# The Bootstrapped Astable Multivibrator

Some time ago, I reverse-engineered a low-cost inverter made by Vector Mfg. (now Black & Decker). It uses a classic 2-BJT astable multivibrator (AMV) but with a circuit design twist, as shown below. What is the purpose of R6?

The function of the AMV is to provide “sawtooth” waveforms for PWMing each half-cycle of the inverter H-bridge which outputs a bipolar square-wave. Each half-cycle of the bridge circuit requires its own sawtooth waveform.

The MMV operates mostly like the classic circuit. Suppose Q1 turns on, grounding the left terminal of C1. Then this 6.2 V decrease occurs on the other side of the capacitor, at the Q2 base, shutting it off. If the –b-e junction of Q2 has not broken down (which it will around 5 V to 7 V), then the Q2 base voltage waveform begins its exponential climb towards the target voltage at the top terminal of R3. When it crosses about 0.55 V, Q2 begins conducting appreciably, Q1 is similarly shut off, and the exponential waveform appears at its base. The BJTs alternate in conducting and being off and the circuit produces a “sawtooth” waveform at both collectors as shown below.

Because of the equal-value timing components, the time constants for each half-cycle are equal (R5·C3 = R3·C1) and the duty ratio is about 50 % which is needed for a symmetrical inverter bipolar square-wave output waveform. The collector voltages rise exponentially because as C1 or C3 charge, the timing-current path is through collector resistors R1, R2 which have a resistance that is not negligible relative to base resistors R5, R3. Each of the collector waveforms is input to a comparator with a reference voltage set by the inverter bridge voltage. If the bridge voltage increases, each half-cycle of the H-bridge turns on at a higher voltage on the exponential, which is later in the half-cycle. (This is called rising-edge PWM because instead of varying when turn-off occurs, the turn-on edge is varied instead.) The on-time thus decreases as does the duty ratio. This keeps the rms output voltage somewhat regulated.

The inverter rms output voltage is the peak voltage (which is the bridge voltage) times √D where D is the duty ratio. Ideally, D varies by the square of the bridge voltage, but for small changes around an operating-point, this scheme approximates a square by an exponential. It is not perfect because of the linear and cubic (and higher) terms in the exponential series expansion. Yet it is a somewhat elegant method for a low-cost inverter. Ideally, the PWM waveform would be parabolic instead.

In the classic 2-BJT AMV, R1, R2, R3, and R5 are returned to the supply, though in this case, it is 12 V, derived from the battery input to the inverter. For a 5 V supply instead, the BJT bases are driven off by a –5 V peak waveform and the b-e ¬ junctions do not break down. The addition of R4 reduces the voltage, to V = 6.2 V, as measured in a working unit. C2 is large enough to keep the voltage at the V node constant.

This leaves for us the opening question: why is R6 needed? Why not return vB to V ? R6 reduces the voltage further, to about 4.3 V, but there is an attenuated exponential waveform at this node. Each half-cycle exponential contributes to vB , resulting in a “full-wave” exponential waveform; the exponential part of the waveform repeats without any constant off interval between them. Because only one half of the circuit has an exponential base waveform at any one time, the opposite half-cycle timings do not interfere with each other. At the same time, R6 further reduces the collector supply voltage of V = 6.2 V to a lower VB = 4.2 V, a voltage low enough to not break down BJT b-e junctions. The higher collector voltage lets the collector resistors be larger and more like “long-tailed” current sources, causing the exponentials to be closer to a sawtooth waveform.

By having a higher target voltage of V for the timing circuits, PWM generation is less nonlinear. The PWM incremental (small-signal) transfer can be calculated from the following plot.

The PWM waveform target voltage is V > VPWM . VPWM is the voltage at which the half-cycle ends, at Ts , and is the highest PWM input voltage of the comparator, vC . At t1 , the comparator voltage is crossed and the inverter half-bridge output becomes high. Its on-time begins at t1 and ends at Ts , the end of a half-period of the inverter cycle. Thus, it is the off-time on the above plot that is the on-time of the bridge because of driver inversion, and the effective duty ratio is actually the plot complement, D ’. Applying the usual exponential formula to the above PWM waveform,

At the comparator voltage, vC ,

Then v (Ts ) = V and

Where VPWM ≈ 4.3 V. Then substituting,

Then to find the actual duty ratio for the inverter of D ’ = (1 – D ),

The change in D ’ with the scaled incremental bridge voltage, vC , is

Ideally, ln(1 – vC /V ) = 1, or vC << V . R6 makes it possible for V to be higher so that the ideal is more closely approached.

## 12 comments on “The Bootstrapped Astable Multivibrator”

1. CC VanDorne
May 24, 2016

…died out by now.

Some classic terms in electronics survive, but others should not.  I submit that the term “multivibrator” should have been put out to pasture with condenser long ago.  Not only for its connotations in other departments in life, but I also need to look the dang thing up every time.  Then when I do, I say to myself “Oh yeah, it's an oscillator.”  Wikipedia yields this for its use:

“The name “multivibrator” was initially applied to the free-running oscillator version of the circuit because its output waveform was rich in harmonics.”

Are these harmonics still such a factor that we can't just say oscillator from now on?  Were they ever?  Sawtooth oscillator?  Sinewave oscillator?  oscillator?  Do what you will, but from now on I am applying a infinite-pole, band-stop filter to the word “multivibrator”.

2. D Feucht
May 25, 2016

CC,

You feel the same way about “multivibrator” that I do about “ac” and “dc”, which are ambiguous oxymorons. However, there is a difference. A multivibrator (MV) is not just an oscillator, it is a particular kind involving RC timing and square-waves. And that is only an “astable multivibrator”. There are also non-oscillator MVs such as the monostable MV (MMV), or using the semi-slang expression, a “one-shot”. A multivibrator entails an RC timing circuit involving square-wave waveforms, whether it oscillates or not.

Although the word “multivibrator” orginally referred to those automotive electromechanical gadgets, the word has a specific meaning in electronics, and I do not know of any suitable replacement. The word is not misleading (as ac and dc are) and is widespread in the literature. So why not keep using it? Do you have a proposal for an improvement? “Oscillator” is not synonymous with “multivibrator”.

3. CC VanDorne
May 25, 2016

I accept your challenge.  I'll think of a better name.  First a few questions: What is actually vibrating?  Also, when specifically dealing with a “one-shot” – a name I actually like, slang though it may be – a single triggering event triggers a single response.  Where's the “multi”?

4. antedeluvian
May 25, 2016

CC, Dennis, Steve

What about running a competition to rename the multivibrator? Winner gets to be famous for 15 minutes and maybe one of those books Steve sometimes has.

5. D Feucht
May 25, 2016

CC,

I accept your linguistic objections. A “vibrator” is something that vibrates and vibration is mechanical oscillation (as in those car gadgets). The only vibration in electronics is at an atomic level, but that can be misleading. So a better word is welcomed.

As for “multi”, it is the same problem. Please carry through on the challenge and we'll all be better off with better wording! I'll think about it too. Perhaps something like “astable” or “monostable” “pulser” might work, but maybe you can do better.

It would be of interest to know what others think of this. Language is important for communications and words are its components and label concepts. If the concepts are mislabeled, confusion results. Planet Analog articles thus become harder to read, and we're out of a job!

6. CC VanDorne
May 25, 2016

For the monostable variant, I have always been quite satisfied with “one-shot”.  It's catchy, easy to remember and it perfectly explains what the circuit does.  No further effort is needed there, imo.

For the astable variant, that'll be tougher since the general term “oscillator” is off to a bad start.  I'm okay with oscillator being in the mix (astable oscillator?) but you (Dennis) apparently are not.  And deference is given to you since I go to your articles to learn about stuff that I should know.

I'll need to read a little more about this topology.  Perhaps some inspiration can be found in there?  TBD.

7. CC VanDorne
May 27, 2016

Dennis, in an effort to get some inspiration for a new name, I simulated this circuit using LT Spice.  The only  vibration involved was me shaking my laptop in a Fonzie-like effort to get the simulation to run.  In other words, it was stable but I saw only a DC output, no oscillation.  I ran a transient response.  Any advice?

8. D Feucht
May 27, 2016

CC,

1. “Astable oscillator” is redundant. If a circuit is astable, it is oscillating in some way.

2. I found this circuit in the Vector (now Black & Decker) VEC043 battery inverter. The collector resistors are 68 kohm, base pull-up Rs are 120 kohm, coupling Cs are 0.1 uF, and the “R6” (R18 in the actual product) is 14.0 kohm, pulled up to 6.4 V. The exponential “sawtooth” waveform at the collectors runs from 0 V (where it is half the time) to 4.4 V peak.

How about building the actual circuit (only 9 parts), which is more accurate than a simulator? The circuit might not start in SPICE because it is too symmetrical. Make one base pull-up R of slightly different R value to give one side more current. Then it might start. A real (precision) circuit can also have this problem, though noise or resistor tolerance usually upsets the perfect symmetry that SPICE imposes.

9. CC VanDorne
May 27, 2016

I was thinking that might be the problem.  I'll try the slightly off-value resistor technique.  Or perhaps I'll build the circuit if I have the parts.  But in our lab that's a pretty big IF.

Noted on the “astable” redundancy.  We keep getting led back to “oscillator”, don't we? 🙂

10. CC VanDorne
June 8, 2016

Okay, I gave up on LTSpice and just built the circuit, as you recommended.  Sorry for the delay.  I had to wait for a lull in the action around here so I wouldn't get caught 'didling with those dang transistors again' when there was other important work to do like reading reems of new “Read and Abide By” notices from our legal department or filling holes in spreadsheets somehow directed to me from people I've never met in departments I've never heard of.

Anyway, if it comes as any relief to you, though I did not see quite the same DC voltages that you did, the circuit works.  I had to substitute .47uF caps where you have .1uF caps, because that's what was handy.  Other than that, it was pretty close.  It yielded a 5.15Vpeak saw-tooth at 13Hz.  The duty-cycle was 50% and the edges were a little jittery.

As for what I'd call this circuit, I tried to imagine what I would say if I happened on a colleague who'd built this circuit as I did.  I think I'd say something like “Ah, cool little saw-tooth generator you've got there.”  And that's about where this naming exercise ends for me.  Call it a saw-tooth generator.  Call it a saw-tooth oscillator.  Call it a simple two-transistor, astable topology that generates a saw-tooth waveform.  All of those would work for me (mostly the first two).  Just leave “multi-vibrator” out of it and I think I'm happy.

P.S. I made a mod that might be interesting, and from it an observation on the behavior of the circuit.  If you are interested, perhaps we can pick that up in another thread.

11. D Feucht
June 8, 2016

CC,

1. The original circuit oscillates at 60 Hz – power-line frequency.

2. The best I could come up with for a name change was “astable timer”. Whatever the circuit class is called, our discussion has highlighted the importance of using well-chosen labels for concepts.

There are even worse misnomers and-or oxymorons well-embedded in the electronics literature. I have a future article on electronics slang and lingo in the Planet Analog article queue about them. Some of the worst are (gasp) ac and dc . Then there is emf for voltage and “magnetizing force” which is magnetic scalar potential, having units of A/m which are not convertible to newtons, N, the unit of force. Go figure. And engineers (no less physicists) are supposed to be logically consistent!

Thanks for your input on bad words. I have been writing technical articles for a long time and continue to find needed improvements in my writing skills.

12. CC VanDorne
June 8, 2016

Thanks, Dennis.  I look forward to that article about your friend Miss Nomer, and especially your beef with 'ac' and 'dc'.

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