YParameter

Y-parameters, or admittance parameters, are a linear two-port representation used in circuit analysis and RF engineering. They express the relationship between port voltages and currents through a 2x2 admittance matrix, making it convenient to analyze networks where currents are naturally related to parallel elements.

For a two-port network with port voltages V1 and V2 and port currents I1 and I2 (currents defined as entering the network), the Y-parameter equations are: I1 = Y11 V1 + Y12 V2 and I2 = Y21 V1 + Y22 V2. In matrix form, [I1 I2]^T = [Y11 Y12; Y21 Y22] [V1 V2]^T. The Y-parameters characterize how the network draws current from each port as the voltages at the ports are varied.

The individual parameters are defined by specific test conditions: Y11 = I1/V1 with V2 = 0, Y12 = I1/V2 with V1 = 0, Y21 = I2/V1 with V2 = 0, and Y22 = I2/V2 with V1 = 0. Practically, V2 = 0 corresponds to short-circuiting port 2, and V1 = 0 corresponds to short-circuiting port 1. These definitions reflect the small-signal, linear behavior of the network around an operating point.

Y-parameters relate to Z-parameters via matrix inversion (Y = Z^-1, when invertible). For reciprocal networks, Y12 = Y21. Y-parameters are particularly useful for networks where parallel (admittance) behavior dominates and are common in low-frequency lumped analysis as well as certain RF applications, provided the network remains linear and time-invariant.