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. V₁ and V₂ represent the voltages at these ports, while I₁ and I₂ 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 I₁ and I₂ as inputs and V₁ and V₂ as outputs, the Z parameters describe the relationship:

• V₁ = Z₁₁ * I₁ + Z₁₂ * I₂
• V₂ = Z₂₁ * I₁ + Z₂₂ * I₂

Z₁₁ is found by making port 2 an open circuit when I₂ is 0, and Z₁₂ is found by making port 1 an open circuit when I₁ is 0. Similarly, Z₂₁ and Z₂₂ 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 Z₁₁ equals Z₂₂.
• A two-port network is reciprocal if Z₁₂ equals Z₂₁.

Y Parameters

In a two-port network, considering V₁ and V₂ as inputs and I₁ and I₂ as outputs, the Y parameters describe the relationship:

• I₁ = Y₁₁ * V₁ + Y₁₂ * V₂
• I₂ = Y₂₁ * V₁ + Y₂₂ * V₂

Y₁₁ is found by making port 2 a short circuit when V₂ is 0, and Y₁₂ is found by making port 1 a short circuit when V₁ is 0. Similarly, Y₂₁ and Y₂₂ 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 Y₁₁ equals Y₂₂.
• A two-port network is reciprocal if Y₁₂ equals Y₂₁.

T Parameters

In a two-port network, with V₂ and I₂ as inputs and V₁ and I₁ as outputs, the T parameters (Transmission parameters) describe the relationship:

• V₁ = AV₂ – BI₂
• I₁ = CV₂ – DI₂

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

• A = V₁/V₂ when I₂ is 0
• B = -V₁/I₂ when V₂ is 0
• C = I₁/V₂ when I₂ is 0
• D = -I₁/I₂ when V₂ 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 V₁ and I₁ as inputs and V₂ and I₂ as outputs, the T’ parameters (Inverse Transmission parameters) describe the relationship:

• V₂ = A’V₁ – B’I₁
• I₂ = C’V₁ – D’I₁

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

• A’ = V₂/V₁ when I₁ is 0
• B’ = -V₂/I₁ when V₁ is 0
• C’ = I₂/V₁ when I₁ is 0
• D’ = -I₂/I₁ when V₁ 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 I₁ and V₂ as inputs and V₁ and I₂ as outputs, the h parameters (Hybrid parameters) describe the relationship:

• V₁ = h₁₁ + h₁₂V₂
• I₂ = h₂₁I₁ + h₂₂V₂

Here, h₁₂ and h₂₁ are unitless, and the units of h₁₁ and h₂₂ are ohms (Ω) and mhos (℧), respectively. The h parameters can be obtained under specific conditions:

• h₁₁ = V₁/I₁ when V₂ is 0
• h₁₂ = V₁/V₂ when I₁ is 0
• h₂₁ = I₂/I₁ when V₂ is 0
• h₂₂ = I₂/V₂ when I₁ is 0

Two h parameters, h₁₁, and h₂₁, can be found by making port 2 a short circuit, and the other two, h₁₂ and h₂₂, can be found by making port 1 an open circuit.

• A two-port network is symmetrical if h = 1, i.e., h₁₁h₂₂ – h₂₁h₁₂ = 1.
• A two-port network is reciprocal if h₁₂ equals -h₂₁.

g Parameters

In a two-port network with V₁ and I₂ as inputs and I₁ and V₂ as outputs, the g parameters (Inverse Hybrid parameters) describe the relationship:

• I₁ = g₁₁V₁ + g₁₂I₂
• V₂ = g₂₁V₁ + g₂₂I₂

Here, g₁₂ and g₂₁ are unitless, and the units of g₁₁ and g₂₂ are mhos (℧) and ohms (Ω), respectively. The g parameters can be obtained under specific conditions:

• g₁₁ = I₁/V₁ when I₂ is 0
• g₁₂ = I₁/I₂ when V₁ is 0
• g₂₁ = V₂/V₁ when I₂ is 0
• g₂₂ = V₂/I₂ when V₁ is 0

Two g parameters, g₁₁, and g₂₁, can be found by making port 2 an open circuit, and the other two, g₁₂ and g₂₂

Two g parameters, g₁₁, and g₂₁, can be found by making port 2 an open circuit, and the other two, g₁₂ 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., g₁₁g₂₂ – g₁₂g₂₁ = 1.
• A two-port network is reciprocal if g₁₂ equals -g₂₁.

Frequently Asked Questions (FAQs)

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

Read More>>>>