Path: utzoo!mnetor!uunet!husc6!purdue!umd5!eneevax!noise From: noise@eneevax.UUCP (Johnson Noise) Newsgroups: sci.electronics Subject: Re: RC twin-T networks in oscillators and filters Message-ID: <1233@eneevax.UUCP> Date: 16 Feb 88 01:31:03 GMT References: <2507@ihlpe.ATT.COM> <971@neoucom.UUCP> <418@pasteur.Berkeley.Edu> <1198@eneevax.UUCP> <580@anasaz.UUCP> <563@pasteur.Berkeley.Edu> Reply-To: noise@eneevax.umd.edu.UUCP (Johnson Noise) Organization: Elec. Eng. Dept., U of Maryland, College Park, MD 20742 Lines: 154 Summary: It exists. 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!