ABCD Parameters (T-Parameters)

ABCD (T) Parameters of a Two-Port Network

Theory

ABCD parameters (also called Transmission parameters) are used to represent a two-port network. They relate the input voltage and current to the output voltage and current.

V₁ = A·V₂ − B·I₂
I₁ = C·V₂ − D·I₂

These equations can be written in matrix form:

| V₁ | | A B | | V₂ |
| I₁ | = | C D | | -I₂ |

Where:
A, B, C, D → Transmission (ABCD) parameters
V₁, I₁ → Input voltage and current
V₂, I₂ → Output voltage and current

How to Calculate Parameters

• A = V₁ / V₂ (when I₂ = 0, open circuit)
• B = V₁ / -I₂ (when V₂ = 0, short circuit)
• C = I₁ / V₂ (when I₂ = 0, open circuit)
• D = I₁ / -I₂ (when V₂ = 0, short circuit)

Important:
A & C → Open circuit condition (I₂ = 0)
B & D → Short circuit condition (V₂ = 0)

Why ABCD Parameters are Important

• Very useful for cascaded networks
• Matrices can be multiplied directly
• Used in transmission lines, amplifiers, and filters

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Numerical Example

Example Circuit

A two-port network consists of:

• Series resistor: R = 2 Ω
• Shunt resistor: R = 3 Ω

This is a cascaded network:
Series element → Shunt element

Step 1: T-matrix of each element

Series Resistor (Z = 2 Ω)

[T₁] = | 1 2 |
| 0 1 |

Shunt Resistor (Y = 1/3)

[T₂] = | 1 0 |
| 1/3 1 |

Step 2: Multiply matrices

[T] = [T₁] × [T₂]

[T] = | 1 2 | | 1 0 |
| 0 1 | × | 1/3 1 |

Step 3: Calculation

A = 1×1 + 2×(1/3) = 5/3

B = 1×0 + 2×1 = 2

C = 0×1 + 1×(1/3) = 1/3

D = 0×0 + 1×1 = 1

🔹 Final ABCD Matrix

[T] = | 5/3 2 |
| 1/3 1 |

🔹 Final Answer

• A = 5/3
• B = 2
• C = 1/3
• D = 1

Summary

• Break circuit into series and shunt parts
• Write individual T-matrices
• Multiply matrices to get final ABCD

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