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Loop gain and metastability relation in bistable circuit

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Newbie level 4
Jun 4, 2007
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I have recently tried to increase my understanding of the cross-coupled transistor pair with resistive collector loads (see above).

The question I am asking me is whether or not the state where tail current is equally shared between the transistor is metastable. With "metastable" I mean that any small disturbance of the circuit would cause it to move to a stable state. With "state" I mean an operating point of the circuit that has a DC solution.

So I thought that by ensuring that the loop gain in the metastable is (or very close to being in the complex plane) greater than unity, then the typically called metastable state will really be metastable since any disturbance would move the circuit into a stable state.

Is showing that the loop gain in a state, is greater than unity enough for concluding that the state is metastable?

The loop gain calculation below (verified with spice) shows that the cross-coupled pair with an RItail value less than 4Vt has a negative loop gain. So according to what I though, but what I am now beginning to question, one can conclude that a RItail value larger than 4Vt, makes the state when the tail current is equally shared stable since the loop gain is then negative.

I have also simulated the circuit with real-time noise and then it seems like that the circuit is always stable independent on how I choose RItail. But if I add some small capacitors over the collector resistances, then the circuit quickly moves to a stable state.

Please share your thougts.


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