Question

The relationship between current gain $\alpha$ in Common Base [CB] mode and current gain $\beta$ in Common Emitter [CE] mode is

• A. $\beta =\alpha +1$
• B. $\beta =\frac{\alpha }{1-\alpha }$
• C. $\beta =\frac{\alpha }{1+\alpha }$
• D. $\beta =1-\alpha$

Answer 1

The correct option is B $\beta =\frac{\alpha }{1-\alpha }$

We define both current gains as $\beta =\frac{I_c}{I_b}$ and $\alpha =\frac{I_c}{I_e}$

Using $I_e=I_c+I_b$

Dividing both sides by $I_c$, we get $\frac{I_e}{I_c}=1+\frac{I_b}{I_c}$

Or $\frac{1}{\alpha }=1+\frac{1}{\beta }$

Or $\frac{1}{\beta }=\frac{1}{\alpha }-1$

$⟹$ $\beta =\frac{\alpha }{1-\alpha }$