max@trinity.uucp (Max Hauser) (01/29/88)
You'd better skip over this article if you are not interested in sinusoidal oscillators or other waveform generators. I've cross-posted to rec.audio because some of the examples are actually from audio test generators. In response to a request in sci.electronics for simple RC sinusoidal oscillators, wtm@neoucom.UUCP (Bill Mayhew) very kindly suggests: > Summary: try a twin T oscillator > > My ancient copy of the ARRL handbook has simple little circuit for > a twin T single transistor circuit. It is quite stable. It > requires one transistor, 4 resistors and 4 capacitors. ... [Followed by neat on-line schematic] > .... Definitely a circuit for Old Farts. I never really did like > the light bulb in a Wien bridge. --Bill Well, Bill posted a helpful reply, which is more than I did, but now this talk about RC sinusoidal oscillators among old farts has got me going, as I used to work with a lot of circuits for waveform generation and shaping, and came up with a few of my own. You will not find them in the Radio Amateur's Handbook, as far as I know. I have to point out first that any objection to a "light bulb" in a Wien-bridge oscillator applies to a twin-tee too, in spades. The essential part of a Wien bridge is just a network with two R's and two C's (a series R and C from input to output of the network; a parallel R and C from output to ground), just as the essential twin-tee is a network with three R's and three C's. In both cases, adding sufficient linear gain around the network makes an oscillator, but a mechanism is needed to regulate the gain if the sinusoid is to have low distortion, not to mention predictable amplitude. You can build either oscillator with an explicit automatic-gain-control (AGC) element (a light bulb as an average-power-sensitive-resistance is an old and cheap, but by no means the only, form); or you can build either oscillator with "no" AGC, as in Bill's example, in which case you are relying on the implicit nonlinearity of the gain element (transistor, say; rec.audio readers can certainly use tubes [valves] if they prefer the sound) to regulate loop gain. This is narrowband AGC or "self-limiting oscillation": as the oscillation tends to grow in amplitude, the gain element begins to distort, and the gain seen by the component at the oscillator's fundamental frequency begins to drop (as more and more of the gain element's output takes the form of distortion, i.e. components at frequencies other than the fundamental). This gain drops to the point required to sustain a steady oscillation amplitude. The RC network as an incidental benefit usually provides some filtering action so that if the circuit's output is taken at the proper point, distortion components there will be small. The advantage of a light bulb or other long-time-constant gain control (often a linear variable-gain circuit is used nowadays) is that it can leave the oscillation signal path extremely linear and thus yield a lower-distortion sinusoid, all other things being equal. If you really want to know "all about" simple sinusoidal oscillators (amplitude limiting, distortion, frequency stability, etc.), I recommend Clarke and Hess, _Communications Circuits: Analysis and Design_ (Addison-Wesley 1971), the veritable bible of oscillator-mixer-receiver designers. In any event, though, simple RC sinusoidal oscillators always entail SOME type of loop-gain control, even if it consists of a person hired to adjust a knob ("manual" gain control: MGC?). Three standard, competing RC sinusoidal oscillator configurations, each based on an RC network added to a gain stage, are the twin-tee network (which needs three Rs and three Cs, and realizes a transmission gain of zero, ideally, at a phase shift of 180 degrees); the three-section phase-shift networks (which also need three Rs and three Cs; the common CRCRCR three-zero form exhibits a phase shift of 180 degrees at a transmission gain of about 1/29, if memory serves); and the Wien-bridge network, needing two Rs and two Cs to show a gain of 1/3 at a phase shift of zero. Many other RC networks can exhibit the essential property of frequency-dependent phase shift that passes either zero or 180 degrees at a well-defined useful frequency (though if you can devise such a network with fewer than two capacitors, I'd like to hear from you ...). Second-order considerations, however, are different for the three common networks I've mentioned; and they favor the Wien bridge heavily, in my opinion. First, it needs only four timing components to set frequency, while the others need six (and the twin-tee has ratios in it as well). Second, and this is more subtle but no less practically important, the Wien bridge is the most straightforward and "designable." The target gain value to turn it into an oscillator is +3, which is both easy to achieve and easy to set. This value can be scaled up or down by ratioing the arms of the Wien network. The phase-shift network is similar in this regard except that it has more loss and therefore requires more gain to make it oscillate. The twin-tee, horror of horrors, when you sit down and analyze it, theoretically requires "infinite" amplifier gain to oscillate, since the basic network realizes an infinitely deep transmission notch as the phase shift passes 180 degrees. No finite gain value will permit it to oscillate. The twin-tee oscillator works in practice because the network exhibits a less-than-infinite notch due to component mismatches, or it oscillates detuned from the nominal center frequency where it matches the magnitude and phase shift of its companion gain stage. Besides the annoyance of a circuit that works more poorly as the components become ideal, it too needs a large (and highly component-sensitive) gain, as well as six critical RC elements. (The "ideally non-oscillating" phase-shift oscillator was a witty topic among bored iconoclast circuit theorists a few years ago.) Several years ago I had occasion to look into this subject in depth, needing cheap sinusoidal audio test-signal generators, and this led to an oscillator circuit that exploited the internal schematic of CMOS NAND gates in a way that their designers surely did not intend. You can take a CMOS gate chip; bias properly to operate the transistors in a linear mode, in which case a 4-input NAND gate becomes a simple op amp with four inverting inputs; embed Wien-type RC networks, one to each input, in a summing-junction topology; add a couple of diodes to a second gate for a controlled soft nonlinearity; and presto, you have a near-minimum-component RC sinusoidal oscillator that will operate at up to four different preset frequencies according to which gate input you enable. This works up to about 40 kHz (M. Hauser, "Programmable sinewave oscillator uses only one CMOS IC," _Electronic Design_ vol. 22 no. 24 p. 200, 22 November 1974; note that a "pi" is missing from the denominator of the frequency expression). I also put a similar one in Popular Electronics for another purpose at about the same time (that was in the Good Old Days, after Poptronics had merged with Electronics World, but when it was still about electronics). If you want continuously variable frequency, these RC networks all lose because they require tandem adjustment of multiple component values. Tom Fredrickson and co. at National Semi were pushing, several years ago in the NSC Linear Application notes, a better approach to easily-tuned RC sinusoidal oscillators based on comparators in feedback with 180-degree phase-shift networks; if you change the network via a single resistor, it changes the 180-degree frequency and also the gain, but the gain no longer matters, since the comparator detects zero-crossings and depends on the phase-shift circuitry to clean up its output waveform. There is always the tack, taken by Intersil in the horrible 8038 and more successfully later by Exar in the 2200 series oscillator chips, of a (integrator-and-hysteresis) triangle-wave oscillator followed by a nonlinear network to shape the triangles into sinusoids. These methods yield easy frequency tuning, but are much more complicated in design than simple fixed sinusoidal RC oscillators. Square waves, of course, are easy to generate by various means, and they can be both extremely stable and also frequency-selectable, via crystals, counters, etc. Unfortunately squarewave frequency sources are awkward starting points for other waveforms over any sort of frequency range, unless you use a high-frequency clock, generate the waveform numerically, and run it through a DAC (shudder); or lock a controllable oscillator of desired waveform to the squarewave source; or employ a variable-frequency filter. Another approach that I used, to convert audio-frequency square waves directly into triangle waves, with constant amplitude over a wide frequency range, uses a capacitor and current switch to generate triangle waves whose slope is set by an external current. In turn this current comes from another subcircuit that measures the period of the incoming square wave, obtains its reciprocal directly (thus an analog current proportional to input frequency) in a little Gilbertoid "translinear" circuit, and uses that to correct the ramp rate for the changes in input frequency so that the triangle amplitude stays constant over different squarewave frequencies. My instrumentation application needed only square and triangle waves, but in principle sinusoids are again available by post-distorting the triangles. An early version of that circuit appeared in _Electronic Design_ ("Square-to-triangle-wave converter provides constant amplitude, rapid response," vol. 25 no. 24 pp. 160-162, 22 November 1977), including further references to triangle-sine converter circuits. I don't think that I can render that or the CMOS circuit on-line as Bill did, but they should be available in technical and college libraries if any circuit hackers are interested. Should you be unable to find them, I do have some copies that I'm happy to part with ("as a service to the net") at least until they are used up. Send a self-addressed stamped envelope to Max Hauser, P. O. Box 7051, Berkeley, CA 94707, USA (no e-mail requests, please). Specify which circuit you want, if not both. Light bulbs, indeed. Max Hauser, circuit hacker max@eros.berkeley.edu / ...{!decvax}!ucbvax!eros!max "This ... demonstrates the soapbox phenomenon. Given any slim excuse, 99.624 percent of all persons will sound off. Given no excuse at all, 99.608 percent of them will do so." -- Mary-Claire van Leunen
noise@eneevax.UUCP (Johnson Noise) (01/30/88)
In article <418@pasteur.Berkeley.Edu> max@eros.UUCP (Max Hauser) writes: > >The twin-tee, horror of horrors, when you sit down and analyze it, >theoretically requires "infinite" amplifier gain to oscillate, since >the basic network realizes an infinitely deep transmission notch as >the phase shift passes 180 degrees. No finite gain value will permit >it to oscillate. The twin-tee oscillator works in practice because >the network exhibits a less-than-infinite notch due to component >mismatches, or it oscillates detuned from the nominal center frequency >where it matches the magnitude and phase shift of its companion gain >stage. Besides the annoyance of a circuit that works more poorly as >the components become ideal, it too needs a large (and highly >component-sensitive) gain, as well as six critical RC elements. > You 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. All passive tuned circuits exhibit finite Q due to resistances in inductors or leakages in capacitors etc. This does affect the resonant frequency slightly, but not to any significant degree in medium to high Q circuits (> 10). Also, an infinite Q tuned circuit will sustain stable oscillations, but cannot deliver any power to an external load. (This would obviously make the Q finite and cause the oscillations to die off.) With this in mind one could design a stable oscillator by simply increasing the Q to infinity with the use of an active component. This can be acc- omplished with either positive feedback or negative resistance (one could argue that they are effectively the same). If one was to apply sufficient negative resistance to cancel all positive resistance (and then some) stable oscillation would result. This circuit could also deliver power. How do you simulate negative resistance? Easy. Positive feedback is one way. There are other ways which exploit the 6 dB/octave roll off of an amplifier (op-amp etc.) which can be considered complex (1/jw; w=gain bandwidth prod). One can also take advantage of the high frequency beta of bipolar transistors, which is also complex (this circuit is analyzed in "Microelectronics" by Milman & Taub). If you think about it, there are several simple (single transistor) negative resistance generators in a variety of configurations. The theory is simple and straightforward. > >Several years ago I had occasion to look into this subject in depth, >needing cheap sinusoidal audio test-signal generators, and this >led to an oscillator circuit that exploited the internal schematic of >CMOS NAND gates in a way that their designers surely did not intend. > CMOS inverters also roll off at 6 dB/octave and can be used to generate negative resistance, simulate inductance etc. I have measured the gain bandwidth product of 74C04's to be about 30 MHz, this compares well with a National Semiconductor application note on the use CMOS gates as linear amps. I didn't dare try it with TTL! > >There is always the tack, taken by Intersil in the horrible 8038 >and more successfully later by Exar in the 2200 series oscillator >chips, of a (integrator-and-hysteresis) triangle-wave oscillator >followed by a nonlinear network to shape the triangles into sinusoids. >These methods yield easy frequency tuning, but are much more >complicated in design than simple fixed sinusoidal RC oscillators. > They also suffer at high frequencies (read limited to < 1 MHz) because of the triangle to sine shaping that they all employ. One could use good low capacitance diodes and do a much better job (like Wavetek). > >Another approach that I used, to convert audio-frequency square waves >directly into triangle waves, with constant amplitude over a wide >frequency range, uses a capacitor and current switch to generate >triangle waves whose slope is set by an external current. In turn >this current comes from another subcircuit that measures the period >of the incoming square wave, obtains its reciprocal directly (thus an >analog current proportional to input frequency) in a little Gilbertoid >"translinear" circuit, and uses that to correct the ramp rate for >the changes in input frequency so that the triangle amplitude stays >constant over different squarewave frequencies. My instrumentation >application needed only square and triangle waves, but in principle >sinusoids are again available by post-distorting the triangles. I like it. > >"This ... demonstrates the soapbox phenomenon. Given any slim excuse, >99.624 percent of all persons will sound off. Given no excuse at all, >99.608 percent of them will do so." -- Mary-Claire van Leunen This too.
john@anasaz.UUCP (John Moore) (02/04/88)
In article <1198@eneevax.UUCP> noise@eneevax.umd.edu.UUCP (Johnson Noise) writes: >In article <418@pasteur.Berkeley.Edu> max@eros.UUCP (Max Hauser) writes: >> >>The twin-tee, horror of horrors, when you sit down and analyze it, >>theoretically requires "infinite" amplifier gain to oscillate, since > You 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. All passive tuned >circuits exhibit finite Q due to resistances in inductors or leakages Not true in this case! The twin-T is not a resonant circuit. "Q" in this case is not the point - stop-band attenuation is. The twin-T is a bridging device, and the stop-band attenuation is only limitted by how well matched the component values are. In effect, the twin-T consists of two equal-gain phase shift networks with opposite phase shift, which results in cancellation of the signal at the frequency where the phase shifts are just right. At that point, the only signal passing (assuming values are tweaked right), is that passed by leakage outside of the twin-T. I have used twin-Tee's to achieve attenuation well in excess of 80dB at 60Hz. -- John Moore (NJ7E) hao!noao!mcdsun!nud!anasaz!john (602) 870-3330 (day or evening) The opinions expressed here are obviously not mine, so they must be someone else's.