
_{12 }Short-circuit reverse transfer admittance - Y
_{21 }Short-circuit forward transfer admittance - Y
_{22 }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 (I
_{1})and the output voltage(V_{2}). - 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.

V_{1} = h_{11}I_{1} + h_{12}V_{2}

I_{2} = h_{21}I_{1} + h_{22}V_{2}

The h-Parameter can be found as follow:

- h
_{11}Short-circuit input impedance: - h
_{21}Forward short-circuit current gain it is dimensionless . - h
_{12}Reverse open-circuit voltage gain it is dimensionless : - h
_{22}Open-circuit output admittance:

The h-parameters are also called hybrid parameters since they consist of both open-circuit parameters (I_{1 )} and short-circuit parameters (V_{2} )

** 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.

I_{1} = g_{11}V_{1} + g_{12}I_{2}

V_{2} = g_{21}V_{1} + g_{22}I_{2}

Here g_{12} and g_{21} are dimensionless coefficients, g_{22} is impedance and g_{11} is admittance.

** 5.(T-Parameters) or ABCD parameters** **Transmission 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.

V_{1} = AV_{2} + B(–I_{2})

I_{1} = CV_{2} + D(–I_{2})

The transmission parameters express the primary (sending end) variables V_{1} and I_{1} by dependence of the secondary variables i.e., V_{2 }(receiving end) and '-I_{2}' . The negative sign of I_{2} 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]_{n }**

**Parallel-connected Two-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]_{n }**

**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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