Barkhausen must be wrong.

Look again at the schematic.

I've looked at it several times. What do you see there that's relevant?

(snip)

The signal input to the right transistor is not from an emitter follower.

You can make an oscillator with just an emitter follower and some r-c's... I did it accidentally ca 1975, and was surprised. The impedances are such that you usually need a darlington to pull it off.

There are a couple of simple 2-terminal-plus-ground RC networks that can have an AC voltage gain above 1.

John

I'm not sure what you mean. Are you sure you're looking at the right schematic, the 5th one down? The one titled "A Practical Twin-T Oscillator"?

But he says this one has no voltage gain. So how does this work?

I think he meant that the transistors have no voltage gain, and maybe he's assuming that an RC network can't have gain. Dunno.

John

POWER gain IS the requirement.

...Jim Thompson

Sorry, I was looking at the second schematic.

The unusual part of this twin T is that the component values are not the usual C and 2*C, 2*R and R. A ratio of about 5 is used, instead. And the way it is connected, instead of the usual notch response, it has a broad bandpass filter response with a peak gain of about 1.089 at about 130 Hz, with the loading effect of the 1n cap but not counting the darlington.

So it is possible to get a little voltage gain from an RC circuit.

Simulating just the twin T, unloaded, the highest possible gain seems to occur close to an R and C ratio of about 4.75, and that voltage gain is about 1.094.

You get an A+. My mathematical assistant says the max gain of 1.08893 occurs with a ratio of 4.83152 at a frequency of 129.128034 Hz

See: "Synthesis of Passive RC Networks with Gains Greater than Unity", Herman Epstein, Proceedings of the IRE, July, 1951, p. 833.

My assistant says that under these circumstances the maximum gain of

would

(snip)

I don't have access to this paper.

In Vorperian's book, "Fast Analytical Techniques for Electrical and Electronic Circuits" there's a 7-page discussion of it as well (under the heading, "RC Filters With Gain" in the chapter, "Passive Filters: Where Inductors and Transformers Still Get Respect," which I rather like :-) ). That's probably short enough to fall under "fair use" if you'd like me to scan and post it.

---Joel

I looked at it as, the Twin-T, because of the component values, is an impedance transformer. It has "voltage gain" in that the output volts are greater than the input volts; but it has a "current loss" which is why you need the darlington - for the light loading on the output end.

The thing is, I don't know if an impedance transformer counts as "gain" - does an ordinary step-up transformer have "gain"?

Thanks, Rich

would

You will very shortly.

Post away!

If one's definition of "voltage gain" is "ABS(Vo/Vi) > 1", then, yes. This is the sense in which Epstein used the word "gain". See my responses to John Popelish.

And, of course, one could get even more particular and speak of "loaded gain" and "unloaded gain".

I imagine that an oscillator could be built which used a small transformer on the output of a network giving phase shift, followed by an emitter (or source) follower for the necessary "current gain". The phase shifting network could even be an all-pass network.

Take a (triode, pentode, transistor, FET) and put the common (cathode/emitter/source) to the CT on a tapped tank coil. Ground one end of the coil. Cap couple the other end to the input (grid/gate/base), biasing as appropriate. Connect supply voltage to other terminal (plate/collector/drain).

Voila. ;)

Tim

-- Deep Fryer: A very philosophical monk. Website @

transformer