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.
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?
Can i ask how you did this? Did you feed it the figures from the spreadsheet?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:
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I'm so confused with this question different answers and calcs everywhere!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%.
Hi 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)).