The β of a transistor is 200, what is its α?

SOLUTION

Concept:

The common base DC current gain is a ratio of the value of the transistor's collector current to the value of the transistor's emitter current, i.e.

\(α = \frac{{{I_c}}}{{{I_e}}}\)   ---(1)

Also, the common-emitter current gain is the ratio of the value of the transistor's collector current to the value of the transistor's base current in a transistor, i.e.

\(β = \frac{{{I_c}}}{{{I_b}}}\)   ---(2)

Using Equation (1) and (2), we get:

\(β =\frac{α}{1-α}\)

\(α =\frac{\beta}{\beta+1}\)

Calculation:

With β = 200, α will be:

\(α =\frac{200}{200+1}\)

α = 0.995