# Exam 1 - ECE472 EXAM#1 FALL 2013 Instructions 1 Closed-book...

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ECE472 EXAM #1 FALL 2013 Instructions : 1. Closed-book, closed-notes, open-mind exam. You may only use the exam objectives dis- tributed in class. 2. Work each problem on the exam booklet in the space provided. 3. Write neatly and clearly for partial credit. Cross out any material you do not want graded. Name : Problem 1 : /20 Problem 2 : /20 Problem 3 : /30 Problem 4 : /30 Total : /100 Periodic Waveforms : v ( t ) = V o + 2 V 1 sin( ωt + θ v 1 ) + 2 V 2 sin(2 ωt + θ v 2 ) + . . . V rms = V 2 o + V 2 1 + V 2 2 + . . . i ( t ) = I o + 2 I 1 sin( ωt + θ i 1 ) + 2 I 2 sin(2 ωt + θ i 2 ) + . . . I rms = I 2 o + I 2 1 + I 2 2 + . . . P = V o I o + V 1 I 1 cos ϕ 1 + V 2 I 2 cos ϕ 2 + . . . DPF = cos( θ v 1 - θ i 1 ) = cos ϕ 1 DF i = I 1 ,rms I rms THD i = v u u t ( I rms I 1 ,rms ) 2 - 1 PF = P S = P V rms I rms PF = DF i × DPF = DPF 1 + THD 2 i only if v ( t ) = V m sin ωt 1

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Problem 1 (20 Points) 2 π 2 - π 2 - 2 -2π 2 - 2 θ v( ) 0 π V m θ (a) Explain why the Fourier series expansion of the above half-wave rectified waveform is of the form: v ( θ ) = a o + a 1 cos θ + a 2 cos 2 θ + a 3 cos 3 θ + . . .
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