yparameters

Y-parameters, or admittance parameters, are a set of two-port network parameters used to characterize linear electrical networks. They relate the currents entering the two ports to the voltages across them through a 2x2 matrix: I1 = Y11 V1 + Y12 V2; I2 = Y21 V1 + Y22 V2, where V1 and V2 are port voltages relative to a common reference, and I1 and I2 are currents entering the ports. Y-parameters are typically expressed in complex form for sinusoidal steady-state analysis, with phasor voltages and currents.

Construction and interpretation: The Y-parameters are defined by applying test excitations: Y11 is the input admittance with the second port short-circuited (V2 = 0) and I1 measured; Y21 is the output current for that same excitation; Y12 is the input admittance with the first port short-circuited (V1 = 0) and I1 measured; Y22 is the output admittance with V1 = 0. In practice, one measures the currents for specified voltages. Reciprocity and symmetry: For reciprocal networks consisting only of passive reciprocal elements, Y12 = Y21. In general, Y-parameters can be complex-valued, depending on frequency and circuit losses.

Relation to other two-port models: Y-parameters are related to Z-parameters by the inverse of the admittance matrix if the 2x2 matrix is non-singular; they can be transformed to H-parameters and ABCD-parameters through standard algebraic relations.

Applications and limitations: Y-parameters are widely used in microwave and RF design, where shunt-type (admittance) representations are convenient, and in small-signal modeling of active devices. They are especially useful when networks are driven by currents or when parallel combinations dominate circuit behavior. They assume linear, time-invariant networks and can be less intuitive for cascaded networks if not converted to another form.