How Do You Calculate AC Waveform Components and Errors?

[Big Jock]

So just calculate all point to 10ms you reckon then make the graph from there? Sorry for being a bit thick been at this for days and my head feels like mush!

 

[gneill]

So just calculate all point to 10ms you reckon then make the graph from there? Sorry for being a bit thick been at this for days and my head feels like mush!

You could do that but...

They asked for a sketch did they not? I wouldn't spend the time calculating points. I'd rough in the boundaries and the periods and free-hand the sine waves. You know how a sine wave looks, and if you have the amplitude and period it's easy enough to rough in.

For the one curve with a phase offset I might find the first zero crossing to fix the shift. After that it's handled the same way -- mark off periods from the zero crossing and lay down the sine waves to fit the within the periods and amplitude bounds.

 

[Big Jock]

Almost got all the point values now so Ill finish that off then put them into open office and create a graph in there. This way I have all the working and graph so surely should tick all the boxes?

 

[gneill]

Sure.

 

[Big Jock]

On thing gneil for the 5th harmonic would it be 14.14sin(1200pi x 0.001-1.2) then just change the time value as I go along till I reach 10ms for my various points?

 

[gneill]

On thing gneil for the 5th harmonic would it be 14.14sin(1200pi x 0.001-1.2) then just change the time value as I go along till I reach 10ms for my various points?

0.001 corresponds to t = 1 ms, yes? Don't you want to start at t = 0?

 

[Big Jock]

Yeah but checking was just as simple as plugging in the 1.2 as my figures for this are as follows
0
0.8
-13..18
13.67
-13.18
7.65
0.8
-13.18
13.67
-13.18
And am not sure those would be correct. Many thanks for your help again. Hopefully you can help clear up this final issue...

 

[gneill]

I can't tell what the numbers "mean" without the corresponding time values associated with them.

However, as I cast my eye down the list I notice the large jumps in values between successive entries, such as -13.18 followed by 13.67 followed by -13.18 again. Looks like your time step is too coarse and you're losing shape of the curve. In digital terms, your sampling rate is too low

 

[Big Jock]

those values are from 0 to 10ms the same as I used for the fundamental and third harmonic. Its only this fifth one which doesn't look correct when plotted...

 

[gneill]

those values are from 0 to 10ms the same as I used for the fundamental and third harmonic. Its only this fifth one which doesn't look correct when plotted...

It's because your sampling rate is not high enough! You need about 10 or 12 samples for each millisecond to resolve the shape of the wave for the 5th harmonic. Try just the first ms of the plot using time steps of 0.0001 second.

If you want to see the shape of the wave, you need to have enough samples over every period of the wave to follow its outline.

This is why I suggested that sketching by hand would be quicker.

 

[Big Jock]

I see your point now I think

 

[NascentOxygen]

The RMS conversion for a sinusoid is just a scale factor. The function of time using the RMS instead of peak for the constants will be a scaled version of the actual voltage waveform. One can always multiply results by √2 to obtain the actual voltage. It's just that the numbers are a bit easier to work with when they're nice multiples of ten

The root 2 needs to trail along. It doesn't make sense to speak of a waveform having an instantaneous value of .. RMS. Whether neater or not!

 

[gneill]

The root 2 needs to trail along. It doesn't make sense to speak of a waveform having an instantaneous value of .. RMS. Whether neater or not!

I agree that the √2 needs to be there if you need the actual instantaneous voltage values. It can be applied to the result values as required. To answer part (i) of the question you'd want to include it, perhaps as a factored value as I showed it in post #42. But I maintain that for the % error calculation it makes no difference. In fact the function could be written as

f(t) = 10sin(ωt) + 2sin(3ωt) + sin(5ωt + 1.21)

for that analysis.

 

[Ebies]

Can I ask, what program do you guys use to plot the graphs with?

 

[gneill]

Can I ask, what program do you guys use to plot the graphs with?

I use MathCad to plot general functions. If it's just a matter of sketching sinusoids I might use Visio to draw them (I made a stencil that includes sinusoidal pieces. They can be re-sized and stretched like any Visio object).

 

[Ebies]

For some reason i do not get the same values if i try to calculate the values of voltage for the fundamental wave, 3rd harmonic or 5th harmonic... For instance if i type 141.4sin(240pi*0.01) into my calculator i get 18.553 as an answer... When from previous posts i know it should be more... Also calculating the voltage at 20ms i get a different answer for each waveform thus giving me an overall incorrect answer... Any ideas...?

 

[gneill]

For some reason i do not get the same values if i try to calculate the values of voltage for the fundamental wave, 3rd harmonic or 5th harmonic... For instance if i type 141.4sin(240pi*0.01) into my calculator i get 18.553 as an answer... When from previous posts i know it should be more... Also calculating the voltage at 20ms i get a different answer for each waveform thus giving me an overall incorrect answer... Any ideas...?

Looks like you've got your calculator set for degrees rather than radians.

 

[Ebies]

Looks like you've got your calculator set for degrees rather than radians.

Yip, yip seems you're right... Thanks, I am feeling a bit like an idiot right now...

 

[grinder76]

iv) Given an ideal V = 100V rms, what is the percentage error at 20ms

Does anyone have a confirmed answer for this question?

 

[gneill]

Does anyone have a confirmed answer for this question?

Show us your own attempt. Helpers cannot simply provide answers to problems, but are more than willing to help you arrive at the correct solution by guiding your demonstrated efforts.

 

[grinder76]

Sorted now thanks

 

[jaff90110]

I have these question as well and wanted to dig this thread up again.
As I need someone's help , Could some genius have a look at this for me please. I using the Excel spread sheet to generate this wave form graph. I'm wondering are these value looks alright?
I have using these expression for each:
for the fundamental = 141.4 Sin (240*Pi*t*)
3rd Harmonic = 28.3 Sin (720*Pi*t)
5th Harmonic = 14.1 Sin (1200*Pi*t - 1.2)

time(sec) Fundamental 3rd Harmonic 5th Harmonic
0 0 0 -13.17903268
0.001 96.79496078 21.80552477 7.65040339
0.002 141.1209794 -27.7987292 0.800419963
0.003 108.9505725 13.63362898 -8.945510095
0.004 17.72211923 10.41792484 13.67371942
0.005 -83.11283467 -26.91489941 -13.17903268
0.006 -138.8954173 23.89448029 7.65040339
0.007 -119.3879687 -3.54693051 0.800419963
0.008 -35.16475005 -19.3726831 -8.945510095
0.009 68.11996952 28.24415641 13.67371942
0.01 134.4793914 -16.63432264 -13.17903268

0.02 83.11283467 + 26.91489941 + (-13.17903268) = 96.85 V at 20 ms. ( for the question 5(iii) )

As the attach pdf. file for the graph, Are they look ok?
I have no idea how to merge them all in one graph.

 

[jaff90110]

Try just the first ms of the plot using time steps of 0.0001 second.

I think I got it to the shape as the post #9 as gneill suggested!
Thank you.

 

[grinder76]

I think I got it to the shape as the post #9 as gneill suggested!
Thank you.

For the 5th Harmonic don't forget to include the effect of the phase angle if you haven't done so already. i forgot!

 

[jaff90110]

For the 5th Harmonic don't forget to include the effect of the phase angle if you haven't done so already. i forgot!

Hi Grinder76
Thank you for let me know that,