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I've built and simulated the circuit below in real life, LTSpice and Stack-Echange-Spice. It behaves in a similar fashion in all of these Environments. When the "LAMP2" load is disconnected, the Base currents become unbalanced, with most going through Q2 - This, in turn, turns Q1 all but off, since only a very small current is going through its base:

schematic

simulate this circuit – Schematic created using CircuitLab

Now i drew myself what i believe is the equivalent circuit of those darlingtons: Equivalent circuit drawing

I suspect that when the top load on the right side is disconnected, the base current of Q2 turns on the "main" NPN of Q2 and allows current to flow through the first BC diode, increasing consumption. But why does this not happen with the load connected as well? What is happening here?

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    \$\begingroup\$ Your model of a transistor explains only what one can see if he tests a PN junction of a transistor one junction at a time. It doesn't at all take into the account the fact that the base is thin, so thin that the thermal random motion of the electrons is much wider than the base layer. That random motion makes a properly biased transistor work so that the electrons jump from the base to collector apparently against how BC-junction should conduct. Use the NPN BJT large signal model shown for ex. in this text: wiki.analog.com/university/courses/electronics/text/chapter-8 It's at 8.4.1 \$\endgroup\$
    – user287001
    Jun 4, 2020 at 22:12

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The double-diode model for transistor is little use here.

What happens is that when you disconnect the load at Q2, there can be no collector current available for the first transistor in the darlington pair Q2, so all the current to drive must come via base terminal.

And therefore, as there must be equal voltages at the base of Q1 and Q2, the Q2 needs more base current to match the VBE drop of Q1.

This is the reason you should not parallel the bases, but have separate base resistance for each transistor, as they may have different VBE drops due to manufacturing tolerances, or different VBE drops due to the collector current.

Same thing with LEDs, you can't parallel a green and red LED with single resistor, only the red one will light up as they have different forward voltage drops.

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    \$\begingroup\$ Connecting base-to-base like that creates a kind of current mirror, in which the current in both collectors is going to be whichever one is less. If you force one to zero current, then the other will follow. \$\endgroup\$
    – Dave Tweed
    Jun 5, 2020 at 0:43

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