Y Parameters (Admittance Parameters) of a Two-Port Network

Y Parameters (Admittance Parameters) of a Two-Port Network

Theory

Y-parameters (also called Admittance parameters) are used to represent a two-port network in terms of currents and voltages. They express port currents as functions of port voltages.

I₁ = Y₁₁·V₁ + Y₁₂·V₂
I₂ = Y₂₁·V₁ + Y₂₂·V₂

Matrix form:

| I₁ | | Y₁₁ Y₁₂ | | V₁ |
| I₂ | = | Y₂₁ Y₂₂ | | V₂ |

Where:
Y₁₁ → Input admittance (output short)
Y₂₂ → Output admittance (input short)
Y₁₂, Y₂₁ → Transfer admittances
Unit: Siemens (S)

How to Calculate Parameters

Condition 1: V₂ = 0 (Output Short Circuit)
Y₁₁ = I₁ / V₁
Y₂₁ = I₂ / V₁

Condition 2: V₁ = 0 (Input Short Circuit)
Y₂₂ = I₂ / V₂
Y₁₂ = I₁ / V₂

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Example: Ladder Network

Given a ladder network with series and shunt resistors, find Y-parameters using short-circuit conditions.

Step 1: Find Y₁₁ and Y₂₁ (V₂ = 0)

• Output short → shunt resistor bypassed
• Equivalent reduction gives:

Y₁₁ = 0.155 S
Y₂₁ = -0.086 S

Step 2: Find Y₂₂ and Y₁₂ (V₁ = 0)

• Input short simplifies network
• Equivalent reduction gives:

Y₂₂ = 0.07 S
Y₁₂ = -0.03 S

Final Y Matrix

| 0.155 -0.03 |
| -0.086 0.07 | S

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Shortcut Using ABCD Parameters

If ABCD parameters are known:

Y₁₁ = D / B
Y₂₁ = -1 / B
Y₂₂ = A / B
Y₁₂ = (BC − AD) / B

Advantage: Faster and more reliable for complex ladder networks.