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Bootstrapping Derivation

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Hi,

In a word, superposition. Make sense?
 
Ahh, good 'ol superposition. Thanks, I'll re-hash that one. Thanks for the hint.
 
Ok, so I'm assuming that finding Vco is equivalent to finding Vee. I am also assuming a positive output from the op-amp.

The equation I have for finding Vee is Vee = Vbb-IbRb - Vbe - IeRee. Since for the Vco derivation, he was ignoring Vbe and since there is no emitter resistor, I omitted the last term. So I have Vbb - IbRb.

Filling in the values from my superposition, I got Vbb to be [R1/(R1+R2)][Vcc-Vout], Ib to be (R1+R2)(Vcc-Vout) and Rb is just R1||R2. Substituting those values doesn't give anything close to his first equation and I'm not sure why. Maybe I did superposition wrong. I figured since the two batteries across the resistor create opposite polarities on the resistors, you would subtract the voltages across each.
 
Hi,

The calculation they did was for the base voltage assuming very small base current.

The voltage at the base due to Vcc is:
v1=Vcc*R1/(R1+R2)

and the voltage at the base due to Vout is:
v2=Vout*R2/(R1+R2)

The superposition of the two is the ADDITION of v1 and v2 because the the algebra of superposition is complete in itself:
V=v1+v2=(Vcc*R1+Vout*R2)/(R1+R2)

Also, it looks as if the transistors collector base junction will become forward biased so perhaps a diode in series with the collectors would help. Otherwise, the bootstrap voltage is clamped to Vcc+0.7v which isnt much more than Vcc.

Im going to have to take a longer look at this circuit. Something doesnt look quite right about it and i think the calculation might have to be done differently.

LATER:
Yeah, looking at the schematic, i assume we want to make the base of the upper transistor more (much more) positive than the supply voltage Vcc, and the capacitor is supposed to supply that extra boost, but if we achieve that goal the base collector diode would forward bias and prevent our signal from going any higher than Vcc+0.7v. Unless i am missing something here it doesnt look like this circuit is going to fly. Perhaps it was never tested.
When i first saw it it looked like the diodes were backwards, but then i saw that maybe they were getting the +cap voltage from the lower part of circuit. But looking at it more carefully, if we achieve that goal then we effectively cut off the negative supply voltage from the op amp, which is not good even when putting out a positive voltage.
All this leads me to believe that this circuit does not work. It's not that bootstrapping in general doesnt work, but this particular circuit doesnt look good at all.
The other thing to keep in mind is that when you bootstrap dynamically like this is supposed to work the signal has to be coming in all the time in order to keep the bootstrap cap charged up. Thus it may not be good for audio where the signal levels constantly change.
 
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Ahh that makes more sense.

I am working through a power electronics book now that I have some downtime and the circuit I analyzed used an 8V zener diode and a resistor to limit the zener current. This was to ensure the op-amp had plenty of bias room and I believe that would also solve the issue of cutting off the negative supply because they would both be held to at least +/- 8V.
The cap in the book's design was a .1uF to serve as an AC short between the pins to bypass noise entirely.

I was wondering how something like that would work in an audio circuit but I see why it wouldn't be very effective. That would explain why it was in a power electronics book as well.

Thanks again for all the help. Pretty cool stuff.
 
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