# Harmonic Content

#### safdar sohi

Joined Sep 16, 2011
8
Harmonic content

I am working on RF (13.56 MHz) Generated atmospheric pressure glow discharge plasma. I have recorded current and voltage wave form by applying Tektronix broad band current and voltage probes.How can I find harmonic content of recorded signals?

#### t_n_k

Joined Mar 6, 2009
5,455
If your recorded signals exist as a time / amplitude sampled data sequence set, then one obvious approach is to use FFT.

What form does your recorded data take?

#### safdar sohi

Joined Sep 16, 2011
8
Recorded data is in time/amplitude form. I do not know how to use FFT?

#### t_n_k

Joined Mar 6, 2009
5,455
If you use Microsoft Excel it has an analytical add-in for FFT analysis. It is referred to as Fourier Analysis under Data Analysis.

Presumably Open Office has something similar.

Otherwise use something like Matlab, Scilab (a free download) or other mathematical analysis applications.

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#### safdar sohi

Joined Sep 16, 2011
8
Thank you very much for your help. I have some queries in using FFT. Can I use Sampling rate of my oscilloscope in analysis? Are number of samples and data points same thing? When i enter the formula =F2*SG$4 message appears the formula contains an error Thanks #### t_n_k Joined Mar 6, 2009 5,455 Thank you very much for your help. I have some queries in using FFT. Can I use Sampling rate of my oscilloscope in analysis? Are number of samples and data points same thing? When i enter the formula =F2*SG$4

message appears the formula contains an error
Thanks
Answer is yes to both questions.

Presumably the error message relates to a formula in an Excel spreadsheet. I'm not sure, but if you are multiplying the contents of cell F2 by the (non-indexed) contents of cell G4 then it should probably just be =F2*G\$4

#### safdar sohi

Joined Sep 16, 2011
8
Thank you once again for your help. I still have some problems. I am confused how to create column F. Two sentences from help are quoted below

"Fill column "F" with the corresponding data, from column "A," point minus one."

"Now we need to calibrate the axis A of the graph to show the dominant frequencies. It may prove beneficial if we create a separate column showing zero through the number of data points minus one (N-1)."

Am i subtract one from column A to create column F

Or fill cells of column F starting from 0 to 2499, because i have 2500 data points.
Thanks for your time and help

#### t_n_k

Joined Mar 6, 2009
5,455
If you are able to post the two column data file as comma delimited plain text I can probably take a look and give you some additional help.

Even posting a single column file of the time response dependent data would be sufficient as long as you state the sampling interval. I'm assuming the data is for equal time steps.

Are you using Excel to do this FFT / Fourier Analysis?

#### safdar sohi

Joined Sep 16, 2011
8
Yes I am using Excel to do FFT. Data File is attached.

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#### t_n_k

Joined Mar 6, 2009
5,455
Your attachment is not visible to me.

#### safdar sohi

Joined Sep 16, 2011
8
Dear i am uploading the zipped file as the .txt file exceeds the limit. Sorry for inconvenience.
Regards

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#### t_n_k

Joined Mar 6, 2009
5,455
OK - I have had a quick look at your data. It appears to me to be a sinusoidal function with a small DC offset. The frequency is around 13.6 MHz. As it appears to be a simple sinusoid, I would therefore assume it has no harmonic complexity.

As a further comment, the time column precision for your sent data (number significant figures) is insufficient. Also I think the signal value data lacks the necessary measurement precision.

What you are looking at isn't particularly interesting or informative.

So what are you hoping to see in this data?

#### safdar sohi

Joined Sep 16, 2011
8
Thank you very much. I am interested in finding the amplitude of third, fifth, seventh and ninth harmonics of the voltage and current wave forms. Could you please send me the FFT analysis of my data?

#### t_n_k

Joined Mar 6, 2009
5,455
I'm afraid your data is not showing those harmonics - in my opinion only the fundamental is evident in the spectrum.

The time plot of your signal indicates a high level of quantization (sampling) "noise" as a result of the digitizing of the waveform through the signal capture on the oscilloscope. See the attached image.

What resolution (bits) are you able to achieve on the oscilloscope capture?

Is the signal data you posted an actual voltage value or simply the scope digitizer binary-to-decimal equivalent.

Also, as I indicated in my previous post, you seem to have lost a number of decimal places in the the time data. For instance there a several occurrences of the time -1.24E-7 in the time data. What's the actual time step?

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#### t_n_k

Joined Mar 6, 2009
5,455

1. I've had a closer look at the time scaling and have now presumed you used a sampling interval of 100 picoseconds. At 13.56MHz this gives about 737 samples per cycle. This agrees with the plotted time domain signal.

2. If you want to do an FFT then normally your data must increase in sample sizes of 2^n. If n=11 this equates to a data 'bin' size of 2048. This value is as close as you an come to 2500 samples. In other words you can only use a contiguous 2048 sample subset of the total 2500 captured samples to do the FFT.

3. A sampling rate of 100 picoseconds with a 'mandatory' FFT sample size of 2048 gives an interval of 204.8 nanoseconds. This equates to a frequency interval of 1/204.8ns or 4.883 MHz in the FFT domain. This is problematic because 4.883MHz isn't an integral divisor of 13.56MHz. The closest you get in the frequency spectrum is 14.648MHz (the 3rd FFT term) which is a fair way off 13.56MHz. One way to resolve this is by increasing the total sampling interval (i.e. capture more samples at the same sample rate). If you had at least 8192 (2^13) samples then the frequency resolution in the FFT domain would be 1.221MHz which would get you to an 11th FFT term of 13.428MHz - a somewhat better approximation to 13.56MHz. This discrete frequency increment of the FFT is an inherent limitation of the FFT method.

I can post an Excel spreadsheet of what I've done - which may not be very useful to you. Anyway, it's up to you. What version of Excel do you use?

#### safdar sohi

Joined Sep 16, 2011
8
Thanks
I am layman in this field. I have first time used oscilloscope and current and voltage probes. I am really thankful to you for valuable suggestions. I will try to find answers of your queries and also check the specifications of my instruments. I will incorporate these suggestions in my future data recording.
I am using office XP 2007. Please post the FFT analysis. It will be helpful for future analysis.
With high regards

#### t_n_k

Joined Mar 6, 2009
5,455
File Attached ...

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#### t_n_k

Joined Mar 6, 2009
5,455
Updated version with some minor additions to aid with doing your own FFT.

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#### KL7AJ

Joined Nov 4, 2008
2,229
Safdar:

Interesting to hear about someone else doing inductively coupled plasmas! When I worked in the UCLA plasma lab, we created the first atmospheric pressure ICP ever....using just over 100KW at 4.83 MHz!

Using FFT as suggested is a good idea. However.....I suspect that you will find the harmonic content almost non-existent...at least we did. The high Q of the matching circuit made the currents nearly perfectly sinusoidal. I am curious to see what you find. Keep us posted!

Eric