AW: 2-comparator sawtooth generators?

[Haible_Juergen#Tel2743]

> A few times the topic of a 2-comparator sawtooth generator has
> come up, whereby the voltage over a capacitor swings between
> two levels guarded by comparators. A capacitor is charged with
> a current until the treshold level of one comparator is reached.
> Then the capacitor is discharged with some kind of electronic
> switch, until the treshold of the second comparator is reached.
>
> The first comparator will work ok, but I wonder if the second
> comparator is functional at all due to the relatively large
> reaction time of a comparator. The LM311 has a reaction time of
> ca. 200 ns. The (dis)charge time for a capacitor via a resistor
> is:
>    t=RC ln( (Vaim-Vstart) / (Vaim-Vtr) )
>
> where Vaim is the voltage the capacitor will ultimately charge
> to, Vstart the initial voltage, and Vtr the voltage we're
> interested in.
> For a typical application where a capacitor of 2.2nF is discharged
> through a 10 ohm switch, initial voltage say 1V, charge voltage 5V
> and a Vtr of 4V, t would be : 10 x 2.2n x ln(4) = 30 ns
>
> So, the discharge time of the capacitor is far far shorter than
> the reaction time of a comparator. So does this work at all in
> practice??

Good point, Rick, and good description of the whole thing.
>From practice: It works; I've built it. Of course there will be a slight
overshot, that depends on the different delay times and the
current limitation of the discharging device.
What effect will the overshot have?
(a) effect on level (i.e. on amplitude of the saw wave):
Might be a remarkable amount, i.e. the amplitude would be larger
than calculated, *but* it will always be constant at any VCO frequency,
cause the effect on volume will almost only occur at the short edge of
the saw.
(b) effect on time (i.e. on frequency of the saw wave):
A fixed amount of delay over the whole VCO frequency range -> we
can compensate to 100% with the usual series resistor at the capacitor.
It is *temperature* dependant - but even for a VCO at 5kHz, 200ns are
1ppm of the period time, so let it change 10% over temperature and
you get 0.1ppm drift from that effect.

So, no problems.

BTW: There are millions of circuits manufactured & sold, that work on that
principle - most of them are labeled "555" on their package. But the 555
has other problems that make its use for musical VCO's difficult. Ask PAIA 
...

JH.