Side-by-side comparison
| Parameter | Z-Parameters | Y-Parameters |
|---|---|---|
| Full Name | Impedance parameters (Z or open-circuit parameters) | Admittance parameters (Y or short-circuit parameters) |
| Definition Condition | Measured with ports open-circuited (I = 0) | Measured with ports short-circuited (V = 0) |
| V-I Relation | V1 = Z11·I1 + Z12·I2; V2 = Z21·I1 + Z22·I2 | I1 = Y11·V1 + Y12·V2; I2 = Y21·V1 + Y22·V2 |
| Matrix | [V] = [Z][I] | [I] = [Y][V] |
| Relation | [Z] = [Y]⁻¹ | [Y] = [Z]⁻¹ |
| Series Connection | Z matrices add directly: [Z] = [Z_A] + [Z_B] | Cannot add directly for series connection |
| Parallel Connection | Cannot add directly for parallel connection | Y matrices add directly: [Y] = [Y_A] + [Y_B] |
| Does not exist when | Network has short-circuit loops (Z undefined) | Network has open-circuit branches (Y undefined) |
Key differences
Z-parameters are open-circuit parameters: Z11 = V1/I1 with port 2 open. Y-parameters are short-circuit parameters: Y11 = I1/V1 with port 2 shorted. Critically, [Z] = [Y]⁻¹ — they are matrix inverses. When two-ports are connected in series, Z matrices simply add. When connected in parallel, Y matrices simply add. For a reciprocal network (passive, no dependent sources), Z12 = Z21 and Y12 = Y21. Z-parameters do not exist for a network that contains a series short; Y-parameters do not exist for one that contains an open branch.
When to use Z-Parameters
Use Z-parameters when two-port networks are connected in series — for example, cascading two T-network filter sections where the Z matrices of each section simply add to give the overall Z matrix.
When to use Y-Parameters
Use Y-parameters when two-port networks are connected in parallel — for example, analyzing a shunt-feedback amplifier or a π-network filter where admittances of parallel sections add directly.
Recommendation
For GATE and university exams, choose Z when you see series connection of networks and Y when you see parallel connection — those two rules cover the majority of two-port network questions. Also remember [Z] = [Y]⁻¹ for quick conversion.
Exam tip: Examiners test whether you know the measurement condition: Z-parameters need open-circuit at the other port; Y-parameters need short-circuit — confusing these is the most common error in two-port problems.
Interview tip: Interviewers at RF and telecom companies ask how you would measure Y21 of a transistor — answer: short port 2 (V2 = 0), drive port 1 with a known voltage, and measure the resulting short-circuit current at port 2; Y21 = I2/V1.