[sdiy] why 10V

[Magnus Danielson]

From: René Schmitz <uzs159 at uni-bonn.de>
Subject: Re: [sdiy] why 10V
Date: Fri, 19 Sep 2003 17:24:38 +0200

> 
> Hi Jürgen and Don,
> 
> >>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?
> 
> Seems like the essentially linear systems theory isn't adressing this 
> because its a nonlinear problem. So I wouldn't expect to find a formula 
> for it.

Non-linear? Where is the non-linearity? The Hilbert transform is a perfectly
linear and doesn't change properties over time. That you can't realize a
perfect Hilbert transform is another thing...

> I think the worst case would be if all peaks of the individual partials 
> come out all at the same time after the delay network. It should be 
> possible to see what the input signal has to look like so that this is 
> the case. (I think this is the reverse thing to the impulse answer. 
> Anyone?!)

Diffrentiate your square-wave. You need a capacitor, a resistor and an op-amp
to form a fairly good diffrentiator. This will create migthy share pulses and
a flat frequency responce up to some quite high frequency.

Anyway, the real issue here is headroom and one of the uses there is to handle
the worst-case Crest-factor. The Crest-factor is the relation between the peak
and the RMS voltage. It is actually a quite interesting exercise to sit down
and look at Crest-factors. In practice the Crest-factor doesn't go very high
and I'd guess that the worst case we ever see in synthesiser designs is a
narrow pulse (PWM), but in practice there we keep the peak-to-peak voltage
stable and let the RMS voltage drop, so it doesn't end up as much of an issue.

Cheers,
Magnus