Amplification using BJTs
Basically, the transistor is useful in amplifiers because the currents at the emitter and collector are controllable by the relatively small base current. The essential mechanisms are easy to understand if various secondary effects are neglected. We shall use total current (d-c plus a-c), with the understanding that the simple analysis applies only to d-c and to small-signal a-c at low frequencies. We can relate the terminal currents of the transistor iE, iB, and ic by several important factors.
In this introduction we shall neglect the saturation current at the collector and such effects as recombination in the transition regions. Under these assumptions, the collector current is made up entirely of those holes injected at the emitter which are not lost to recombination in the base. Thus ic is proportional to the hole component of the emitter current iEp:
The proportionality factor B is simply the fraction of injected holes which make it across the base to the collector; B is called the base transport factor.
The total emitter current iE is made up of the hole component iEp and the electron component iEn) due to electrons injected from base to emitter
The emitter injection efficiency is
For an efficient transistor we would like B and to be very near unity; that is, the emitter current should be due mostly to holes , and most of the injected holes should eventually participate in the collector current (B = l).The relation between the collector and emitter currents is
The product B is defined as the factor α, called the current transfer ratio, which represents the emitter-to-collector current amplification. There is no real amplification between these currents, since α is smaller than unity. On the other hand, the relation between ic and iB is more promising for amplification.
In accounting for the base current, we must include the rates at which electrons are lost from the base by injection across the emitter junction (iEn)
and the rate of electron recombination with holes in the base. In each case, the lost electrons must be resupplied through the base current iB. If the fraction
of injected holes making it across the base without recombination is B, then it follows that (1 - B) is the fraction recombining in the base. Thus the base current is
neglecting the collector saturation current. The relation between the collector and base currents is found
The factor β relating the collector current to the base current is the base-tocollector current amplification factor. Since α is near unity, it is clear that β
can be large for a good transistor, and the collector current is large compared with the base current.