# complex waves

Discussion in 'Homework Help' started by ninjaman, Dec 5, 2013.

1. ### ninjaman Thread Starter Member

May 18, 2013
307
1
hello

I have some questions about complex waves

is the following formula correct for adding the 3rd and 5th harmonic to a fundamental,

(4/pi) * 100 + (4/pi) * 33 + (4/pi) * 20

this should equal 193v, but when I graph this on excel it is below 100v?

the formula I used on excel was to add each row then multiply by (4/pi)
this gave the correct shape for a 1st, 3rd and 5th complex wave. but not the right amount?

then I have this question

If the 5th harmonic has a lag of 70º
a) Produce graphs of individual waves and resultant complex waveform.
b) Produce a multisim simulation to support your graph.
would the formula, v * sin(70) be correct for showing a wave that is lagging?
also, does anyone know how to use multisim to show waves like this. the only idea I have is to make a circuit with an inductor in that would cause a lag. but the problem there is all the waves would lag.
any help would be much appreciated!!!
thanks
simon

2. ### WBahn Moderator

Mar 31, 2012
20,225
5,749
What, precisely, are these numbers:

(4/pi) * 100 + (4/pi) * 33 + (4/pi) * 20

What, for instance, is "33"? Is it the amplitude of the third harmonic?

Where does the (4/pi) come from?

What, precisely, are you trying to find?

3. ### ninjaman Thread Starter Member

May 18, 2013
307
1
hello

the 33 is the peak voltage of the third harmonic, the 20 is the peak voltage of the fifth harmonic. the fundamental is 100v peak (70v rms). the initial voltage values given on the assignment were 70vrms 50Hz fundamental, 23v for the 3rd and 14v for the 5th. so I took the 23 and 14 as rms. so the 33 and 20 are rounded(up)

I looked on the page for square waves and the formula for the fundamental and each harmonic was written on there.

I took the (4/pi) *.....+ from there. I inserted the values for the first third and fifth. which I think came to 193v, which I was told is the peak to peak value. which would make sense. I used excel to get the three wave forms and added them together using the formula in excel, B4+C4+D4*(4/pi) that gave me the complex wave which looked about right for a first third and fifth. otherwise I haven't got a clue about what im doing. trying to make sense of it. my tutor hasn't really given me much to go on. he said "im supposed to research it myself".
I also have to show in multisim, the fifth harmonic with a 70degree lag and the resultant complex waveform. so im guessing I have to get the first third and fifth, the fifth having the lag and show the resultant waveform and simulate it on multisim. so I have to make a circuit that would show the first and third waves and the third with a 70 degree lag. I was told that maybe the delay function on multisim may help create the lag. but I have to build a circuit first to provide a sinwave.
I thought it would be better to get a function generator, create a square wave with that. make a passive filter that would only pass the first third and fifth and somehow get the fifth to lag. I was thinking a low pass using inductors as an inductor would cause lag. I don't know if that would work. im guessing it would be something to do with RLC circuits. but I haven't learnt that on my course and it wasn't mentioned at all.
so that's it so far. probably doesn't make any sense.
all the best
simon

4. ### WBahn Moderator

Mar 31, 2012
20,225
5,749
Draw two sine waves, one of which is at twice the frequency of the other. Make them any amplitude you want -- perhaps make one of them twice the amplitude of the other.

Make two plots -- one with both sine waves peaking at t=0. The other with one sine wave peaking and the other troughing (at it's minimum) at t=0.

Now sketch (or plot) the sum of both waves in each plot. What, if anything, does the sum of their amplitudes have to do with the amplitude of the sum of the waves?

5. ### ninjaman Thread Starter Member

May 18, 2013
307
1
What, if anything, does the sum of their amplitudes have to do with the amplitude of the sum of the waves?[/QUOTE]

yeah I don't understand that, thanks though

6. ### Papabravo Expert

Feb 24, 2006
11,129
2,172
It is a straight forward question. The answer is nothing. The amplitude that results from adding three sine waves together will depend on how the peaks of the varios components line up. You have already begun to use Excel, so use it to refine your understanding.

You could also attempt to derive the formula for a sum of sine waves.

7. ### WBahn Moderator

Mar 31, 2012
20,225
5,749
One thing you should take away from this little excercise is that phasors, and all the formulas involving them, are good at a single frequency. You can't use them to do anything with signals that are not at the same frequency.

8. ### ninjaman Thread Starter Member

May 18, 2013
307
1
hello
yeah im still struggling to get this stuff.

so phasors are only good at one frequency?
please could you tell me what that frequency is!

I haven't had any confirmation on what the formulas are. I don't know what they are. I don't know how they work.

so im guessing (and im also guessing that I wont get a straight answer on this) that I have to know everything about phasor diagrams to understand phasors and that will answer my question.

1. I don't know what the formulas are for this. so if I have a fundamental a third and fifth I can use phasor diagrams to find the total voltage?

2. does the formula (4/pi) * voltage (fundamental) + (4/pi) * voltage(3rd harm) + (4/pi) * voltage (5th harm) have anything to do with adding waves to get complex waveforms?

thanks
I appreciate the help its just not much of it makes sense. I understand the part about the individual amplitudes having nothing to do with the amplitudes of both added together. I don't know the best way to use excel to help understand the complex waves or adding waves or phasor diagrams.
simon

9. ### WBahn Moderator

Mar 31, 2012
20,225
5,749
Correct. Because a phasor is nothing more than a shorthand notation for the following:

v(t) = Vo * cos(ωt + θ)

The three parameters involved are the amplitude, Vo, the frequency, ω, and the phase, θ. If we have a linear circuit that is driven by one or more sources all of which are at the same frequency, then all of the various voltages an currents that arise in the circuit in response will be at the same frequency, just different amplitudes and phases. So we only need to keep track of the amplitude and the phases and that is what a phasor does -- it represents the amplitude and phase of a sinusoid and can be combined with other phasors provided both phasors are using the same frequency for the sinusoid they represent.

You pick. But once you pick, you are stuck with it. When working with harmonics, you analyze the circuit multiple times, once with each harmonic at that harmonic's frequency. You then take those answers back into the time domain and add them there. You cannot add them as phasors because they are not at the same frequency.

Pretty much. It is unrealistic to expect people in an online forum to teach you everything. You need to take on some of that responsibility yourself.

Think about this. We've already established that phasors can't be used to add signals that are not at the same frequency. Are the fundamental, third, and fifth harmonic all at the same frequency?

For that specific example, but not in general. Go look at the relationship between a Fourier series and the signal it represents.

Excel is a great tool for lots of things. It's not bad for this kind of stuff, though there are better tools out there. Excel is a general-purpose tool. Like all tools, you have to spend time with them learning how to use them.

10. ### atferrari AAC Fanatic!

Jan 6, 2004
2,838
939
Hola Hombre Ninja,

Could you show what you have up to now?

I have no idea of Multisim but with Excel you could get most of in minutes.

Here, harmonics are in phase with the fundamental. Just shift the 5th by 70º and you are there.

You add amplitudes at every instant. Do you know how to do that in Excel? It's simple.

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11. ### WBahn Moderator

Mar 31, 2012
20,225
5,749
If the harmonics are in phase with the fundamental (what ever that means since they aren't at the same frequency, though a meaningful interpretation is certainly possible, I just don't know if it is standard), then why is there a need to shift the phase of the 5th harmonic -- after all, isn't it in phase with the fundamental? Or isn't it.

12. ### atferrari AAC Fanatic!

Jan 6, 2004
2,838
939
To make the OP to think a little of all this? If so, it is also misleading.

I agree with you. I found myself confused because albeit not the same the frequency, a fundamental and its harmonics have a clear stable relationship. Just in case I implemented what I believe he is required to do.

To visualize things I made the lea/lag variable at will (+70/-70). Even Excel 2003 (spin buttons et al) is enough for many things.

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14. ### ninjaman Thread Starter Member

May 18, 2013
307
1
thanks mike,
I thought it looked like a rectifier but there are so many different versions of circuits it becomes confusing. I guess following the voltage through any circuit would explain things. I guess im onto the right track with the simulation. I did something very similar but without the resultant complex wave. I had the three power supplies, in series and had to add a resistor to avoid "convergence problems" with multisim. though I had both ends of the series supply going to ground so im guessing that may be why they didn't add. where as you had yours going to an output and one ground on the end. I don't know how I would do that on multisim.
I like the excel thing that atferrari did. im still a little unsure about adding the sine waves. someone I know said V*sin70, I don't know if that means adjust the main formula of that sinewave to Vmaxsin(2*pi)frequency
(that last formula is not complete, I cant remember the rest)

thanks for your help, I feel im getting a lot closer. did this make sense to anyone else when they were first starting out? my brains in knots at the moment.

all the best, CHRISTMAS SOON, WAHOOOO!!!
simon