## Fourier Series Representations of Switching Functions

To take full advantage of Fourier analysis, we need to consider series representations of switching functions. The idea is to figure out the Fourier Series of a switching function in some general way, in order to avoid recomputing it multiple times in the future. Since any switching function is either 0 or 1, and is normally periodic, a plot of […]

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## Fourier Series of an Inverter Circuit

One of the simplest inverters switches between polarities of a DC input to create a square wave. This wave can be filtered to give an approximate sinusoidal output. Let’s find the Fourier Series of a square wave of radian frequency . We will also determine which components are wanted and the amplitude of the wanted components. These specifications will have […]

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## Power and Average Power in Fourier Series

In a power conversion sysytem, the major issue is the control of energy flow between a source and a load. The usual measure of energy flow in an electrical network is the average rate at which energy is transfered, or the average power . This can be computed from the instantaneous power, , with the average integration Average power can […]

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## Fourier Series of Full-Wave Rectifier Circuit

In an earlier post, we established that there is typically only a single component of the Fourier Series desired in most cases. All other components are effectively noise. An example of a typical full-wave rectifier circuit will help to illustrate this idea. Let’s compute the Fourier Series of a full-wave rectified signal . What is the fundamental frequency? Which is […]

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## 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 […]

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## Review of Fourier Series

Nearly any periodic function of time , such that , can be written as a sum of sinusoids known as the Fourier Series. where the radian frequency is defined as . This result applies to signals with jump discontinuities which are often encountered in the world of power electronics. While there are few very special periodic functions without Fourier Series […]

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