Addition of Fundamental & Harmonic Waveforms

[linguist]

If I have a fundamental waveform of 110V 50Hz with a 3rd harmonic waveform of 15V 150Hz how do I find the sum of the instantaneous voltages.

For instance if I want to find the sum of the instantaneous voltages at 50deg:

I have
e = Vpeak x sin 50deg
= 110 x 0.766
= 84.26V for the Fundamental waveform

For the 3rd harmonic waveform do I just do the following & then add the two together?
e = Vpeak x sin 150deg
= 15 x 0.5
= 7.5V

Somehow this doesn't seem correct?

Cheers

 

[MrAl]

Hello there,


The sum is rather easy to find. Assuming 110v is peak and 15v is peak (as per your own post examples) we have for the first wave:
E1=110*sin(2*pi*50*t)

and for the second wave we have:
E2=15*sin(2*pi*150*t)

and the sum we'll call E3 then is simply:
E3=E1+E2=110*sin(2*pi*50*t)+15*sin(2*pi*150*t)

and that's about all there is to it unless you use a trig identity for 3x angles in which case you can make a slightly different equation.

 

[Ratchit]

linguist,

Somehow this doesn't seem correct?

Your intuition is correct, in that your calculations are wrong. The composite wave has the same period or frequency as the fundamental. So, you have to evalate both the fundamental and harmonic wave at 50°, not one at 50° and the other at 150°. The attachment shows how this is done, and includes a plot for each wave. Notice how knowing the frequency or period is not necessary to compute the answer. In other words, time does not enter into the calculation. Only the frequency ratio and amplitude of the waves are necessary for the answer. The correct answer is 99.42 .

Ratch

 

[linguist]

MrAl & Ratchit,

Thank you for the replies, sorry for the late reply as I have been without a computer for a few days.
I can see how it is done now.

Cheers

 

[kevs926]

oh man you've been tricked by Ratchit, i am terribly sorry but we have to correct stuff like this.

first of all, your 1st post is 100% correct
fundamental waveform has an equation of
V(t) = 110*sin(t)
3rd harmonic waveform has an equation of
V(t)= 15*sin(3t)
evaluate at t=50
then you get what you did at your first post
then just add them

if you noticed, the very simple mistake ratchit did in his calculation is making the Vpeak of fundamental waveform 120V