## The Significance of Fourier Analysis

The switch action in a conversion circuit is most often periodic. The waveforms themselves are rather choppy and sometimes discontinuous. We must form an approximate DC output of a rectifier, for instance, by piecing together ‘chunks’ of the AC input. Given the strange waveforms and the periodic action, how can we determine whether a conversion operation is successful? What filtering is required to make the output sinusoidal? How can alternative methods be compared to determine which works best? What should be done to get some specific frequency conversion such as 60 Hz to 400 Hz or something else?

These questions, along with such basic issues as the choice of switching frequency and the nature of switching functions can be answered through Fourier analysis. You recall the idea: Any physically reasonable periodic signal can be expressed as a sum of sine waves with frequencies that are integer multiples of the fundamental. In a power converter, a waveform can be represented as a Fourier Series. As in the case of circuit laws, this is more than a mathematical construct. The sine waves in the series have physical reality, and we can examine the series to find out whether it contains the desired result. We can compare different waveforms to see which one gives the largest desired sinusoid while producing the small possible coefficients at other frequencies.

In many other electrical engineering specialties, the Fourier Transform gives helpful representations for unknown or highly variable signals, In power electronics, the waveforms are usually well-known, and it is the process of generating the waveforms that is of interest. We are often concerned with a single frequency. The Fourier Series tends to be more directly applicable to the problems of power electronics than the Fourier Transform.

Fourier analysis is a very powerful tool for both analysis and design of power converters, It guides the selection of switching frequencies and helps define the switch action for a desired conversion result. It helps us pick out the salient features of pieced waveforms. It is used directly for control of many high-power inverter circuits. It is even the basis for some modern standards that define the quality of a near-sinusoidal electrical source, In the following post, a short review of Fourier Series analysis will be provided. The analysis is then applied to converter waveforms and to switching functions. One crucial aspect is the ability of a converter to control the flow of energy. Fourier Series analysis identifies some fundamental requirements to make energy transfer successful.