A General Definition for Impedance

Electrical impedance is usually defined in terms of alternating-current steady-state values of current and voltage. When network problems are approached using the Laplace transformation, impedance takes on a different character, as now both transient and steady-state currents and voltages are considered. It is therefore useful to develop a general expression for impedance in the form of a time domain operator. This operator is a rational function in powers of the differential operator D=d/dt. One can then show that the phasor and Laplace transform expressions for impedance are compatible.