voltage divider bias

[dragonwarrior]

hi everyone..

I need help to understand the amplification process in a bjt amplifier with self or potential divider biasing circuit..
I couldn't understand the following :
1)Why R1 should be greater than R2 ? (where R1 and R2 are the voltage dividing resistors or base resistors )
2)Why the product of Beta(current gain) and Emitter resistor Re should be greater than 10 times R2 ? (book says only then we can use approx analysis.)
ie Beta *Re >10 R2
3)How to find the Base current (Ib) ?
4)They say that The Base resistors R1 and R2 appears parallel to each other..but how voltage gets divided when they are in parallel ?

Thanks in advance..

 

[Cabwood]

1) Base voltage is usually low compared to supply voltage. That's why the resistors biasing the base have such a ratio
2) You want apparent base input impedance to greatly exceed base bias resistances, so that base current fluctuations have minimal effect on base bias voltage
3) Find the maximum collector current you'll ever get from your design (about Vsupply / Rcollector), divide by transistor beta
4) To an AC signal is injected into your circuit at the junction of R1 and R2, both R1 and R2 represent a path to an unchanging potential - ground or +ve supply. Thus both represent a cause of "stiffness" that the signal has to fight against. The AC signal does not care that the resistors connect to different potentials, only that they connect to a stiff unchanging potential. Thus from the perspective of an input signal trying to "wiggle" the base, both supply rails are the same obstruction, and R1 and R2 might as well be connected in parallel. Thus input impedance is calculated as such. Of course they aren't really connected in parallel.

 

[dragonwarrior]

thanks for your reply cabwood..but how would you know the value of transistor Beta ? i mean, we can find its value during manufacturing or after the whole design of the circuit ?

 

[Cabwood]

Since the manufacturer doesn't guarantee beta (except for some "special" transistors), you will have to measure it somehow. Typically base current can be 1% of collector current, so unless you use resistors of much better tolerance than 1% (unlikely), the only way I can think of to determine base current is by placing a sensitive ammeter in that path.

If you are willing to settle with the manufacturer's tolerance for beta (they might specify 50 to 100 for example) then you can calculate the range of possible quiescent base currents. That is, minimum (probably not very useful information) and maximum (more useful) base current.

I say quiescent because you mustn't forget that as collector current rises and falls (causing collector voltage to swing) the base current must also be changing. Base current will be near-zero when the collector voltage is greatest, and will be at a maximum when collector voltage is lowest (just above emitter voltage). If you are interested in finding maximum possible base current, find out the collector current (through RC) when collector voltage is lowest, and divide by the worst possible beta for your transistor.

 

[dragonwarrior]

Thank you cabwood and that was useful..

 

[colin55]

when collector voltage is lowest (just above emitter voltage) should be:
when collector voltage is lowest (just below emitter voltage)

 

[Cabwood]

when collector voltage is lowest (just above emitter voltage) should be:
when collector voltage is lowest (just below emitter voltage)

How so? How can the collector voltage ever drop below emitter voltage? Vce during saturation is 0.1V or so. It never goes negative.

 

[unclejed613]

when collector voltage is lowest (just above emitter voltage) should be:
when collector voltage is lowest (just below emitter voltage)

?????

think of the transistor as a lever, and beta as the ratio of the distances of the ends to the fulcrum. if the base end of the lever is 100in, and the collector end of the lever is 1 in, the ratio is 100:1. pushing up on the base with 1lb of force will pull down the collector end with 100lb of force.


measuring the beta is simple with a constant current source. you set a constant current source at, let's say 100uA, and feed it into the base of the transistor, then measure the resulting collector current.

 

[unclejed613]

so here's a beta tester. the base current on Q2 is 100uA, the collector current result is 7.2mA when the sim is run, so the beta is 72.

the current source part of the circuit is Q1, D1, D2, R1, R2. R1 sets the current, and that current should be equal to the voltage across D2 divided by the resistance of R1. because of variations in the Vf of diode and transistor junctions, the value of R1 should be determined experimentally.

i ran it here as a sim, but with real components it works the same. even with the sim, i had to play with the value of R1 to get 100uA. with real components, a DMM from Q1 collector to ground in current mode, and without Q2 in circuit is suitable for measuring the source current. Collector current in Q2 is determined by measuring the voltage drop across R2

 

[colin55]

I was assuming the lowest effective base voltage to be 0.6v

 

[unclejed613]

that depends on the particular Vf of the transistor 0.5-0.8V is the usual range for silicon. 1.0-1.6V for silicon darlingtons. for germanium, the Vf is 0.1-0.4V. other transistor types (there are a lot of new types, such as SiC and SiGe) will have different Vf bias voltages. the beauty of the current source is that it doesn't care what the Vf is, it supplies the same amount of current regardless.