# Principal frequencies of a Waveform

rude man
Homework Helper
Gold Member
Ok thanks RM, I'll give the pdf a thorough read and try again.
Good. I would like to see the thread continue until everyone's happy!

Gremlin
Gold Member

## Homework Statement

Identify the principal frequencies in the current waveform

## The Attempt at a Solution

From the excel file, I have identified 3 principle frequencies at 52Hz, 246Hz and 351Hz. Is this correct? What does the term principle frequency actually mean?
Part 1 of this questions asks you to obtain the Fourier Transform for the data using the Fourier Analysis Tool of Excel. The transformed data should commence in cell D2.

I have done the analysis (attached spreadsheet), but am unsure exactly what data/figures i should put in my write up - can anyone advise?

#### Attachments

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Gremlin
Gold Member
Or is it inferred that you've done it from subsequent answers?

Gremlin
Gold Member
Thats the darndest thing, the sample interval does not state the time units. "The supply current was sampled 1024 times over a very short time interval" thats all it gives me with regards to time, I assume we can use any sensible small time period. If you hover the mouse cursor over cell I3, it does state that the sampling frequency is 360/20ms=18000. I re-ran the simulation at 20ms:

View attachment 83707
View attachment 83708
Can i ask how you did this? Did you feed it the figures from the spreadsheet?

rude man
Homework Helper
Gold Member
I'm leaving this in the hands of earthloop and electest.
r m

Gremlin
Gold Member
Or is it inferred that you've done it from subsequent answers?
To answer my own question i can only assume it's inferred from subsequent answers that you've done it.

Gremlin
Gold Member
The final part of this question is

Attempt to synthesise the shape of the original waveform from its principal harmonics [e.g. sketch the waveforms of the harmonics on the same time axis and add them together].

The principle waveform is at f = 52.7Hz and the harmonics are at 246.4Hz & 351.6Hz - what axis should i use for the waveforms?

Gremlin
Gold Member
Can anyone offer the any assistance as to what axis to use when plotting the fundamental and the 2 harmonics?

I'm unsure how to get them to 'overlap' so i can subtract them.

Please see post #44. I again strongly advise scrutiny of the attached pdf file for the DFT theory.
Also, the attached excel file in that post gives the correct rms values (column G).
Keep in mind that the frequencies are the bin frequencies and the rms values the corresponding bin current values. If the data sampled three discrete frequencies the dft frequencies will be approximate of course.

To answer your question, you do take the rms of I1, I2 and I3 in the THD formula. (Actually, you could use the amplitudes too. Works either way).

I don't understand why you multiplied your I2 terms by √2 but the I2 values are incorrect anyway. I get THD = (1/22.46)*√(12.402 + 8.842) = 67.8%.
I'm so confused with this question different answers and calcs everywhere!

As the question asks for Rms, I found the square root of the I^2 values (which I assume are peak?), multiplied this by sqrt 2 to get RMS then plugged the values in??

1/5.635 Sqrt (4.1822^2 + 3.5364^2) then multiplied the whole thing by 100 to find the percentage.

Am I way off?

Thanks :-(

HDG
Sorry to go all the way back to the beginning but...

The spreadsheet shows principal frequency as being the highest peak (I believe this is both I1 and n=1). This is 52hz with a magnitude of 15.878. I'm confused though as to Why 15.878 is just rounded up to 16 yet the 2 distortion frequencies are not rounded and stay at 8.77 and 6.25 respectively.

I've used data analysis on excel to produce the same graph but am in 2 minds what number to use for 1/(I1) when using the THD formula. Do I use 1/square root 15.878 etc etc or stick
with 1/square root 16 etc etc detailed above.

Thanks

HDG
Using 16 = 96.89%
Using 15.878 = 97.26%

Both obviously equate to 97% but Just wondering if there was something I'd missed about needing to round up a fundamental or something

HDG
Grappled with this for a few days and I'm happy I've got the answer. It's done using 15.878.

For part iv) I changed the 3 magnitudes to rms values ((square root of magnitude)x0.707). I then used the formula:

Amplitude(rms)*sin(2pi x f x t)

in 3 separate columns in excel (for each frequency and it's associated rms magnitude) and just dragged the formulas down to complete the 1024 entries. I then summed all of the 3 entries, created another column for time(s) and then inserted a scatter graph to synthesis the original waveform. Only did it over a short time period though as the graph wouldn't accept all 1024 entries.

(To get the formula to drag down I had to lock some of the fields when writing the formula with the $sign) e.g.$b$2*sin(2pi*$a$3*a8)). Grappled with this for a few days and I'm happy I've got the answer. It's done using 15.878. For part iv) I changed the 3 magnitudes to rms values ((square root of magnitude)x0.707). I then used the formula: Amplitude(rms)*sin(2pi x f x t) in 3 separate columns in excel (for each frequency and it's associated rms magnitude) and just dragged the formulas down to complete the 1024 entries. I then summed all of the 3 entries, created another column for time(s) and then inserted a scatter graph to synthesis the original waveform. Only did it over a short time period though as the graph wouldn't accept all 1024 entries. (To get the formula to drag down I had to lock some of the fields when writing the formula with the$ sign) e.g. $b$2*sin(2pi*$a$3*a8)).
Hi HDG,

Did you get the question correct? I got a final answer also of 97.271%

How did you select the fields to create the scattergraph?

Thanks for any help!