max@trinity.uucp (Max Hauser) (02/06/88)
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
noise@eneevax.UUCP (Johnson Noise) (02/16/88)
In article <563@pasteur.Berkeley.Edu> max@eros.UUCP (Max Hauser) writes: >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. ... > >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. > Didn't I say that? When I was talking about tuned circuits I implied bandpass. >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. > You want see one with one capacitor and one resistor? I made some remote mention of it in my earlier posting. Here is the circuit: No I refuse to try and draw it. 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 gain of the amp K is -1 K = -------- jw/wt when w3dB < w < wt where wt = gain bandwidth product. This assumes that the amp rolls off at 6 dB/octave, which is true for most op amps. (Actually it is true for all amplifiers in which bandwidth is limited by capacitance. The proof is left to the reader. It is not difficult.) Anyway, if we apply the Miller theorem to our circiut (the one with resistor, remember?): R Zin = ---------- 1 - K This is the input impedence at the inverting terminal. Substituting for K: R Zin = ------------- 1 + 1/(jw/wt) Writing this as admittance Y = 1/Z: 1 1 Yin = -- + ------- R jwR/wt What is this you might ask? Look at it closely. It is just a resistance R in parallel with an inductance L equal to: L = R/wt Now, If I connect a capacitor C from the inverting terminal to ground, I have a parallel resonant circuit with "Q" equal to Q = R/wL --> Q = w/wt What is wt? For most FET input op-amps ~4.0Mhz, bipolar (741 etc.) ~1.0Mhz, CMOS inverter ~30MHz. Actually, those numbers are ft (wt/2*PI) but so what. Look at the numbers. At 40 KHz I can get a Q of 100 without 10000 turns on some ultra mondo ferrite or 13 resistors and capacitors matched to infinite tolerance. The circuit can be made to oscillate very, very easily. Just take the output and feed it back to the +input (it is an amplifier, after all). The output will have to be attenuated of course (still have some light bulbs left over from your Wien bridge days?) in order to get a nice unclipped sine wave. You don't believe me, huh? Yes I have built the circuit, and yes it does work. It works exactly like the theory predicts. You have to be a little careful about the frequency and the op-amp you choose, as it may break more than once leading to something other than 6dB/oct. You still don't believe me, well think about the assumptions I've made -- all very reasonable. Don't try and disprove Miller either. Build the circuit! Don't need the oscillator? Use it as a tuned amplifier. Replace all those silly IF coils in your pocket radios. Whatever. Q too low? Use a higher frequency op-amp. Q too high? Add another resistor in parallel with the capacitor, you know how to do that. Build the circuit! >Maybe someone not yet made skeptical by too much technical training, >and therefore unaware that it cannot be done, will do it. (There are This circuit is not my design (not all of it at least). The basic premise was introduced to me by an old government (NASA) fart, whom I will always consider as my mentor. No, he is not skeptical, just a very sharp individual who looks at the basics just as much as anything else. >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.) > I just say "Oh, yeah." and nod agreeably. They usually get nervous and don't say much more. Level head. Honestly, what is he going to do? Boot you? That's fine. Only 4.0e+6 places left to get a job. >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. > My circuit is obviously a bandpass. It is left as an excercise to the casual observer to make it notch (hint: another amp). >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. > I did a similar thing, but with my circuit at 100KHz. One 2N2222 used as an oscillator/mixer, one quad FET input op-amp. Could be used (for small bandwidth app.) from 1 to 50MHz with three (passive) component changes and some tweaking. I never played with ceramic filters much up to then. Anyway, a transistor and a quad amp don't cost much. I'm not suggesting that you techniques are wrong or bad, just that I admire simplicity and sharp thinking. I've got some other circuits working in the backround (transformerless matching networks for switching supplies, amps etc.). Good night Max, thanks for listening. I'll be looking for your reply. Oh, and by the way... Build the circuit!
max@arches.uucp (Max Hauser) (02/17/88)
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