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Design >> Analog Design >> frequency spectrum analysis of full-wave retified sine wave
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Message started by lhlbluesky_lhl on Jan 24^th, 2013, 6:18am

Title: frequency spectrum analysis of full-wave retified sine wave
Post by lhlbluesky_lhl on Jan 24^th, 2013, 6:18am

for a sine wave of 50hz, if full-wave rectified, the wave can be 100hz. but at the transition point, that is, the connection point of adjacent two half sine wave, the frequency can be a little higher(2k~10khz maybe, because it is very sharp at this point), but i want to get the exact frequency of the transition point. i used fft, but didn't get any useful information.
thanks.

Title: Re: frequency spectrum analysis of full-wave retified sine wave
Post by raja.cedt on Jan 24^th, 2013, 7:58am

hello,
Full wave rectifier has not only contains 100hz, but also all even harmonics so you can represent such a sharp transition with higher order harmonics. Think abut square wave though it has some frequency F, still it has sharp edges' which is in corresponding to inf frequency.

Thanks,
raj.

Title: Re: frequency spectrum analysis of full-wave retified sine wave
Post by Dave Jackson on Jan 25^th, 2013, 11:16am

Hi lhl,
I want to comment on your statement, "i used fft, but didn't get any useful information."

It is very important when using the dft function to set up your simulation properly. If you do not set up your simulation properly, you will get spectral leakage and your "useful information" will be hidden in spectral leakage, aliasing, etc. Here is what you should do:
1) Make sure that the output of your rectifier is bandlimited to the maximum frequency that you care about. A pure sinusoid is bandlimited, but a sinusoid that is perfectly rectified (with ideal components) has infinite harmonic content. If you try to compute the dft on a signal that has frequency content to infinite frequency, you will need to use an infinitely small timestep to avoid aliasing. Instead, use a high order filter (10 pole Gaussian, for example) to limit the frequency content at the input to your dft computation.
2) Simulate for at least a full period of your incoming signal. I often simulate for five periods. In addition to these periods, make sure that your circuit is settled (in other words, some circuits take a while to start up, and you have to run for this time PLUS at least one period).
3) Use the parameters maxstep and strobeperiod to force the simulator to produce enough timepoints. Divide the period of your input by an integer to get maxstep and strobeperiod. For example, if you care about content out to 10kHz, choose a maxstep/strobeperiod that is at least as small as 1/10kHz = 100us, and also an integer dividend of 1/50Hz = 20ms. Since 20ms/100us = 200 is an integer, you can use 100us for strobeperiod/maxstep. Maxstep tells the simulator that it isn't allowed to take bigger time steps than the specified amount, and strobeperiod tells the simulator that the output file should only contain data at integer multiples of the strobe period.
4) Run your simulation and set up the dft command using the following parameters:
-- from: choose a time when your circuit is fully settled (when all startup transients have settled out; when the circuit output has become purely repetitive)
-- to: set this to the "from" time PLUS an integer number of periods of your input. Example: if from equals 1.1ms, to should be 1.1ms + 1/50Hz = 1.1ms + 20ms = 21.1ms
-- number of samples: an integer power of 2 (128, 256, 512, etc). In our example, we used strobeperiod=100us, and maybe we ran for 40ms (2 periods of 50Hz). This means that we have generated 40ms/100us = 4000 points. We set N to 4000 rounded up to the next highest power of two, which is 4096.
-- window type: if your circuit is completely periodic (no drift from period to period) then you can use a rectangular window. However, if there is any drift from period to period, a non-rectangular window like Blackman, Hamming or Hanning makes the unsettled behavior at the beginning and end of the period less important (the window gives this content less weight). In your case, you can compare rectangular to one of the other windows to see if you see a big impact.
-- the other parameters I generally leave alone.
5) Plot dB20 of your dft result. Remember, you will only see frequency content out to the frequency specified by strobeperiod.

Finally, remember that if you build a rectifier, the actual frequency response will be highly dependent on the parasitic components in your circuit.

Hope this helps.
Dave