Q of a super-inductor

Hey, if you guys were plotting Q of a simulated inductor (e.g,. from a
gyrator), would you plot Q as just staying at infinity once the resistance
goes negative? Or would you just plot it as negative Q?

It's interesting to me that the resistance from gyrator inductors start
heading south (drop below 0 ohms with a vengeance) generally well before the
imaginary part starts to degrade similarly; anyone for an intuitive
explanation as to why this is?

---Joel

 

If you'll thumb back through the old threads about gyrators I think
you'll find that I attributed it to excess phase in the OpAmps.

...Jim Thompson

 

Joel:

So called "Q-enhancement" is common in active RC networks, is a well known
phenomena and was studied and written about ad infinitum back in the 70's.

As Jim [Thomson] points out Q-enhancement is usually caused by excess phase
shift in the OpAmps.

The search for better active RC circuits [gyrators, gic's, etc...] always
led to inventions of novel circuitry that somehow reduces that excess phase
shift.

There are passive compensation methods that "tune out" the Q-enhancement,
but...

The "best" circuits use active compensation of the OpAmps wherein the excess
phase of one [of usually two] OpAmp in a circuit approximately cancels that
of it's paired [matched] OpAmp.

The Akerberg-Mossberg circuit was the first such 'active compensation"
circuit that appeared in the literature.

There is a lot of information on excess phase compensation, and a catalogue
of the "best" circuits, including the celebrated Antoniou gyrator invented
by Andreas Antoniou, now at University of Victoria, in Victoria, BC Canada,
laid out, analysed and described in the book:

Adel S. Sedra and Peter O. Brackett, "Filter Theory and Design: Active and
Passive", Matrix Publishers, Champaign, IL 1978.

In fact the "best" gyrator circuit, the one invented by Andreas, is depicted
in the cover artwork on that book.

FWIW...

 

Peter O. Brackett wrote:
(snip)

Another book that concentrates on active excess phase compensation is
"Theory and Design of Linear Active Networks" by Natarajan. The
performance of almost every opamp circuit described is compared to a
similar one that has the excess phase shift compensated, to show how
much more ideally it functions.

 

I would plot the Q as going negative, or I would plot 1/Q as a nice
straight line. Plotting the Q as staying at infinity would indicate a
lossless, mild-mannered circuit rather than the threat to system
stability that you'd really be dealing with.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Posting from Google? See http://cfaj.freeshell.org/google/

"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html

 

So perfect, they seem a bit like Schroedinger's cat, always existing in a
state of of crypto-stability. I've seen unplottable drifting Q's of maybe
1000-5000 one minute and then to infinity and beyond when the temperature
changes.
Despite excess phase, pos or neg inductor "loss" resistance, appears from
normal practical circuit layout.
Predictable enough to allow fixing Q at say a much less perilous 100X. Or
conversely, guarantee (in oscillator format) a gentle startup.
john

 

An oscillator in a filter's clothing, eh?

Thanks, I think I will just plot it as going negative... maybe on a log
scale (something like sgn(Q)*log(abs(Q)))...

 

Thanks for the advice Peter, I do have your book sitting on the bookshelf
and will take another look at it shortly (it was actually the first book I
read that went through the whole approach of using 1/s as an op-amps gain if
you're doing hand calculations and are looking to come up with the pole-zero
locations of a given op-amp circuit... funny how somehow this never made it
into my coursework in college...)

---Joel

 

OK... I'll have to drop your configurable op-amp into a simulation soon
(since it of course includes that excess phasE) and see how it compares
(using data sheet values) to simulations done with, e.g., Linear Tech. SPICE
models.

---Joel

 

Doesn't 'active' mean 'might oscillate'?

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Posting from Google? See http://cfaj.freeshell.org/google/

"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html

 

Probably.

That reminds me of a co-worker who is hesitant to use IIR filters since
their stability is not guaranteed (as FIR filters are) nor completely
trivial to predict once everything is quantizied (i.e., the Z-transform of
the unquantized system don't tell you the whole story)... I tell him that he
might as well protest any use of active continuous-time circuits containing
feedback, since it's not completely trivial to predict oscillation given
imperface real-world components either...!

 

Why are you using Q anyway? Just use the resistive (potentially
negative resistance) and reactive components you know you have, if
you're using a simple linear model, or better, put in a full model of
the gyrator with decent models for the op amps, and you won't have to
worry about "negative Q". As Tim was pointing out, remember that there
are things we call "negative resistance oscillators." A "Q multiplier"
(used in the old days to add selectivity to a receiver's IF section)
could, of course, be made to oscillate by advancing the gain too much.
Q is often an over-worked term (especially when people try to apply it
to multiple-resonator filters, but that's a topic for another thread).

Cheers,
Tom

 

Don't forget anything with noise.

I discuss predicting the effects of quantization in IIR filters in my
book, by the way, including finding bounds on limit cycles (although I
bet I don't say it quite so clearly -- hmm).

Of course, you can't completely characterize your FIR filter performance
with the z transform, either -- you can just come a lot closer because
the quantization effects are less severe.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Posting from Google? See http://cfaj.freeshell.org/google/

"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html

 

Because sometimes plotting Q is more useful than plotting re(Z), im(Z) or
whatever... My original question was prompted just by building a bunch of
"probe" components for SPICE that you could drop down on a schematic to plot
various "useful" things; I was using a gyrated inductor as the test case for
them.

---Joel