APPENDIX B

BASIC VOLTAGE WAVEFORM FOURIER COEFFICIENTS

B.1 INDEFINITE INTEGRALS

The following indefinite integrals will be used in determining the Fourier coefficients of the basic voltage waveforms v1(t), v2(t), v3(t) and v4(t):

image

The equal expressions ωn = 2πfn = 2πnf = 2πn/T will be substituted for one another whenever it is appropriate.

B.2 THE BASIC VOLTAGE WAVEFORM v1(t)

The basic voltage v1(t) is defined for one full period, as follows:

image

Therefore,

image

This follows from trigonometric identity A-13 of Appendix A, in the form

image

image

This follows from trigonometric identity A-9 of Appendix A, in the form

image

B.3 THE BASIC VOLTAGE WAVEFORM v2(t)

The basic voltage waveform v2(t) is defined for one full period, as follows:

image

Therefore,

where

The final expression for b2n results from the above definition ...

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