Question

In a BJT, α and β are related by the expression:
1. \(\alpha = \frac{1}{{1 - \beta }}\)
2. \(\alpha = \frac{1}{{1 + \beta }}\)
3. \(\alpha = \frac{\beta }{{1 - \beta }}\)
4. \(\alpha = \frac{\beta }{{1 + \beta }}\)

Answer 1

Correct Answer - Option 4 : \(\alpha = \frac{\beta }{{1 + \beta }}\)

The common emitter current gain (β) is the ratio of the collector current (IC) to the base current (I­B)­.

\(\beta = \frac{{{I_C}}}{{{I_B}}}\)

The common base current gain (α) is the ratio of the collector current (IC) to the emitter current (I­E).

\(\alpha = \frac{{{I_C}}}{{{I_E}}}\)

The relationship between α and β is given by,

\(\alpha = \frac{\beta }{{\beta + 1}}\)

IC = α IE

\({I_C} = \frac{\beta }{{\beta + 1}}{I_E}\)

As β is very high, IC ≈ IE