Multivibrator Sawtooth+Triangle Generator

 

Schematic of Multivibrator

I've been researching transistor voltage-controlled multivibrators in order to design a precision linear 24576-32768 Hz differential squarewave oscillator for down-conversion frequency synthesis. I certainly recall seeing a wide variety of circuit designs for multivibrators in the 1970s.  But except possibly for searches on expired patents, the WWW and search engines have not proven that useful in uncovering discrete transistor circuit designs in detail. Possibly this is "lost knowledge," information just too old for the Internet.

Instead, I have found that older books indicate much more design detail and practicum. So, I've been collecting a variety of discrete transistor circuit design books from the late-1950s onward. I recently obtained Guidebook of Electronic Circuits, ed. by John Markus, 1974. I had an earlier version of it, but I could not find it. That edition got lost somehow during a garage reorgnization (the kind of thing I now call an "archeology dig"). So, I bought another (later) copy from a used bookstore instead. What a gold mine! This later edition is quite a tome, having a very useful collection of some 3600 circuit designs. Not all are transistorized, and some vacuum tube circuits are included. Some circuits also include early op amps (uA709 and uA741, plus Motorola and Signetics variants) and digital ICs (DTL and TTL devices). But there is still a lot of transistor circuit design history in this volume to learn and adapt from.

Using this new reference to look into multivibrators, the circuit design in the schematic above is an adaption from S. Chang, A New Astable Direct Coupled Multivibrator, Proc. IEEE, Aug. 1970, p 1278-9.

The circuit was not directly voltage controlled, but I had a hunch it was different somehow. That turned to be the case, as it was really interesting because it does not produce square waves! I had thought multivibrators always generated square waves. This one does not. Instead, it generates sawtooth waves (at the collectors) and triangle waves (at the emitters)! 

What's even more interesting is that the sawtooth waves are offset by a half-phase, and the triangle waves are differential (e.g. paraphase wrt each other). This is done with direct coupled transistors, which have cross-coupled base-collector connections. As a result, the output amplitudes are controlled by transistor Vbe. 

And this leads to a deeper insight, something I've seen before with transistor circuits: they work with both voltage and current, simultaneously. This circuit effectively has a form of differential pair transistors.

Differential operation has interesting effects with same-type (NPN or PNP) transistors, in that it can produce a form of balance, much like complementary symmetry (NPN and PNP) transistors can. That occurs here. Differential Vbe stack up, or ΔVbe plays a role here. In this case, there are two differential sums, and they draw out the sawtooth waves from the triangle waves. But in so doing, any change in Vbe for either transistor is cancelled as |ΔVbe| for both transistors. I generally do thermal testing with transistor circuits, and what I saw from this circuit is that all four signal amplitudes were unchanged under thermal impulse, while the frequency did in fact move. So, for thermal changes, the voltages will balance, but the currents change, hence affecting frequency.

The source waves are the triangle waves at the emitters, which have a ≈700 mV (1 Vbe) amplitude. After summation, due to differential |ΔVbe| action, ≈1400 mV sawtooth waves are produced (2 Vbe) at the collectors. With the differential phasing and symmetry of the triangle waves, these become phased apart one half cycle.

The circuit does have some little warts, traits that can be improved. But it seems this circuit could be further augmented to provide a multifunction LFO and VCO. Some additional ideas along these lines now follow. Representative oscilloscope traces follow after that.

Looking closely, you can see that the 700 mV triangle wave is slightly non-linear due in that it has a shallow RC shape. So, like some early vacuum tube and transistor sweep generators, a limited portion of the exponential slope of a RC waveform approximates a straight line. 

For a fixed frequency application, changing the frequency can be accomplished by a change in the capacitor values, or a combination of changed values for pairs of resistors and the capacitors. For flexible frequency operation, like some other linear- and logarithmic response voltage-controlled multivibrators, a controlled current source (VCCS) could be introduced to drive the timing capacitors. 

With a PNP VCCS, complementary symmetry operation could be engaged to stabilize thermal effects on frequency variation. The current source would also linearize the triangle waveform slopes as well, improving waveform fidelity. Further augmentations could include pickoff amplifiers to provide voltage gain and drive for output circuits. Alternatively, or in addition, DC or AC coupled emitter followers could be added to allow further waveshaping of the triangle waves. For example, for sine wave generation. Adding the two sawtooth waves together results in an octave higher sawtooth wave.

Upgrading the linearity of the triangle waveforms would for sure improve the sawtooth waveforms. You can see very slight bowing between limited RC slope segments that are added together. The bowing would disappear with linear waveshapes. The precision of these voltage summations for the sawtooth waveforms could otherwise be improved merely by using 1% resistors instead of 5% resistors. Use of precision resistors would add further thermal stability.

For an application truly requiring precise duty cycle balance, a trimmer in the charging circuit might be useful to calibrate out capacitor tolerance, and the tolerance of any ΔVbe for PNP transistors in the charging circuit. On the other hand, for an electronic music application, strict waveform fidelity is not necessarily a goal. The sawtooth to triangle convertor in the Moog modular 901 VCO from the 1960s had a little glitch at the waveform peak. After modest filtering, this artifact did not materially affect the sonic utility of the triangle waveform.

Still! This two transistor circuit already does quite a lot: it provides four outputs! Add a few more transistors, the circuit has great potential in a modular synthesizer.


C1=C2=0.01μF ±1%. Overlay of outputs at the same V/div scale: excellent symmetry

Waveforms separated out for visibility

Waveforms with C1 = C2 = 0.1μF

Frequency shift under thermal impulse (hot air tool)



Comments

  1. Do you think it could be use as LFO with 0.5 to 2o hz range adding a double pot?
    Ben

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    Replies
    1. It could be a LFO just be scaling the capacitor. A double pot would not be needed.

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