Fourier Series Representations of Switching Functions

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

Power 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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Fourier Series of Full-Wave Rectifier Circuit

Diode bridge rectifier

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

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

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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