#### Consortium for Mathematics and its Applications

Product ID: 99696
Supplementary Print

# Design of Simple Power Supplied Using Fourier Series (UMAP)

### Author: John S. Robertson

This module discusses the components of a typical power supply that uses household electricity. A simple mathematical model is used to represent the time-varying voltage inside the power supply. The concepts of mean and root-mean-square voltages are introduced. Fourier series are used to examine the output of a full-wave rectifier. The Fourier coefficients represent voltage levels of constant or sinusoidal voltage signals that can be realized as output through the proper selection of filters. Applications of Fourier series to other types of power supplies are briefly discussed.

INTRODUCTION

MODELING VOLTAGES
Direct Current (DC) and Alternating Current (AC)
Household AC

HOW POWER SUPPLIES WORK
Transformer
Rectifier
Filter
Other Components

ANALYSIS OF RECTIFIER OUTPUT
Calculation of the Fourier Coefficients
What's Really in the Rectifier Output

DESIGNING THE POWER SUPPLY
Identification of Needs
Selection of Filters
Other Possibilities

CONCLUSION

REFERENCES

UMAP Module
19 pages

#### Mathematics Topics:

Differential Equations

#### Application Areas:

Engineering & Construction , Physical Sciences , Electrical Engineering

#### Prerequisites:

Differential equations (boundary value, Fourier series); introductory physics