A.C. Voltage waveforms and harmonics?

1. Sep 17, 2011

alex.daciz

Hi, I have the following question:

An A.C. voltage, V comprises of a fundamental voltage of 100V rms at a frequency of 120Hz, 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.

(1) Write down an expression for the voltage waveform

(2) Given an ideal V = 100V rms, what is the percentage error at 20ms (milliseconds)?

I have an idea for the first part (see below) but clueless as to the second, can anyone help please? I guess the first step would be to work out the voltage at 20ms but from there...?

(1) Since V = Vrms x sqrt2 = 141.4V at 120Hz

3rd harmonic = 20% of 141.4 = 28.3V at 360Hz

5th harmonic = 10% of 141.4 = 14.1V at 600Hz

v = [141.1sin(240πt)] + [28.3sin(720πt] + [14.1sin(1200πt+1.2)]

2. Sep 17, 2011

rude man

You're comparing two voltages and so error should be obvious? If you get $0.38 in change and you should have gotten$0.40, what's the error in the change you got? :-)

3. Sep 17, 2011

Staff: Mentor

Once you have the expression for voltage as a function of time, you can substitute any value of t to determine the instantaneous value at that time. Compare this with the value of an undistorted sinusoid at that time.

4. Sep 18, 2011

alex.daciz

Ok so using the equation in (1), V at 20ms = 36.8 + 20.1 + 13.7 = 70.6V

Would this mean that the error is 29.4% !? That seems like a massive error, where has my equation gone wrong?

5. Sep 19, 2011

Staff: Mentor

For many applications, providing the approximation to a sinusoid gives the same heating or average effect as would the ideal waveform, it will satisfy our need. To judge whether your answer is probably correct, or probably not, try graphing V(t). You could overlay it with a sinusoid and adjust its phase shift for best fit, to visualize the error. An online plotter may be convenient. http://rechneronline.de/function-graphs/" [Broken]

Last edited by a moderator: May 5, 2017