General Transistor Equation

General Transistor Equation

In the active region of the transistor, the emitter is forward biased and the collector is reverse biased. The generalized expression for collector current I_C for collector junction voltage V_C and emitter current I_E is given by

If V_C is negative and | V_C | is very large compared with V_T, then the above equation reduces to

If V_C, i.e., V_CB, is few volts, I_C is independent of V_C. Hence the collector current I_C is determined only by the fraction a of the current I_B flowing in the emitter.

From equation (5) we have

Since I_C and I_E are flowing in opposite directions

The large-signal current gain (β) is defined as,

Comparing the equations (7) and (9) we get the relationship between the leakage currents of transistor common-base (CB) and common-emitter configurations as

From this equations, it is evident that the collector-emitter leakage current (I_CEO) in CE configuration is (I + β) times larger than that in CB configuration. As I_CBO is temperature dependent, I_CEO varies by large amount when temperature of the junction changes.

Expression for Emitter Current

The magnitude of emitter-current is

I_E = I_C + I_B

Substituting equation (7) in the above equation,

We get

Substituting the equation (6) in the (11), we have

DC Current Gain

The dc current gain is defined as the ratio of the collector current I_C to the base current I_B. That is

As I_C is large compared with I_CEO, the large signal current gain (β) and the de current gain (h_FE) are approximately equal.