admittances

Admittance is a complex quantity that characterizes how easily an electrical network conducts alternating current for a given applied voltage. It is defined as the ratio of complex current to complex voltage, Y = I/V, and is the reciprocal of impedance Z. The unit is the siemens (S). In engineering, the imaginary unit is denoted by j.

Written as Y = G + jB, admittance has a real part G, called conductance, and an imaginary part B, called susceptance. Conductance reflects current in phase with the voltage, while susceptance represents the current component that leads or lags the voltage. For capacitors, B = ωC (positive); for inductors, B = -1/(ωL) (negative). Resistors have G = 1/R and B = 0. Here ω is the angular frequency (ω = 2πf).

In circuit operations, admittance and impedance invert each other: Y = 1/Z and Z = 1/Y. In parallel connections, admittances add: Y_total = ∑Yi. In series connections, impedances add: Z_total = ∑Zi. The frequency dependence of Y stems from the reactive parts (capacitive or inductive), while the real part G is generally frequency-independent for ideal components.

Applications of admittance include nodal (circuit) analysis, AC power calculations, impedance matching, and filter design. Admittance is also used in Y-parameter network models and is measured with admittance meters and vector network analyzers, especially at radio and microwave frequencies.