# Astable Multivibrator Circuit Analysis

I have been trying to understand why the following astable multivibrator works, but I've hit a wall. Before I explain what's confusing me, I should mention that I don't have a background in electronics (though I'm trying to learn). My knowledge of electronics does include the following, though: (a) I know KCL/KVL, (b) I can set up and solve the differential equation that describes the voltage across a capacitor in a series RC circuit, and (c) I know that npn transistors act as closed switches if $$\V_{BE} >= 0.6V\$$.

The most useful explanation of the circuit that I've run across so far is this website. Ray's website helped me understand that we're basically dealing with two RC circuits, and the oscillation is driven each time by a capacitor turning on a transistor (when that transistor's base-emitter voltage crosses the 0.6V threshold), which induces a negative voltage across the opposite transistor's base-emitter junction and turns off that transistor. (That's my best rough description of the mechanism at play, anyway.)

A few things are still confusing me, though:

(1) I still don't fully understand the bit about a transistor turning on inducing a negative voltage. Is there a simple way to set this up with KVL/KCL or something along those lines to see this mathematically?

(2) One reason I've struggled with this circuit is that I feel like I should be able to write down some equations to fully describe this circuit, which I can then try to solve. Is there a simple way to do that here? Ray's page talks about the differential equation governing a series RC circuit, which I understand, but I don't get how that applies straightforwardly here. Don't we need to take into account all of the voltages and currents in the circuit here? I guess I just don't get why we can zoom in on one sub-RC circuit and analyze that.

Any help would be greatly appreciated!

• if you replace C1 with a 9 V battery, with the positive terminal connected to the collector of Q1 ... what will be the voltage at the base of Q2 when Q1 turns on? Jul 8 '20 at 0:20
• Just curious. Have you tried typing in "astable multivibrator" into the search bar here? With that aside, you cannot do KCL/KVL on this to get the astable behavior -- that math can't produce that result. You'd have to inject at least one assumption, probably more. But as it turns out the very definition of "stable" can get quite technical, including such technical terms as "marginally stable." This circuit has two states that it moves rapidly into, followed by a gradual change that eventually tips the circuit over into the opposing state, which is again followed by that gradual change, etc.
– jonk
Jul 8 '20 at 0:28
• This circuit simply IS. Imagine some mathematical statement (or group of simultaneously true statements) that could produce an astable result that you are searching for. Just produce any hypothetical closed mathematical arrangement that you feel exhibits "astability" or binary stability. You may think to construct a surface with multiple folds, cusps, or pockets in it. And I could imagine such a surface with just two, and a marble rolling around on it, plus an added "periodic agitation" so that the marble is caused to move from one, to another. But I'd like to see it written.
– jonk
Jul 8 '20 at 0:37
• Note that this circuit is prone to NOT starting if you intentionally make all parts have exact values. Normally slight differences in beta or R values cause it to self-start.
– user105652
Jul 8 '20 at 0:39
• Staying with your interest in mathematics: There is one and only one book I've read on the kind of mathematics that may apply. It's "Catastrophe Theory for Scientists and Engineers" by Robert Gilmore. While it is enjoyable, and I could imagine a pleasant few years thinking about how to apply it in electronics, I've never seen that theory actually applied in electronics. So I'd be very interested to see it done.
– jonk
Jul 8 '20 at 0:41

Citation : <<< Appendix : Frequency change when connecting LEDs with R1 and R4 in series As mentioned above, one way to connect LEDs into the multivibrator is by putting them in series with R1 and R4. One interesting thing I noticed is that when doing so the frequency of the LED blinking is much faster than the calculated frequency. >>>

It seems that the site cited by the OP has missed also something of the behavior that appears when the B-E junction of the transistor is reverse biased.

This happens when the supply voltage exceeds the breakdown zener voltage (around 5V). So, analysis is not complete ...

Simulation made with voltage generator of 3V. Here is what is generally used ...

You can note that the voltage of the capacitor return (theoritically) to Vcc which is 9 V (first picture, Vb1 voltage, simulated).

Secondary effect (not shown) when a Led is inserted ... The voltage of the capacitor will not return to Vcc but to Vcc-Vled = ~ 7.5 V. Vled = ~ 1.5V.

And what happened when voltage supply is higher ...

Simulation made with voltage generator of 8 V.

Do you notice the Zener effect at -5 V ?

And finally, real behavior ... also simulated (but what you see really on a scope).

Here Without breakdown ...

Here, I have simulated with a "Zener equivalent" device.

Notice the higher frequency generated (Zener breakdown).

If you abruptly turn on the power, imbalances in charges and currents and voltages will turn one transistor fully on and turn the other transistor full off ---- with that state continuing as the base of the Off transistor slowly rises from -VDD or similar levels (unless the emitter-base breakdown serves as a clamp on the negative_going excursion). And that bas continues rising, moving above ground to turn ON what was previously OFF. And the cycle continues.

On the other hand, if you bring up the VDD very very slowly.......

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Chua developed a chaotic circuit for electronics, decades ago.

But I recall it requires a non-linear element.

https://en.wikipedia.org/wiki/Chua%27s_circuit