Path: utzoo!mnetor!uunet!lll-winken!lll-lcc!lll-tis!ames!sri-spam!rutgers!gatech!mcnc!uvaarpa!umd5!eneevax!noise From: noise@eneevax.UUCP (Johnson Noise) Newsgroups: sci.electronics Subject: Re: Lots more about R-C sinusoidal oscillators Message-ID: <1198@eneevax.UUCP> Date: 29 Jan 88 19:30:52 GMT References: <2507@ihlpe.ATT.COM> <971@neoucom.UUCP> <418@pasteur.Berkeley.Edu> Reply-To: noise@eneevax.umd.edu.UUCP (Johnson Noise) Organization: Elec. Eng. Dept., U of Maryland, College Park, MD 20742 Lines: 89 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.