Square from sine waves with the right amplitudes

180

01:33:56

These are (close to) the right amplitudes to actually produce a square wave from an infinite number of odd harmonics.  Somewhat short of infinity, we only have 4 harmonics here, but it proves the point that it could be done with infinite harmonics.  (If you get more overshoot with more harmonics, they're not scaled correctly.)

To make +-1v square wave:
  1khz  1.23v
  3khz  388mv
  5khz  209mv
  7khz  125mv
  9khz  76mv
No phase shift

Derivation of the amplitudes:
http://everycircuit.com/circuit/6122013801578496

published 7 years ago

jason9

7 years ago

This won’t make a 1V square wave, but if you make the voltage of the source the reciprocal of the frequency (1kH>1V, 3kH>333mV, etc.) it will produce a perfect sine wave with an infinite number of harmonics. However, the overshoot will gradually reduce not to zero, but to a fixed value greater than zero. Adding more harmonics won’t fix overshoot, just reduce it slightly so it’s ever so slightly closer to the fixed value.

hurz

7 years ago

Depends on how exact you need this 1V. But right the math behind needs 1/n falling sequence. Ringing is caused if begin and end of periode do not fit together and cause a jump. Mathematicaly "discontinuously" cause ringing and overshot. Else a high number of harmonics does help to come closer to original waveshape

eekee

5 years ago

The more I look at the 1/n sequence, the worse it looks. It has peaks on every rising and falling edge which don't correspond to anything IRL. The peaks don't go away with increasing accuracy. With infinite harmonics, the peaks might reduce to zero width, but I still don't like it.

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