Path: utzoo!mnetor!uunet!husc6!think!ames!pasteur!arches!max
From: max@arches.uucp (Max Hauser)
Newsgroups: sci.electronics
Subject: Re: RC twin-T networks in oscillators and filters
Message-ID: <773@pasteur.Berkeley.Edu>
Date: 16 Feb 88 19:54:52 GMT
References: <418@pasteur.Berkeley.Edu> <1198@eneevax.UUCP> <580@anasaz.UUCP> <563@pasteur.Berkeley.Edu> <1233@eneevax.UUCP>
Sender: news@pasteur.Berkeley.Edu
Reply-To: max@eros.UUCP (Max Hauser)
Organization: UC Berkeley
Lines: 109
Summary: "Active-R" filters -- the Thing that Wouldn't Die

In article <1233@eneevax.UUCP> noise@eneevax.umd.edu.UUCP (Johnson Noise) writes:
> In article <563@pasteur.Berkeley.Edu> max@eros.UUCP (Max Hauser) writes:
>
> >What the world really needs is a simple passive RC circuit 
> >exhibiting a high-Q pole pair [like a parallel LC circuit].
> 
> 	You want see one with one capacitor and one resistor? ... 
> Picture if you will an op amp (or other suitable amplifier of your 
> choice with gain greater than 1 and finite bandwidth) with the output
> fed back to the inverting input via a resistor R.  [The amplifier
> gain falls with frequency and the result is a synthetic inductance].

This is a special case of what are called, generically, "active-R"
filters (because, on casual inspection, they contain only amplifiers
and resistors -- they lack the capacitors of more conventional active-RC
filters). They were the rage in the late 1970s in papers by filter 
theorists. I have most of the papers and would cite them here if I were
not so busy (this is ISSCC week! most of the solid-state circuit hackers
are there, instead of reading the Usenet), though I have cited their
definitive refutation [1] below.

I agree that "active-R" filters are a neat idea, and like so many neat
ideas they are fine for a casual circuit or two. I deliberately did not
mention them earlier because for the larger province of manufacturable,
commercial products, they have a couple of fatal flaws. To wit:

1. Much of the past discussion of these filters was naively and, for
"professionals," rather fatuously predicated on the filters' "lack of 
capacitors"; but of course they do indeed contain capacitors, usually 
explicit ones, inside the op amps that furnish the frequency dependence.
The active-R filter designer is thus by no means getting something for 
nothing, and indeed is managing in some respects to turn gold into lead,
since that very capacitor that frequency-compensates the op amp internally
can be put to far better use as a timing component than leaving it in an
internal op amp minor-loop integrator.  Unfortunately the theorists did
not think in terms of what was "inside" an op amp, but merely took it for
granted as a circuit block, even though it too was designed out of 
transistors from scratch, and even though it is entirely cost-effective to 
design custom chips that make different use of the internal components in
an op amp, for the mass-produced products (like audio products and modems)
that "active-R" filters were proposed for.

In short, "active-R" circuits are really active-RC; they still rely on
capacitors to set their time constants and hence frequency response.

2. Worse, the op-amp frequency dependence was never designed to be used
as a time constant in a filter; it was designed to be suppressed as much
as possible with feedback. It is poorly controlled, unstable with 
temperature and other factors, and nonlinear. The op-amp gain-bandwidth 
product, which is the starting point in "active-R" filter design, normally
arises in an op amp as a Gm/C ratio; several factors usually influence the
Gm, and the C is often a low-quality device like an MOS capacitor, intended
solely to stabilize a feedback loop, not to serve as a primary circuit
component. Accordingly the Gm/C ratio often varies by 3:1 or so at
manufacture, far more than the tolerance of even the capacitor alone; and it
varies further, often dramatically, with temperature and supply. Worse still,
the open-loop gain path of op amps is normally dramatically nonlinear --
even more so at frequency, if a nonlinear monolithic capacitor like an MOS
sandwich is used -- since gain-path nonlinearity again was intended to be a
second-order consideration rather than to determine direct input-output 
characteristics as it does in an "active-R" design.

This tirade is not of course directed at Johnson, who unwittingly touched
a nerve. In 1978 Barrie Gilbert sent a sober, tactful, and no-nonsense
correspondence, technically unimpeachable, to _Electronics Letters_ (which
had carried a slew of papers on "active-R" designs based on specious
precepts) to point out that, in effect, the emperor had no clothes [1].
To the considerable discredit of some active-R advocates, in my opinion,
they not only seemed to miss the plain hard realities in Gilbert's
criticism, but moreover continued publishing enthusiastically on the 
subject, still blithely implying that these filters were stable, linear,
manufacturable, and that they deftly avoided the need for capacitors.
The case has become something of an infamous example of the realities of
modern engineering research.  O tempora! O mores!

Still, for a small-run circuit, or a special situation -- bearing in mind 
all of their second-order effects -- these circuits are useful. One firm
(National Semiconductor?) makes a line of op amps with temperature-stable
gain-bandwidth products, thus answering one of the several objections
(any one of the others of which is still fatal enough to preclude large-
scale commercial utility). Just keep in mind that you are not getting 
something for nothing -- Johnson's synthetic LC circuit has two capacitors
(one inside of the op amp), not just one. (In any event it does not answer 
my challenge, which asked for *passive* RC circuits -- no amplifiers. 
Johnson could have suggested a gyrator, another tried and true route to a
synthetic inductor, since it's indeed passive -- though nonreciprocal -- 
from its input-output properties, and therefore admissible on a 
technicality; but that too violates the spirit, since gyrators are in 
practice assembled from active amplifier stages.)

>    I'm not suggesting that you techniques are wrong or bad, just that
> I admire simplicity and sharp thinking.  

Me too.

> Oh, and by the way...  Build the circuit!

Actually, I did, in the early 1970s. My version used not an op amp but
instead an explicit, large-signal variable-transconductance circuit to 
vary the Miller multiplication under external control, while staying 
linear and stable in the signal path.  With a parallel capacitor it 
formed an audio bandpass filter, electronically tunable over a decade 
or two. So I too believe in synthetic inductors, believe it or not ...

[1] B. Gilbert, "Simulation of inductors and capacitors using 
operational-amplifier compensation pole: A caution,"
_Electronics Letters_ vol. 14 p. 832, 1978.

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