Here is the description of a design, to meet an invented requirement, where saturation limits the BC547's collector current (IC).
REQUIREMENT
You would like to have a red LED turn on, in your workshop, when the wind is blowing. For adequate brightness the LED requires 5mA of forward current (If). At this If, the forward voltage (Vf) of the LED is 1V. However the LED will blow if If exceeds 9mA. You have a 12V power supply to power the LED.
TURBINE
You make a little wind turbine using a model electric motor as the generator and blades made from bent aluminum sheet. You test the turbine with your multimeter and get the following results:
Light Breeze: 5V DC output, but the generator will only deliver 250uA current.
Gale: 50V DC and the generator able to deliver 250mA.
DESIGN CONSIDERATIONS
Obviously, the turbine has more than enough current capacity to illuminate the LED in a gale, but not in a light breeze. So you decide to use a transistor to increase the current. You find from the datasheet that a BC547 will easily handle 5mA IC. The BC547 also has a high current gain (HFE) of 100 minimum and 500 maximum (round numbers).
If the turbine fed its output current to the base of the BC547, with a light breeze the BC547 collector current (IC) would be between, 100 * 250uA= 25mA (min HFE) and 500 * 250uA= 125mA (max HFE). These currents would destroy the LED and obviously, at any higher wind speed the LED, would be obliterated not to mention the BC547. So there is a problem!
THE DESIGN
Attached is a design which solves the problem by feeding the LED with a constant 5mA for wind speeds from a light breeze to a gale.
One thing to know is that when a silicon NPN transistor is conducting, its base voltage (VBE) is always 600 millivolts more positive than its emitter voltage. It does not matter if the collector current is 1mA or 100mA, the VBE is still 600mV (see note 1).
Another thing to know is that the voltage between the BC547 collector and emitter (VCE) can never drop below 400mV (VCEsat) (see note 2). At VCEsat the transistor is said to be saturated.
Choosing R1 In a light breeze, the turbine produces 5V DC so the voltage across R1 is, 5V- 600mVBE = 4.4V.
The BC547 IC is required to be 5mA to illuminate the LED, so the minimum required BC547 base current (Ib), assuming you have a BC547 at the lower end of the HFE range is, 5mA/100 = 50uA. The turbine can supply 50uA OK in a light breeze.
Thus, the value for R1 is, 4.4V/50uA = 88k Ohms.
Choosing R2When the LED's If is 5mA its, Vf is 1V and the BC547's VCEsat is 400mV, so R2 can only ever have a maximum voltage of (12V-1V)- 400mV= 10.6V across it. So R2= 10.6V/5mA = 2.12k Ohms.
FINISHED DESIGN
And that finishes the design: just one transistor and two resistors and you have a system where the LED is off in no wind and, in any wind, the LED has a constant 5mA forced through it.
APPARENT ANOMOLY
You may be wondering about this circuit. After all, in a gale, the turbine output voltage is 50V. So the voltage across R1 is 50- 600mVCE= 49.4V. R1 is 88k, so the current flowing through R1 is, 49.4V/88k= 561uA which will be the IB of the BC547. And, If you had a BC547 with an HFE of 500, that would mean an IC of 500 * 561uA= 281mA which would not only blow the LED but also stress the BC547.
But no, this is not the case. The maximum possible current that could ever flow through R1 and the LED is (12V - 1V)/2.12k. You can prove this by removing the BC547 from the circuit and connecting the lower terminal of R2 to the OV supply line (negative terminal of the battery).
What happens is that when VCEsat is reached the BC547 is saturated and the current gain drops such that VCEsat is maintained.
OPTIMIZATION
Having arrived at the initial schematic you would then optimize the design. In this case only the value of R1 would be changed to ensure that the BC457 is fully in saturation at all times. From the datasheet the HFE of a BC457 in saturation drops to a minimum of 20. So the minimumBC457 Ib should be 5mA/20 = 200uA.
From the previous calculations the minimum voltage across R1 is 4.4V, so the optimized value for R1 is 4.4V/200uA= 22k. This means that, with a gale and a BC457 at the high end of the HFE range, the maximum current through R1, and hence the IB for the BC457, will be 49.4V/22K = 2.25 mA. The BC547 will be quite happy with an IB of 2.25mA.
COMPONENT RATIONALISATION
The components on the schematic have the theoretically calculated values but for a practical design you would chose the nearest standard value.
UBIQUITY
The rationalised and optimised circuit, and variations of it, are used universally for driving LEDs.
HOW TO ARRIVE AT THE ARCHITECTURE
There are two ways to arrive at the architecture. For a standard architecture just look on the internet, or in text books. Very often the component datasheets have application circuits. For a non-standard architecture, for a unique application, you are on your own. But it is not quite that bad. Generally there are parts of other designs that you can combine and adapt. And, of course, experience helps.
This is the end of the sermon.
Note 1 VBE does in fact increase a bit with collector current and base current. VBE is also inversely proportional to temperature (-2mV/degC), but just use a constant 600mV for general designs.
Note 2 VCEsat is more variable, but 400mV is a good value to use for a BC547 with 5mA collector current. Some high-power transistors may have a VCEsat of only 200mV with an IC of 1A.