Re: No Exit & Sartre

On Sat, 27 Aug 2005 17:30:02 -0500, Ric Locke <warlocke@xxxxxxxxxxxx>
wrote:

>On Sat, 27 Aug 2005 20:20:13 GMT, Jonathan L Cunningham wrote:
>
>> On Sat, 27 Aug 2005 18:28:25 GMT, whheydt@xxxxxxxxxxx (Wilson Heydt)
>> wrote:
>>
>>>And then there's how you get a sine wave out of an analog computer. You start
>>>by assuming you have one as input. integrate it twice, invert it, and then
>>>feed the result back in where you assume you had one. Works in practice even
>>>though "theory" says it shouldn't.
>>
>> Whose "theory"? That's just another name for "oscillator" :-).
>>
>> I bet the tops and bottoms of the waves are ever-so-slightly clipped.
>
>Not necessarily, given judicious selection of gains. Precision sinewave
>generators are a common piece of test equipment, and they work exactly as
>Hal described.

If the gain was constant, over the range of values of the
the sine wave, (which it won't be, using real, physical components)
then for it to oscillate, the gain would *have* to be exactly 1 (which
is impossible) or greater than 1, else the oscillation would die out.

Hmmm. You (and Wilson) are right. If the gain is *almost* exactly
one, but ever-so-slightly more at low voltage, and ever-so-slightly
less at a higher voltage, then you'll get a wave which is almost
exactly (but not quite) a perfect sinewave, of a given fixed
amplitude, without any clipping.

I still have an oscillator I built as part of an electronics
practical class, when I was at university. In that, the gain
was controlled by a thermistor, so that it was "theoretically"
unity.

I think you'd both agree that, even if you couldn't measure it,
nothing physical like that could generate a *perfect* sinewave,
even ignoring noise. (If you think about it, in this particular
example, even though the time-constant for the thermistor to
heat up and cool down might be tens of thousands of cycles of the
oscillator, that just means the sine-wave would deviate
from "perfect" by around one part in tens of thousands, or
some simple function of that.)

I haven't talked about feedback delays, because (in the steady
state) they may be part of the explanation for whatever the
gain actually *is*, but aren't part of the reasoning above.

Jonathan
(A theoretician, not a practical can-build-things person ;-)

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