Bipolar Junction Transistor:

The notations utilized here for voltages and currents correspond to the following conventions : DC bias values are mentioned by an upper case letter with upper case subscripts, for example I_{C ,} V_DS. Instantaneous values of small-signal variables are mentioned by a lower-case letter with lower-case subscripts, e.g. υ_s, i_c. Total values are indicated by a lower-case letter with upper-case subscripts, foe instance. υ_BE, i_D. Circuit symbols for independent source are circular and symbols for controlled sources have a diamond shape. Voltage sources have a ± sign within the symbol and current sources have an arrow.

Figure illustrated the circuit symbols for the NPN and PNP BJTs. The collector-base junction is reverse-biased and the base-emitter junction is forward biased in the active mode. For the NPN device, the active-mode collector and base currents are specified by

                               i_C  = I _S  exp(υ _BE /V_T) ; i_B  =   i_C / β                   

Figure: BJT Circuit Symbols

where V_T   refer to the thermal voltage, I_S refer to the saturation current, and β is refers to the current gain. These are given by

V_T  = kT/ q = 0.025 V  for T = 290; K = 25.86 m V for T = 300 K

I_S   = I_SO (υ_CE /V_A)

and

β= β₀ (1 +  (υ_CE /V_A ))

where V_A is the early voltage and I_SO and β_o, respectively, are the zero values of I_S and β.

Because  I _S/ β = I_SO/ β₀ , it follows that i  is not a function of υ_CE. The equations apply to the pnp device if the subscripts BE and CE are reversed.

The emitter-to-collector current gain α is defined as the ratio i_C / i_E .To solve for this, we

may write

i _E  = i _B   + i _C = ((1/ β )+ 1)  i _C = (1 + β/ β) i _C 

It follows that

α= i_C/ i_E  =        β/1 + β

Therefore, the three transistor currents are associated by the equation

i_C  =β i_B  = α i_E