Many folks start out pondering what a LED driver does, and this topic has been often covered. First, a driver transistor gives a boost, to a more feeble input.
Like I said, hopefully readers can gain some additional insight.
First, (see diagram), your input flows down through the transistor BASE, and encounters a sort-of BACK-VOLTAGE, or 'reaction voltage'. That is typically going to be near 0.6 volts, likely maybe 0.75 volts. So this is considered 'transistor ON' as that input current, and resulting 'back voltage'.
Now, a question arises: What if the 0.6 volt input measured, base to ground, is not enough? Well, you work through the current GAIN situation, to check if there is strong enough input, to let an LED and load resistor conduct the full switched-on current, that it would naturally have if user had simply grounded theload resistor, without using a transistor switch.
But that's a different case ? You might be thinking.
It turns out, a fully conducting transistor output, viewed as 'Collector to Ground', is quite low, and is often ignored, in designing your GAIN and output requirements. Most circuits show maybe 0.010 volts there. Indeed: in finding a higher voltage, (collector terminal), such as 2.4 volts, you can start assuming that the transistor is either OFF, or very poorly conducting partially on, (linear region).
So you use your transistor's typical or minimum GAIN, simply as a ratio: input to output (current).
Problem remaining: You have to account for the small voltage loss, in the BASE to Emitter, (the typical 0.
.
That's it, for example if your input voltage is 4 volts, then you will want to use (4.0 - .
as the input resistor
voltage. Course, that then sets the input current, that then determines output current. Now if that output capability exceeds your connected load, then you can have confidence, that your circuit will pull AT LEAST what you want, and more if needed by some other load. This is giving a good definition of 'SATURATION',
the transistor-LED circuit will be considered fully ON.
Mostly, I'm not familiar with driving in the linear region, for brightness control: Most of what I have seen uses PWM or pulse-width to control LED brightness by average power delivered, by way of full-power pulsing ( the LED and it's current limiting resistor).
By the way: a transistor in linear region is going to have issues with power / heat as it presents a voltage drop, exceeding that low value (0.010 volts) that a fully
turned on transistor has. (Remembering that power is voltage times current: Watts=V x I).
-thanks, RJ