what is an FFT graph?

[keantoken]

I was looking for a way to find distortion with my simulator and found in another thread that someone used an FFT. I use LTSpice/SWCADIII and I have found the FFT option but I don't know what an FFT is or how to use it to calculate distortion (is it specifically for distortion?) . Any replies are appreciated!

[HFGuy]

Fast Fourior Transform

Basically its the approximate spectral energy of your signal. In english that means the frequency content of your signal. A pure sine wave will have one impulse at that frequency. A square wave will have a large peak at its fundamental and then odd harmonics until the system starts to roll off. An FFT is only a approximation because for a wave to be a single frequency it needs to go on infinity, but the FFT samples your signal in finite periods so its just an approximation.

[SY]

Basically, an FFT is a computer algorithm to efficiently calculate an approximate Fourier Transform. A Fourier Transform, to anticipate the next question, is a means of converting from the time domain to the frequency domain (and vice versa).

For example, consider a 1kHz sine wave. If we graph amplitude versus time, we get the familiar wavy trace. If we graph amplitude versus frequency, it's zero everywhere except for an infinitely narrow spike at 1kHz. That's the Fourier Transform of the sine wave. The sine wave is the inverse FT of the infinitely narrow spike.

Every periodic function of time (and under certain formal assumptions every nonperiodic function) has its own frequency spectrum and vice versa. That's the basic thing to understand.

The formal mathematical definition can be found in any college-level physics text. If your calculus is still working, it's basically the integral over time of the time domain function times exp(-iwt), where w is two pi times the frequency and i is the square root of -1.

[keantoken]

Okay, so an FFT basically plots a curve that shows the volume of the different frequencies at the probe? Just so I understand properly, which I frequently have problems with (maybe because I'm 13), could you analyze the plot of an amp I made? Whether it's the worst amp you have ever seen, or it is impossibly pure, I want your input! here it is:

[keantoken]

The input signal is a 1kHz sine wave at .01V/~1uA. I will only show my design if I am asked to due to the fact that I have sometimes gotten some sarcastic comments. I also have not found a way to properly bias this design so it cannot be official. if you want to see it, ask, and you will be given.

[HFGuy]

Its easier to get a PASS/FAIL kind of figure from the THD+N. I find the FFT useful for determining the cause of the distortion and not as a figure of merit.

[poobah]

Use your spice and do an FFT of a squarewave. You will see your fundamental frequency as a spike on the left. Let's just say it's at 100 dB (height or magnitude). Then you will see 3 times that frequency at 90.5 dB... then 5 times at 86 dB.

Now to see how these harmonics add up... write a program in EXCEL to graph one cycle of a sine wave... like:

Y = sin (X)

Then do

Y = sin (X) + (sin 3*X)/3

Then do:

Y = sin (X) + (sin 3*X)/3 + (sin 5*X)/5

You can keep going if you want with more "odd" numbered harmonics.

You will see how the harmonics add together to form a squarewave. This should give you an "a-ha" moment.

[keantoken]

hmm... so how can I get a distortion figure? how do I tell if my circuit passes or fails? I am quite a noober at amps and biasing. I know what harmonics are... I am supposing that if the output is a pure sinewave then there won't be many notches and dips... Am I right? Every step is supposedly a victory... I might need to run a marathon!

[poobah]

Yes... you are right. Not so much notches and dips... but a floor with spikes...

Here is good write up on the method for calculating THD.

[SY]

Don't worry, at your age I was still doing ham radio. It took a couple more years for me to discover audio.

OK, you've filled in context. In your case, you're feeding in a sine wave at a single frequency, and the frequency spectrum would ideally just have a peak at that frequency. Fourier's Theorem says that any periodic function can be broken down into a sum of harmonic frequencies, so distortion will show up as additional spikes at whole-number multiples of the test frequency. In your case, there's something goofy in some setting somewhere in your software- you shouldn't see the baseline tilt, the scale is suspicious, and the noise doesn't look natural.

A good spectrum (and I mean good in a measurement sense, not an amplifier sense) should have a flat baseline, maybe some small spikes at line frequency (50 or 60 Hz) and its multiples, a big peak at the test frequency, and smaller peaks at whole-number multiples of the test frequency.