# Barkhausen must be wrong.

Discussion in 'Electronic Design' started by The Phantom, Oct 10, 2007.

1. ### Simon S AysdieGuest

That's what I always thought. One doesn't, per se, care about "gain"
from the negative resistance viewpoint either.

3. ### John LarkinGuest

Presumably one could cascade such circuits.

John

4. ### The PhantomGuest

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.

5. ### The PhantomGuest

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.

6. ### John LarkinGuest

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

John

7. ### The PhantomGuest

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?

8. ### John LarkinGuest

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

Can anybody post the paper?

John

9. ### john jardineGuest

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

10. ### John LarkinGuest

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

11. ### The PhantomGuest

On Wed, 10 Oct 2007 17:24:16 -0700, John Larkin
SNIP
I'll post it over on ABSE

12. ### Robert BaerGuest

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

13. ### john jardineGuest

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

14. ### Fred BloggsGuest

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.

16. ### Phil HobbsGuest

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