They reinforce this by going on to describe the Transistor Man that looks at the Base-junction circuit acting independently and then sets the effective resistance of the Collector in order to achieve I_C = Beta * I_B. (Up to transistor saturation at 0 Ohms, or rather 0.2 V drop.) Also fine.

The next thing they discuss is the emitter-follower. 10V at the Collector, Base receives variable V_in=V_base, and Emitter passes through resistor R to ground. V_out=V_emitter measured between Emitter and resistor.

My initial analysis (using mostly their equations):

V_out=V_in-0.6 (their equation)

dV_out = dV_in (theirs)

dI_out = dV_out / R = dV_in / R (theirs)

Depending on how you look at it, I either implicitly assumed that I could treat the Base-junction circuit separately or, as I describe below, I may have implicitly assumed that the current:voltage relationship across the Base junction continued to hold such that the voltage drop was 0.6 regardless of current. Anyway, I then did:

dI_in = d(V_in-0.6) / R = dV_in / R

Of course, if dV_out = dV_in (theirs) my assumption implies bad things like dI_collector=dI_out - dI_in = 0, which would be a good indication that I shouldn't do transistor analysis this way...

By their calcuation,

I_out = I_in + I_collector = (1+Beta)*I_in

Hence, dI_in = dI_out / (1+Beta)

Since dI_out = dV_out / R and dV_in = dV_out,

dI_in = dV_in / [(1+Beta)*R]

(rather than my dI_in = dV_in / R)

This was confusing the *crap* out of me. After banging my head against the wall for awhile, I realized that my assumption about the fixed 0.6 V drop may be the problem. A diode has an exponential I:V relationship, so you can usually just assume a 0.6V (or 0.7) drop and then treat it like a short circuit. However, maybe that's not the case here; if I treat the collector as a super-diode that has I:V relationship 100 times that of the base (and is magically dependent on the Base-Emitter voltage drop), then it seems like that might somehow be able to save me.

At the outset, I thought I could just calculate i_Base by converting the Base junction to a diode and independently calculating the current of that circuit assuming a 0.6V drop across the diode. Then take the current multiplier, and the Collector either delivers that current or delivers as much as it can under saturation. (As with the lamp-example.) But if I treat the Base-junction voltage drop as fixed 0.6V, then I seem to get bad answers.

If it isn't fixed at 0.6V, what voltage drop should I be using in order to calculate the Base current?? Something dependent on the Beta multiplier? Would that approach deal properly with transistors in saturation?

Or did I make some other silly mistake and I'm off in left field?

Sorry for the long post...thanks for reading it.