Trying to understand how this pnp works

My answer to SE EE question Trying to understand how this pnp works

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I have been familiar with this BJT driving technique for a long time... but now I came up with a new original explanation through a "dynamic resistor" concept...

Answer

OP:  How can this pnp be turned off?

A more in-depth conceptual answer to this question can be given if the main BJT input property is taken into account: BJT can be more easily controlled by voltage than current since its input base-emitter junction behaves as a voltage-stabilizing element.

This property can be seen in its input IV curve having an almost vertical part. This means we can control it more easily by small voltage changes instead of large current changes.

So, the problem of turning off the transistor only by an "opto" is that we try to do it by decreasing the current instead of the voltage… and it opposes us. Let's see how...

The output collector-emitter part of the photo-transistor can be thought of as a varying "base resistor" that, in this case, increases its resistance.At the same time, the base-emitter junction of the PNP transistor behaves as a dynamic resistor that also increases its resistance trying to keep up the voltage; so it opposes the input base resistance variations.

The two "resistors" in series can be thought of as a "dynamic voltage divider". Since both resistances simultaneously increase, the output (base-emitter) voltage does not decrease… and the transistor can not be turned off.

Connecting a resistor in parallel to the base-emitter junction solves this problem since its resistance shunts the increasing base-emitter resistance. Only, a problem appears when the "opto" decreases its collector-emitter "resistance" trying to turn on the PNP transistor. Now, the two "resistors" in parallel form a current divider... and the lower additional resistance diverts a part of the base current. So the value of the additional resistance must be chosen somewhere in the middle between the two extremes.

I hope this more conceptual explanation will appeal to those who have a penchant for a more "philosophical" thinking...