The figure above shows that the various transistor current components which flow across the forward biased emitter junction and the reverse biased collector junction.
- The emitter current IC component consists of hole current IpE (holes crossing from emitter into base) and electron current InE (electrons crossing from base into emitter).
- The ratio of hole to electron currents IpE/InE, crossing the emitter junctions in proportional to the ratio of the conductivity of the p material to that of the n materials. Since the doping of the emitter is made much larger than the dopin of the base, emitter current consists almost entirely of holes in p-n-p transistor.
- If the emitter were open circuited, no carriers are injected from emitter into the base and emitter current IE=0. Under this condition, the collector-base junction JC acts as a reverse-biased diode and therefore , the collector current ICO would equal to the reverse saturation current ICO.
- Therefore, when emitter-base junction is forward-biased and collector–base junction is reverse-biased, the total collector current will be sum of two currents . Hence
IC=IPC+ICBO ------> (a)
Now we define the various parameters which relate the Transistor Current Components are defined and described below
Emitter Efficiency δ
It is the ratio of current of injected carriers at emitter-base junction to total emitter current.
δ = IpE / (IpE + InE) = IpE /IE ------> (b)
Where IPE is the hole diffusion current at emitter junction.
Since emitter is nearly doped IpE >>InE and δ ~ 1
Transport Factor β
It is the ratio of injected carrier current reaching at collector-base junction JC to injected carrier current at emitter-base junction JE.β =IpC / IpE ------> (C)
Large – Signal Current GainThe ratio of the negative of the collector current, increment to the emitter – current change from zero (cut-off) to IE is called the large –signal current gain of a common base transistor. It is denoted by α,
Large signal currne gain α = (IC – ICO) / IE ------> (d)
Since IC and IE have opposite signs, α is always positive.
Since IpC + IC – ICO.
α = IpC / IE
= (IpC / IpE) x (IpE / IE)
Using equation (b) and (C),
α = β x δ ------> (e)
- Hence the transistor alpha is the product of the transport factor and the emitter frequency. This assumes thath the collector multiplication ratio α* is unity. α*nis the ration of the total currnet crossing collector junction to the hole current ( for p-n-p transistor) arriving at the junction. For most transistors α* = 1.
IC= –αIE + ICO ------> (f)
- In the active region IC is independent of collecto voltage VC and depends only upon IE. In order to generalise equation (f) i.e. for any value of VC replaces ICO by the current I=Io(ev/ηvr-1) in a p-n-p diode.
IC = αIE + ICO(1-eve/vr) ------> (e)