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# What is Two Port Network?

By BYJU'S Exam Prep

Updated on: September 25th, 2023

**Two Port Networks** can be used to represent any complex electrical network into a simple equivalent model. The electrical components like transmission lines and transformers can be modelled in two-port network models. Similarly, electronic components like transistors and op-amps can also be modelled in two-port network models.

This article gives an overview of two-port network parameters and how to calculate them. In this article, we also provided the condition for symmetry and reciprocal for the given network concerning two-port network parameters. These conditions will help check the given network whether it is symmetrical or not and similarly reciprocal or not.

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Table of content

## What is Two Port Network?

Pair of terminals is known as a port. Here, the current enters through one terminal and leaves from the other terminal. So, the electrical components like resistor, inductor and capacitor are examples of one port network.

### Two Port Network Definition

It is known as a two-port network if the network has two such ports. In the following two-port network, there are two ports, namely port 1 and port 2. V_{1} and V_{2} are the voltages across port 1 and port 2, respectively. Similarly, I_{1} and I_{2} are the currents flowing through port 1 and port 2, respectively.

**Figure:** Two Port Network

### Two Port Network Example

A few examples of Two Port Network are:

- filters,
- small-signal models for transistors
- matching networks,
- transmission lines,
- transformers,

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## Two Port Network Parameters

In the two-port network, we can give the input to any port; similarly, we can take the output from any port. Since we have two electrical quantities, voltage and current, obviously, the input and output also will be among those two forms.

The parameters that we will use in two-port networks are known as two-port network parameters. Since there are four variables, V_{1}, V_{2}, I_{1} and I_{2,} we will get six sets of parameters for the two port networks. Now, let’s see the following two port network parameters.

- Z Parameters
- Y Parameters
- T Parameters
- T’ Parameters
- h Parameters
- g Parameters

#### Z Parameters

Among the four variables V_{1}, V_{2}, I_{1} and I_{2} of a two-port network, let’s consider I_{1} and I_{2} as independent variables and V_{1} and V_{2} as dependent variables. That means I_{1} and I_{2} are the inputs, whereas V_{1} and V_{2} are the outputs of the two-port network. The two equations of this two-port network and the corresponding Z parameters are mentioned below.

- V
_{1}=Z_{11}I_{1}+Z_{12}I_{2} - V
_{2}=Z_{21}I_{1}+Z_{22}I_{2} - Z
_{11}=V_{1}/I_{1}, when I_{2}=0 - Z
_{12}=V_{1}/I_{2}, when I_{1}=0 - Z
_{21}=V_{2}/I_{1}, when I_{2}=0 - Z
_{22}=V_{2}/I_{2}, when I_{1}=0

Here, the ratio of output (voltage) and input (current) gives the value of impedance, and the units are Ohm (Ω). Hence, these two-port network parameters are called impedance parameters or Z parameters. We can find two Z parameters, Z_{11} and Z_{21,} by making port 2 an open circuit. Similarly, we can see the other Z parameters, Z_{12} and Z_{22,} by making port 1 an open circuit. Hence, we can call Z parameters as open circuit impedance parameters.

- A two-port network is said to be a symmetrical network if Z
_{11}=Z_{22}. - A two-port network is said to be reciprocal if Z
_{12}=Z_{21}.

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### Y Parameters

Among the four variables V_{1}, V_{2}, I_{1} and I_{2} of the two-port network, let’s consider V_{1} and V_{2} as independent variables and I_{1} and I_{2} as dependent variables. That means V_{1} and V_{2} are the inputs, whereas I_{1} and I_{2} are the outputs of the two-port network. The two equations of this two-port network and the corresponding Y parameters are mentioned below.

- I
_{1}=Y_{11}V_{1}+Y_{12}V_{2} - I
_{2}=Y_{21}/V_{2}+Y_{22}V_{2} - Y
_{11}=I_{1}/V_{1}, when V_{2}=0 - Y
_{12}=I_{1/V}_{2}, when V_{1}=0 - Y
_{21}=I_{2/V}_{1}, when V_{2}=0 - Y
_{22}=I_{2/V}_{2}, when V_{12}=0

Here, the ratio of output (current) and input (voltage) gives the value of admittance, and the units are mho (℧). Hence, these two-port network parameters are called admittance parameters or Y parameters. We can find two Y parameters, Y_{11} and Y_{21,} by making port 2 a short circuit. Similarly, we can see the other two Y parameters, Y_{12} and Y_{22,} by making port 1 a short course. Hence, we can call Y parameters short circuit admittance parameters.

- A two-port network is said to be a symmetrical network if Y
_{11}=Y_{22}. - A two-port network is said to be reciprocal if Y
_{12}=Y_{21}.

### T Parameters

Among the four variables V_{1}, V_{2}, I_{1} and I_{2} of a two-port network, let’s consider V_{2} and I_{2} as independent variables and V_{1} and I_{1} as dependent variables. That means V_{2} and I_{2} are the inputs, whereas V_{1} and I_{1} are the outputs of the two-port network. The two equations of this two-port network and the corresponding T parameters are mentioned below.

- V
_{1}=AV_{2}-BI_{2} - I
_{1}=CV_{2}-DI_{2} - A=V
_{1}V_{2}, when I_{2}=0 - B=-V
_{1}I_{2}, when V_{2}=0 - C=I
_{1}V_{2}, when I_{2}=0 - D=-I
_{1}I_{2}, when V_{2}=0

Here, A and D do not have any units. In contrast, the units of B and D are ohm (Ω) and mho (℧), respectively. ABCD parameters are also called Transmission parameters or T parameters in short. We can find two T parameters, A and C, by making port 2 an open circuit. Similarly, we can see the other two T parameters, B and D, by making port 2 a short course.

- A two-port network is said to be a symmetrical network if A=D.
- A two-port network is said to be reciprocal if AD-BC=1.

### T’ Parameters

Among the four variables V_{1}, V_{2}, I_{1} and I_{2} of the two-port network, let’s consider V_{1} and I_{1} as independent variables and V_{2} and I_{2} as dependent variables. That means V_{1} and I_{1} are the inputs, whereas V_{2} and I_{2} are the outputs of the two-port network. The two equations of this two-port network and the corresponding T’ parameters are mentioned below.

- V2=A’V1-B’I1
- I2=C’V1-D’I1
- A’=V
_{2}V_{1}, when I_{1}=0 - B’=-V
_{2}I_{1}, when V_{1}=0 - C’=I
_{2}V_{1}, when I_{1}=0 - D’=-I
_{2}I_{1}, when V_{1}=0

Here, A’ and D’ are not having any units. Whereas the units of B’ and D’ are ohm (Ω) and mho (℧) respectively. A’B’C’D’ parameters are also called Inverse Transmission parameters or T’ parameters in short. We can find two T’ parameters, A’ and C’, by making port 1 an open circuit. Similarly, we can see the other two T’ parameters B’ and D’, by making port 1 a short course.

- A two-port network is said to be symmetrical if A’ =D’.
- A two-port network is said to be reciprocal if A’D’-B’C’=1.

### h Parameters

Among the four variables V_{1}, V_{2}, I_{1} and I_{2} of a two-port network, let’s consider I_{1} and V_{2} as independent variables and V_{1} and I_{2} as dependent variables. That means I_{1} and V_{2} are the inputs, whereas V_{1} and I_{2} are the outputs of the two-port network. The two equations of this two-port network and the corresponding h parameters are mentioned below.

- V
_{1}=h_{11}I_{1}+h_{12}V_{2} - I
_{2}=h_{21}I_{1}+h_{22}V_{2} - h
_{11}=V_{1}/I_{1}, when V_{2}=0 - h
_{12}=V_{1}/V_{2}, when I_{1}=0 - h
_{21}=I_{2}/I_{1}, when V_{2}=0 - h
_{22}=I_{2}/V_{2}, when I_{1}=0

Here, h_{12} and h_{21} do not have any units. The units of h_{11} and h_{22 }are ohm (Ω) and mho (℧), respectively. The h parameters are also called Hybrid parameters. We can find two h parameters, h_{11} and h_{21,} by making port 2 a short circuit. Similarly, we can see the other two h parameters, h_{12} and h_{22,} by making port 1 an open circuit.

- A two-port network is said to be symmetrical network, if h=1, i.e., h
_{11}h_{22}-h_{21}h_{21}=1. - A two-port network is said to be reciprocal if h
_{12}=-h_{21}.

### g Parameters

Among the four variables V_{1}, V_{2}, I_{1} and I_{2} of a two-port network, let’s consider V_{1} and I_{2 }as independent variables and I_{1} and V_{2} as dependent variables. That means V_{1} and I_{2} are the inputs, whereas I_{1 }and V_{2} are the outputs of the two-port network. The two equations of this two-port network and the corresponding g parameters are mentioned below.

- I
_{1}=g_{11}V_{1}+g_{1}I_{2} - V
_{2}=g_{21}V_{1}+g_{22}I_{2} - g
_{11}=I_{1}/V_{1}, when I_{2}=0 - g
_{12}=I_{1}/I_{2}, when V_{1}=0 - g
_{21}=V_{2}/V1, when I_{2}=0 - g
_{22}=V_{2}/I_{2}, when V_{1}=0

Here, g_{12} and g_{21} do not have any units. At the same time, the units of g_{11} and g_{22} are mho (℧) and ohm (Ω), respectively. The g parameters are also called Inverse Hybrid parameters. We can find two g parameters, g_{11} and g_{21,} by making port 2 an open circuit. Similarly, we can see the other two g parameters, g_{12} and g_{22,} by making port 1 a short circuit.

- A two-port network is a symmetrical network if g=1, i.e., g
_{11}g_{22}-g_{12}g_{21}=1. - A two-port network is said to be reciprocal if g
_{12}=-g_{21}.

This article discussed the two-port network parameters and how to calculate them. We also mentioned the condition for symmetry and reciprocal for the given network concerning two port network parameters. Whenever we want to check whether the given network is symmetrical or not and similarly common or not that time, we can use those conditions.