Table of Contents

## Introduction

Two-port networks simplify complex electrical circuits. They represent components like transmission lines and transformers, as well as electronic ones like transistors. This overview explains two-port network parameters, how to calculate them, and conditions for symmetry and reciprocity, aiding in network analysis.

## What is a Two-Port Network?

A port is a pair of terminals where current enters one and exits the other. Components like resistors, inductors, and capacitors are examples of one-port networks, where electrical interactions occur at a single pair of terminals.

A two-port network has two pairs of terminals, here named port 1 and port 2. V_{1} and V_{2} represent the voltages at these ports, while I_{1} and I_{2} represent the currents flowing through the respective ports.

## Two Port Network Example

A few examples of Two Port Network are:

- Filters,
- Small-signal models for transistors
- Matching networks,
- Transmission lines,
- Transformers,

## Two Port Network Parameters

In a two-port network, you can provide input to any port and extract output from any port. The parameters used to describe such networks are called two-port network parameters. There are six sets of these parameters, named Z, Y, T, T’, h, and g parameters, involving voltage (V) and current (I).

### Z Parameters

In a two-port network, with I_{1} and I_{2} as inputs and V_{1} and V_{2} as outputs, the Z parameters describe the relationship:

- V
_{1}= Z_{11}* I_{1}+ Z_{12}* I_{2} - V
_{2}= Z_{21}* I_{1}+ Z_{22}* I_{2}

Z_{11} is found by making port 2 an open circuit when I_{2} is 0, and Z_{12} is found by making port 1 an open circuit when I_{1} is 0. Similarly, Z_{21} and Z_{22} are obtained. These parameters are called impedance parameters or Z parameters. They represent the ratio of output voltage to input current and are measured in Ohms (Ω).

- A two-port network is symmetrical if Z
_{11}equals Z_{22}. - A two-port network is reciprocal if Z
_{12}equals Z_{21}.

### Y Parameters

In a two-port network, considering V_{1} and V_{2} as inputs and I_{1} and I_{2} as outputs, the Y parameters describe the relationship:

- I
_{1}= Y_{11}* V_{1}+ Y_{12}* V_{2} - I
_{2}= Y_{21}* V_{1}+ Y_{22}* V_{2}

Y_{11} is found by making port 2 a short circuit when V_{2} is 0, and Y_{12} is found by making port 1 a short circuit when V_{1} is 0. Similarly, Y_{21} and Y_{22} are obtained. These parameters are called admittance parameters or Y parameters, representing the ratio of output current to input voltage, measured in mhos (℧).

- A two-port network is symmetrical if Y
_{11}equals Y_{22}. - A two-port network is reciprocal if Y
_{12}equals Y_{21}.

### T Parameters

In a two-port network, with V_{2} and I_{2} as inputs and V_{1} and I_{1} as outputs, the T parameters (Transmission parameters) describe the relationship:

- V
_{1}= AV_{2}– BI_{2} - I
_{1}= CV_{2}– DI_{2}

Here, A, B, C, and D are constants obtained under specific conditions:

- A = V
_{1}/V_{2}when I_{2}is 0 - B = -V
_{1}/I_{2}when V_{2}is 0 - C = I
_{1}/V_{2}when I_{2}is 0 - D = -I
_{1}/I_{2}when V_{2}is 0

A and D have no units, while B and D have units of ohms (Ω) and mhos (℧), respectively. The ABCD parameters are also known as T parameters. A and C are obtained by making port 2 an open circuit, while B and D are obtained by making port 2 a short circuit.

- A two-port network is symmetrical if A equals D.
- A two-port network is reciprocal if AD – BC equals 1.

### T’ Parameters

In a two-port network, with V_{1} and I_{1} as inputs and V_{2} and I_{2} as outputs, the T’ parameters (Inverse Transmission parameters) describe the relationship:

- V
_{2}= A’V_{1}– B’I_{1} - I
_{2}= C’V_{1}– D’I_{1}

Here, A’, B’, C’, and D’ are constants obtained under specific conditions:

- A’ = V
_{2}/V_{1}when I_{1}is 0 - B’ = -V
_{2}/I_{1}when V_{1}is 0 - C’ = I
_{2}/V_{1}when I_{1}is 0 - D’ = -I
_{2}/I_{1}when V_{1}is 0

A’ and D’ have no units, while B’ and D’ have units of ohms (Ω) and mhos (℧), respectively. The A’B’C’D’ parameters are also known as Inverse Transmission parameters or T’ parameters. A’ and C’ are obtained by making port 1 an open circuit, while B’ and D’ are obtained by making port 1 a short circuit.

- A two-port network is symmetrical if A’ equals D’.
- A two-port network is reciprocal if A’D’ – B’C’ equals 1.

### h Parameters

In a two-port network with I_{1} and V_{2} as inputs and V_{1} and I_{2} as outputs, the h parameters (Hybrid parameters) describe the relationship:

- V
_{1}= h_{11}+ h_{12}V_{2} - I
_{2}= h_{21}I_{1}+ h_{22}V_{2}

Here, h_{12} and h_{21} are unitless, and the units of h_{11} and h_{22} are ohms (Ω) and mhos (℧), respectively. The h parameters can be obtained under specific conditions:

- h
_{11}= V_{1}/I_{1}when V_{2}is 0 - h
_{12}= V_{1}/V_{2}when I_{1}is 0 - h
_{21}= I_{2}/I_{1}when V_{2}is 0 - h
_{22}= I_{2}/V_{2}when I_{1}is 0

Two h parameters, h_{11}, and h_{21}, can be found by making port 2 a short circuit, and the other two, h_{12} and h_{22}, can be found by making port 1 an open circuit.

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

### g Parameters

In a two-port network with V_{1 }and I_{2} as inputs and I_{1} and V_{2} as outputs, the g parameters (Inverse Hybrid parameters) describe the relationship:

- 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 unitless, and the units of g_{11} and g_{22} are mhos (℧) and ohms (Ω), respectively. The g parameters can be obtained under specific conditions:

- g
_{11}= I_{1}/V_{1}when I_{2}is 0 - g
_{12}= I_{1}/I_{2}when V_{1}is 0 - g
_{21}= V_{2}/V_{1}when I_{2}is 0 - g
_{22}= V_{2}/I_{2}when V_{1}is 0

Two g parameters, g_{11}, and g_{21}, can be found by making port 2 an open circuit, and the other two, g_{12} and g_{22}

Two g parameters, g_{11}, and g_{21}, can be found by making port 2 an open circuit, and the other two, g_{12} and g, can be found by making port 1 a short circuit.

, can be found by making port 1 a short circuit.

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

## Frequently Asked Questions (FAQs)

#### What is meant by the two-port network?

A two-port network is an electrical network or circuit with two pairs of terminals, allowing independent input and output variables. It’s commonly used to model complex systems in a simplified manner.

#### What is the use of two-port?

A two-port is used to model and analyze complex electrical systems, simplifying their representation. It aids in understanding and designing circuits, facilitating the study of signal flow and interactions.

#### What is the formula for 2 ports?

The general representation of a two-port network involves four variables: V1 and I1 as input voltage and current, and V2 and I2 as output voltage and current. Different parameter sets like Z, Y, T, h, and g parameters express the relationships between these variables.

#### How many numbers is a port?

A port in a two-port network consists of a pair of terminals through which electrical signals enter and exit. A two-port network has two such ports, providing input and output connections.

**Read Also:**

- Maximum Power Transfer Theorem | Formula, Proof, and, Limitations
- Superposition Theorem | Procedure, Limitations, and Applications
- Norton’s Theorem
- Reciprocity Theorem | Statement, Limitations, and Applications

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