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I modified your circuit, at least so that it works for slowly varying input. I show the current into two separated loads RLt and Rlb as the Opto-isolator current I1 sweeps slowly from zero to 2mA. Normally, I1=0 would be the off state, while (arbitrarily) I1=2mA is the on state. The first question is what happens to the currents through Q3 and Q4 as the input slowly sweeps through its range?
Ideally, when I1 =0, Q4 is capable of sinking 4A, and Q3 is fully off. As I1 increases, Q4 turns off almost completely, but Q3 begins turning on, with just a bit of overlap, and then as I1 increases a bit more, then Q4 is fully off, and Q3 is fully on. I use a trim pot to establish the amount of overlap, and I show that with the pot wiper 78% up from the bottom, there is just a bit of overlap. The goal would be to reduce the shoot-through current where both PNP and NPN are turned on at the same time.
However, when I tested the driver in the time domain using it to drive a capacitive load at a high slew rate (fast changing I1), the performance is disappointing.
For the high to low transition of I(I1) and V(out), both the PNP and NPN are on at the same time, so the shoot through current is so large as to be unuseable. The delays through Q1 and Q2 are asymmetrical, so the design will have to be modified to solve this problem.
I am out of time to work on this, so I include the .asc file in case you want to play with it more...
There are about 100 different versions of IC that are built to do this job. This one FL3100 works up to 18 volts and 2A. There are much bigger available. Higher voltage if you want.
There is a simple way to get a negative output voltage if you really need it. (drive +10V and -4V)