Barkhausen must be wrong.

would

Budak also has some coverage of RC circuits w/ v-gain, IIRC.

My assistant has given me this link:

would

Presumably one could cascade such circuits.

John

would

One could certainly cascade them (I'm assuming you mean without an intermediate buffer), but would you expect the cascade to have voltage gain? Care to guess what the result will be with the network we've been discussing? I'll run the analysis and report the result.

I think "power gain" is necessary, but not sufficient, to give oscillation. If the RC network in the example under discussion is replaced with one which doesn't have "voltage gain", then in spite of the substantial power gain in the cascaded emitter followers, there will be no oscillation.

>

One would

Certainly the voltage gains would multiply, if the component values were right. But the impedances would get crazy fast.

John

One would

When you said "such circuits", I assumed you meant the very circuit we've been discussing, the one in the oscillator on the referenced web page. I didn't realize you intended "such circuits" to mean something like "similar circuits, but with varying impedance levels". With that meaning, I suppose that cascading might give even more gain. But, Epstein showed in his paper that the maximum gain that a passive network can have is 2. So, if one cascaded networks with impedance levels going up by an order of magnitude or so ad infinitum, one would think that the voltage gain would be unlimited. What would cause the voltage gain to remain below 2?

One would

Not having seen the paper, I can't say. Possibly a gain of 2 requires an infinite output impedance, or something like that, which prevents unlimited cascading.

Can anybody post the paper?

John

loop. One would

1.08893

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we've

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suppose

paper

Greater than 2 seems certainly doable. Did Epstein add some of those weasely "yes but's" or "assuming ... "?.

You'd think that if you can get a stage gain of, say, 1.1 with maybe a

100:1 loading ratio, then 10 stages would get you above 2. Spice could do that, but the real world probably can't.

100^10 is a bunch of ohms.

John

On Wed, 10 Oct 2007 17:24:16 -0700, John Larkin SNIP

I'll post it over on ABSE

Could have fooled me; the two look exactly like a darlington emitter follower.

of

voltage

been

I

magnitude

I'm up at 1e11!. For fun I'll put a sim pic on A.B.S.E.

Get real. I don't recall that the basic criterion for feedback oscillation is called Barkhausen's Conjecture, it is called the Barkhausen rule or something dumb like that.

--
Apparently:

http://web.mit.edu/klund/www/weblatex/node4.html

This is very well known. It's not difficult to make high order PLLs (for example) that behave pretty well. Third order PLLs are especially useful for situations involving constant frequency drift rates, e.g. accelerating spacecraft, because third order loops have zero phase error due to a linear rate of change of frequency.

You do have to make it act like a second-order loop during startup and big transients, or it's liable to exhibit nonlinear oscillations.

Cheers,

Phil Hobbs