2-Port Network becomes the important topic for gate aspirants. Every year one or two question is expected from this topic. The article is framed to help you to solve questions on 2-port network.

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A 2-port is an electrical circuit or device with 2 pairs of terminals. They find application in transistors, filters etc.

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.

In this two of the four variables are given, while the other two can always be derived. 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.

**Z-model **:

we know I_{1 }and I_{2 }That means they are independent variables and V_{1 }and V_{2 }are dependent variables. Here we use KVL to evaluate V_{1 }and V_{2.}

where

Here,

** V _{1 }= Z_{11} I_{1}+Z_{12}I_{2}**

** V _{2 }= Z_{21} I_{1}+Z_{22}I_{2}**

All four parameters *Z*11,*Z*12 ,*Z*21 , and *Z*22 represent impedance. In particular, *Z*21 and Z12 are transfer impedances.

_{ }

**Y-Model** :

we know V_{1} and V_{2 }That means they are independent variables and I_{1} and I_{2 }are dependent variables. Here we use KCL to evaluate I_{1 }and I_{2}

where

**I _{1 }= Y_{11} V_{1}+Y_{12}V_{2}**

** I _{2 }= Y_{21} V_{1}+Y_{22}V_{2}**

These four parameters *Y*11,*Y*12 ,*Y*21 , and *Y*22 represent admittance. In particular, *Y*21 and *Y*12 are transfer admittances.

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**ABCD -model (Transmission Model)**:

we know V_{1} and I_{1 }That means they are independent variables and V_{2} and I_{2 }are dependent variables. Here we use KVL to evaluate V_{2 }and KCL to evaluate I_{2}

where

*A *and *D* are dimensionless coefficients, *B* is impedance and *C* is admittance .A negative sign is there to the output current *I*2 in the model, as the direction of the current is out-ward, for easy analysis of a cascade of multiple network models.

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**H-model (Hybrid Model) **:

In the H-model or hybrid model,*V*2 and *I*1 are known, and find *V*1 by KVL and *I*2 by KCL:

where

Here *h*12 and *h*21 are dimensionless coefficients, *h*11 is impedance and *h*22 is admittance

**g model (inverse hybrid model) : **

*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.

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**Important Tips to Remember:**

We must know important tips that must be considered to solve questions of two ports network.

**#1**

When I_{2 }= 0, it means line at output port is at open circuit. There is only one current I_{1. }Similarly if I_{1} =0 , it means line at input port is at open circuit. This is assumptions we use to find impedance.

**#2**

when impedance or any other coefficients is to be find, try to find out its equation using KVL or KCL as required. For voltage KVL will be used, for current KCL will be used. For example,

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

_{ }

If Z_{11 } is to be find. Try to find V_{1 }using KVL, then subsequently we will get Z_{11. }Similarly ,

If

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

_{ }

_{ }

_{ } If Y_{21 }is to be find then find I_{2 }using KCL. Then subsequently we will get Y_{21}

**#3**

Before solving , simplify the circuit as possible. For this you may have to convert delta to start conversion. If two resistance are in parallel , convert them into single resistance.

Similarly if two resistance are in series convert into single resistance.

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**Example From Gate :**

** Gate 2014**

In the h – parameter model of 2 – port network given in the figure shown

the value of h_{22} (in siemens) is _____________

**Answer : **

We know formula of

** I _{2 }= h_{21} I_{1}+h_{22}V_{2}**

_{ }

_{ }We can redraw the figure as :

As the resistors are in parellel,We can redraw this in to :

Further, solving we can solve (2*3)/(2+3) this in to :

In order to find h_{22, }we have to apply KCL.

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

_{ }Assuming I_{1} =0,

I_{2 }= V_{2}/(6/5 +6/5) +V_{2}/(6/5).

12 I_{2 }= 15 V_{2}

_{ }h_{22 } = I_{2 }/ V_{2 = }1.25

Suppose if we need to calculate impedance , then we had to apply KVL, Before apply KVL (if we had to apply in above final circuit), to simplify convert **delta to star conversion** for simplification.

We hope you got a detailed idea how questions can be solved.

**Best Wishes !!**

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