HI FRIENDS,
In a BJT .we have a relation in active region β=Ic/Ib
if we make base current zero the gain would be infinite.If the width of the base is zero then there would be no possibility of recombination,I know that recombination is crucial here but i dont know how it is playing such a key role,please explain the role of the base in a transistor.How it is helping in amplification?

 

Zero times any number is zero. Beta is a fixed number, not infinite though. Beta is current gain.

************************

To answer your second question, you have the formula. Ic = β Ib. A transistor is a current amplifier, so the collector current is the gain of the transistor times the base current.

 

Zero times any number is zero. Beta is a fixed number, not infinite though. Beta is current gain.

Actually, you have to be careful here. If you define beta to be current gain, then it is not really a fixed number. Beta depends on temperature, current, frequency and other operating conditions. Sometimes we forget this (or at least I do). We all realize that beta changes significantly from transistor to transistor (even if they are the same part number), but it also changes while operating.

The uncertainty of beta due to manufacturing variations is why most transistor circuit designs are made beta insensitive. The fact that the changes in beta due to manufacuring variations is greater than the operational changes in one particular device makes us forget that beta is not really constant.

The simple transistor model as a current controlled device with current gain is somewhat misleading. The famous Ebers-Moll model (I believe the spice transistor model is based on this) is a much more accurate (albeit nonlinear) model that treats the BJT as a voltage controlled device. You can use this model to show that, under some conditions, you can treat the transistor as a current controlled device with beta as a nearly constant number.

 

In a BJT .we have a relation in active region β=Ic/Ib
if we make base current zero the gain would be infinite.

Note that you are not in the active region when base current is zero. Also, the gain is not infinite because Ic/Ib = 0 / 0. Zero divided by zero is not infinite, but is ill-defined and has no meaning in this context.

 

Isn´t beta defined as β=ΔIc/ΔIb?
Or is that Hfe?

 

Isn´t beta defined as β=ΔIc/ΔIb?
Or is that Hfe?

Yes, that's a good question. Personally, I think either Hfe or β is correct terminology for ΔIc/ΔIb. This relates to my previous point that current gain is not constant. Your definition of β is approriate for AC small signal calculations. Often people use β for DC calculations, which implies the use of β=Ic/Ib. So, you could say that there is a DC beta and an AC beta. If β were truely constant, then there would be no need for the distinction, since β=Ic/Ib would be the same as Hfe=ΔIc/ΔIb.

 

The datasheet for the 2N3904 transistor shows a typical hFE (DC current gain) of 230 at VCE=5VDC, IC=2mA and 25 degrees C and and a typical hfe (AC current gain at 1kHz) of 130 at the same conditions except VCE=10V.
The saturated current gain is far less.