Path: utzoo!utgpu!water!watmath!clyde!rutgers!ukma!gatech!udel!rochester!bbn!uwmcsd1!ig!agate!pasteur!trinity!max
From: max@trinity.uucp (Max Hauser)
Newsgroups: sci.electronics
Subject: RC twin-T networks in oscillators and filters
Summary: stability, job interviews, inductorless radio
Message-ID: <563@pasteur.Berkeley.Edu>
Date: 5 Feb 88 16:34:38 GMT
References: <2507@ihlpe.ATT.COM> <971@neoucom.UUCP> <418@pasteur.Berkeley.Edu> <1198@eneevax.UUCP> <580@anasaz.UUCP>
Sender: news@pasteur.Berkeley.Edu
Reply-To: max@eros.UUCP (Max Hauser)
Organization: UC Berkeley
Lines: 80

In article <1198@eneevax.UUCP>, noise@eneevax (Johnson Noise) argues

>  [that I, MH,] seem to suggest that the T network exhibits infinite Q
>  requiring infinite gain in order to sustain stable oscillations.  This
>  is of course theoretically true, but not realistic. ...

Certainly; as I pointed out in my original, only ideally does the twin-T
oscillator fail to work ...

Then the article, without warning, shifts to interesting details about
resonant circuits, in the bandpass sense, which however was not what I
was talking about and which actually obscures the point I was trying
to illuminate. So I'll try it again.  Indeed, in article 
<580@anasaz.UUCP>, john@anasaz (John Moore) astutely points out:

>  	The twin-T is not a resonant circuit. "Q" in this case is not
>  the point - stop-band attenuation is. ...

If I may elaborate on this a bit in the interest of attacking a source
of confusion, what we'd really like inside a sinusoidal oscillator is
high Q *and* low attenuation at center frequency. A bandpass resonance
(near-imaginary conjugate pole pair), which is what Johnson (using first
names) was alluding to, gives us both; a notch (near-imaginary zero pair)
only gives us one, not the other. Indeed, in all other respects besides
frequency selectivity, the properties of the notch are harmful, rather
than beneficial, in an oscillator. Hence twin-T oscillator notoriety.

Frequency selectivity in both bandpass and notch means that if either is
used in an oscillator, a sharper tuned response will tend to desensitize
oscillator frequency to changes in gain in the associated loop amplifier,
because sharp tuning implies a high slope of gain versus frequency.

But in a notch filter, sharper tuning implies deeper loss at center 
frequency; therefore more absolute gain will be needed to sustain 
oscillation. As larger gain magnitudes are harder to obtain accurately
from simple amplifier stages, this introduces additional sources of gain
uncertainty and may indeed mean that the resulting oscillator is less 
ultimately stable in frequency with a sharper notch, rather than more.
In contrast, with a bandpass loop filter like an LC tank, sharper tuning
requires less amplifier gain instead of more, and this aids rather than
fighting the stabilizing tendency of the sharp tuning. Finally, bandpass
networks have the built-in fringe benefit of maximally filtering the 
output waveform for low distortion.

What the world really needs is a simple passive RC circuit (either
an impedance or a 2-port) exhibiting a high-Q pole pair, like a
parallel-LC impedance. And preferably with no more than two
capacitors. That would solve a lot of circuit problems in oscillator
and filter design. If only mathematics didn't get in the way.

Maybe someone not yet made skeptical by too much technical training, 
and therefore unaware that it cannot be done, will do it. (There are
precedents, after all. Just as there are technical quizzes that
engineers usually miss because they think too theoretically rather
than intuitively. I used to keep a few of those in mind when I was
interviewing for jobs, right out of college, to offer (humbly) if
some smart-ass young theoretical engineer started plying me with 
obviously-off-the-wall questions (troughs of mercury, that sort of 
thing; Hewlett-Packard divisions are known for these) intended not to
test any reasoning but instead to make the interviewee sweat. They 
usually found my trick questions both more revealing and more fun.)

What twin-T networks *are* good for, in my opinion, and apparently
in John Moore's too, is filters: either notch filters (their original 
purpose and what they do best) or, as feedback elements, in high-gain 
bandpass filters, where their deep notch again works in your favor.

About 1973 I built an AM superhet receiver without a single inductor
or transformer, using a 160-kHz IF strip (actually 159.155 nominal;
anyone guess where that number came from?) made of discrete-component
RC-active filters with twin-T networks and little JFET-bipolar 
feedback amplifiers. Worked like a charm (although from a practical 
point of view it would have been simpler and cheaper to use commercial
mass-produced ceramic-resonator IF filters, of course). I was in high
school at the time (not yet an old fart, just a young fart) and wanted
to demonstrate that coils were not as essential to radio circuits as 
some people religiously assumed.  Should have written it up 
for Poptronics.

Max Hauser / max@eros.berkeley.edu / ...{!decvax}!ucbvax!eros!max