You cannot buy any transistor with a certain beta. Beta is a range of numbers and you get whatever is available.
The constant current sink transistor has a reference voltage at its base, not a current. So the series base resistor is not needed.
Hi there audioguru,
Surely you didnt think i meant that you have to go out an buy a transistor with an exact beta of 100 or 50 or something, did you? What i was saying is that we estimate the beta using perhaps a typical value and go from there to estimate the other circuit values. Once we do this, we can explore the circuit operation by using several values of Beta and see if the circuit operation will remain stable for the range of possible real life Betas we might encounter.
About the series base resistor...
I asked you to look at this again because this isnt your typical voltage follower. A voltage follower has as its input a voltage at the base, and as its output it has a voltage at the emitter (im sure you are well aware of this). To put it another way, we would be using a voltage to control another voltage.
With this actual circuit however, we are going to want to be able to control a current with a voltage, ie control the current though the LED (which also is in the collector circuit not the emitter circuit BTW) with the voltage coming out of the microcontroller chip pin. Not only is this not the same type of control, but it's not even the same type of circuit. Because the load is in the collector circuit we have a common emitter amplifier here, not a voltage follower. If you want to however, you can look at it as a voltage follower anyway and reckon the voltage across the emitter resistor as being converted into a current and thus it still controls the LED current, however, because of the other constraints of the circuit we can not apply a voltage (such as +5v with Vcc=+5v for example) to the base directly because then that would not allow enough collector voltage freedom. We'd be restricting the range of collector voltage to about +4.5v to +5v which just isnt enough range to get this circuit to work with the LED in the collector circuit.
To say it another way, if we apply +5v to the base directly then the emitter voltage goes up to about 4.3v and that means even with a saturation voltage of 0.000 volts we'd only be able to get the collector to go down as low as 4.3v, and with a 2v Vf LED that would not be enough voltage to get it to light up.
With a base resistor however, the uC pin goes to +5v but the emitter voltage only goes as high as dictated by the other circuit parameters and components, which will be much much lower, and that will allow a saturated transistor to put enough voltage across the LED to get it to light up brightly. Too brightly in fact, unless the emitter resistor is chosen correctly or the transistor is pulsed to limit average current.
You can easily verify what i have stated above by doing a simple simulation.