Expansion of the Ohm's Law in Nonsinusoidal AC Circuit

In a nonsinusoidal alternating current (ac) circuit, the instantaneous impedances of the linear inductance and the linear capacitance have not been defined because no applicable law as the Ohm's law exists; hence, the analysis of the nonsinusoidal ac circuit is incomplete, and the design of the nonsinusoidal ac circuit lacks systematic consideration. This paper presents an expansion of the Ohm's law in the nonsinusoidal ac circuit by defining instantaneous impedance, instantaneous admittance, and analytic signals of the instantaneous voltage and current. It has been demonstrated that the presented definitions are reasonable generalizations of the Ohm's law in the nonsinusoidal ac circuit including ac/dc link circuit in theory analyses and experimental results in this paper. The presented expansion of the Ohm's law provides a distinct instruction for analyzing and designing nonsinusoidal circuit including ac/dc link circuit particularly for the power electronic circuit.