[sdiy] why 10V

[jhaible at debitel.net]

Interesting!

JH.


>    > Date: Fri, 19 Sep 2003 12:29:50 +0200
>    > From: jhaible at debitel.net
>    > 
>    > >    > Next question: If you run a +/-5V audio signal thru a chain of N
>    > >    > unity-gain all pass filters, what will be your worst case
> maximum
>    > >    > level at the end of the chain ?
>    > > 
>    > > A Hilbert transform is probably the worst case scenario.
>    > > 
>    > > The Hilbert tranform is a 90-degree phase shift that's constant over
>    > > frequency.  If you apply a square wave to a Hilbert tranform, the
>    > > result is a waveform with huge spikes.
>    > > 
>    > > So if the all pass filter aproximates a constant 90 degree phase
>    > > shift, the output peaks could be maybe ten times the input square
> wave
>    > > voltage.
>    > 
>    > Thanks for adressing this, Don!
>    > 10 times is more than I expected. How did you calculate this?
> 
> I guessed!  :-)  Hey, it was late at night.
> 
> You weren't specific about the all pass filter, so I considered the
> case where the all pass filter shifts phase by a constant 90 degrees.
> As such this isn't realizable, but perhaps you'd want to come
> arbitrariliy close to that.
> 
> Apply a 1 volt zero-to-peak square wave.  The harmonic content is:
> 
>   square = 1.414 (sinx - (1/3)sin3x + (1/5)sin5x - (1/7)sin7x ...)
> 
> Shifting the phase 90 deegrees:
> 
>   shifted square = 1.414 (cosx - (1/3)cos3x + (1/5)cos5x - (1/7)cos7x ...)
> 
> For cosines the sign of the coefficient doesn't matter, and so the
> peaks of this waveform add up to:
> 
>   peaks = 1.414 (1 + 1/3 + 1/5 + 1/7...) 
> 
> For 100 harmonics that's 4.15 V.
> For 1000 harmonics it's 5.78 V.
> For 10000 harmonics it's 7.5 V.
> 
> If the realization of the Hibert transform was sloppy, one way or
> another, you could have larger peaks.
> 
> Sure, it's a silly case.  What I really meant to say is that it
> completely depends on the all pass filter, and it's possible to come
> up with some crazy all pass filters.
> 
>   -- Don
> 
> -- 
> Don Tillman
> Palo Alto, California
> don at till.com
> http://www.till.com
> 
> 
> 




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