A half-wave rectifier passes the positive half of a sinusoidal voltage and blocks the…

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Fourier analysis and integral transforms · Fourier analysis and integral transforms

Mathematical Methods for Physics, Ch Fourier series and periodic decomposition

Problem

A half-wave rectifier passes the positive half of a sinusoidal voltage and blocks the negative half. Writing

x

for time, its output is

v(x) = V_0\sin(2\pi x/L)

for

0 \le x \le L/2

and

v(x) = 0

for

-L/2 < x < 0

, repeated with period

L

, where

V_0 = 10.0\,\mathrm{V}

and

L = 20.0\,\mathrm{ms}

. This waveform is neither even nor odd. ((a)) Without evaluating any coefficient integral, predict which of the

a_n

and

b_n

vanish. ((b)) Compute

a_0

b_1

and

a_2

. ((c)) Decide whether the series of

v

may be differentiated term by term once, and find the value in

\mathrm{V/ms}

that the differentiated series takes at

x=0

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