Generalized in-plane circuit averaging

The authors present an unified approach to in-place circuit averaging that is applicable to resonant-type circuits as well as pulse-width-modulated (PWM) circuits. The approach allows the refinement of an averaged circuit model to obtain an arbitrary degree of accuracy. In the context of a particular circuit, an approximate averaged representation for each branch variable consists of a subset of the Fourier coefficients (index-k averages). The selection of this subset is determined by the dominant harmonic content of the circuit waveforms. For instance, in a series resonant DC-DC converter, the index-1 averages would be selected for the resonant tank variables, whereas the index-0 averages would be selected for the load side elements. In a PWM converter one would normally use the index-0 averages to obtain a low-frequency approximate model. These models can then be refined by including additional coefficients. This procedure is illustrated for a PWM up-down converter and for a DC-DC series resonant converter