Deriving a Sine Wave from a Square Wave

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01:59:36

A square wave is the sum of an infinite series of sine waves, having a fundamental and harmonics of higher frequencies. The fundamental can be seperated from the rest of the harmonics by filtering it out using multiple stages of a low pass filter. Here, I'm using 4 stages of a 2nd order active low pass filter. All stages, except the third, have a passband gain of 1. The third stage has a passband gain of 2 to boost the voltage of the obtained sine wave, as it too gets attenuated by the filter due to the fact that it lies near the cut-off frequency. Note that the square wave has a frequency of 1kHz, which means that it has a fundamental sine wave of 1kHz frequency and is seen at the output. Adding anymore filter stages will yield diminishing returns.

published 5 years ago

kiani

5 years ago

what is THD !

PrathikP

5 years ago

Donno. Probably low I guess, given that it has been filtered 4 times? There are no math functions here so I can't calculate TDH

kiani

5 years ago

you could use an LCR (in series) filter (notch) to eat all 1khz stuff. whats left is THD.

Molar

5 years ago

Nice, clean circuit and detailed description. Thanks.

fatcat2

5 years ago

What response characteristic does this filter posses with a D.F. of 1, bessel? I have the transfer function for a butterworth sallen key filter and so, I though that I would manually find the THD (it takes a great deal of time!) but I don't know what response does this filter possess. In that case, the best idea is to use a notch.

Molar

5 years ago

Haha. Love your comments. Don’t understand them thanks to my inferior brain, but love them.☺️

PrathikP

5 years ago

@fatcat2 I have cascaded 4 Butterworths, so simple raise the transfer function to the power 4. Now working with the transfer function and doing manual math is an absolute waste of time.

PrathikP

5 years ago

Don't worry too much about TDH. I have cascaded 4 second order low pass filters, so the output should be sufficiently pure.

fatcat2

5 years ago

@Molar --- 🥰

PrathikP

5 years ago

What do you mean "how is this a Butterworth"? Just look at the circuit. Do you not recognise it? It is 4 Butterworths connected in series!

fatcat2

5 years ago

Hey there! All of this depends on the caps ratio. I simulated various values in multisim and I got different results; if the ratio is 1:2, it is butterworth whereas if it is 11:15, it shows a bessel response. Cool! For the latter case (i.e., the Bessel filter), cutoff frequency is not equal to 1/2pi.sq.(RC). I didn't believe it first but then I understood it. I got this info from small signal BJT design by Douglas Self.

fatcat2

5 years ago

Sorry, the transfer function doesn't change but the response changes according to DF. It was indeed a careless mistake... This is certainly not a butterworth filter.

kiani

5 years ago

looks like copy paste replys..! LOL....very interesting thank you @fatcat2

fatcat2

5 years ago

I just wanted an answer. Hey, it's not a copy of my previous one. It's what's called #give&taketheknowledge! I told you about this because I found it very interesting.

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