How to sketch harmonic component graph?

  • #1

Homework Statement



An a.c. voltage, V, comprises of a fundamental voltage of 100 V rms at a frequency of 120 Hz, a 3rd harmonic which is 20% of the fundamental, a
5th harmonic which is 10% of the fundamental and at a phase angle of
1.2 radians lagging.

(i) Write down an expression for the voltage waveform.
(ii) Sketch the waveforms of the harmonic components.
(iii) Determine the voltage at 20 ms.
(iv) Given an ideal V = 100 V rms, what is the percentage error at 20 ms?


Given:
V1 = 100 V rms
f = 120 Hz,
V3/V1 = 20% = 0.20
V5/V1 = 10% = 0.10
= 1.2 rad
t = 20 ms = 0.020 s


The Attempt at a Solution



(i) Completed


(ii) the instantaneous values of third and fifth harmonic as function of time t , respectively
V3(t) = 28.28 cos(720∏ - t)
V5(t) = 14.14 cos (1200∏ - t +1.2)




How do you then draw the sketch the waveforms from the two above equations? I've seen the actual graph, but I am being really stupid here, as when I crunch the numbers in to my calculator I don't get any where near the value I need?


This is the graph I was told is correct off a friend, but I don't want to just draw it without knowing how as I won't learn that way

graph.jpg



Thanks
 
Last edited:

Answers and Replies

  • #2
ehild
Homework Helper
15,530
1,901
[
(ii) the instantaneous values of third and fifth harmonic as function of time t , respectively
V3(t) = 28.28 cos(720∏ - t)
V5(t) = 14.14 cos (1200∏ - t +1.2)
These V(t) functions are not correct. Recall the form of the function that describes a simple harmonic motion of given frequency.

ehild
 

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