Electrical energy conversion with distributed parameter modelling: A study of a step-down converter

Abstract

Energy is converted in an electric circuit. For example, when a DC-DC power converter uses the current in an inductor to decrease the input voltage. However, the underlying physical mechanism by which energy is converted is not visible on a circuit diagram that uses lumped parameter models. The spatial information is missing but can be included via distributed parameter modelling with transmission lines. The mechanism of energy conversion using transmission line modelling is yet to be reported in literature. A theoretical step-down converter topology is studied with the inductor substituted for a high impedance, one-dimensional, lossless transmission line model. Simulated outputs show that the converter functions comparably with the lumped and distributed inductor models for a 10V input and 50% duty cycle at 25kHz. The converter switch initiates step waves that propagate in the transmission line and produce a characteristic stepped output waveform. A reflection diagram for the transmission line inductor yields spatial distributions of voltage, current and instantaneous power. These distributions show the energy conversion process produces voltage and current from energy at rest purely in the magnetic field. The wavefront is the site of energy conversion where energy at rest is converted and brought into motion. The wavefront power is decomposed into components for the electric field and magnetic field on the basis of changes in energy density. These components provide a means to describe the energy conversion process with respect to the action of the wavefront on the underlying electromagnetic fields. Reflections of the wavefront show the energy conversion process within the inductor is biased towards the storage of energy purely in the magnetic field. Wavefronts diminish in magnitude over time, so the repeated switching of a converter creates new wavefronts that sustain the energy conversion process. Examining the effects of impedance mismatch reveals a trade-off between converting energy in-place and transporting energy to the load. This work supplies greater insights into the fundamental mechanisms of energy conversion in inductors, which may be a prerequisite step for further significant innovation in power converters.