The common-emitter current gains of two transistors are β = 60 and β = 150. Determine the corresponding common-base current gains. (b) The commonbase current gains of two transistors are α = 0.9820 and α = 0.9925. Determine the corresponding common-emitter current gains.

Given Information:

Common-emitter current gains = β = 60 and 150

Common-base current gains = α = 0.9820 and 0.9925

Required Information:

Common-base current gains = α = ?

Common-emitter current gains = β = ?

Answer:

Common-base current gain = α = 0.9836 and 0.9933

Common-emitter current gains = β = 54.55 and 132.33

Explanation:

The current gain beta is the ratio of change in collector current and the change in base current and is called beta (β)

The current gain alpha is the ratio of change in collector current and the change in emitter current and is called alpha (α)

The relationship between alpha and beta is

α = β/β + 1 and β = α/1 - α

(a) Common Base Current Gain (α)

For β = 60:

α = 60/60+1 = 60/61 = 0.9836

For β = 150:

α = 150/150+1 = 150/151 = 0.9933

(a) Common Emitter Current Gain (β)

For α = 0.9820:

β = 0.9820/1-0.9820 = 0.9820/0.018 = 54.55

For α = 0.9925:

β = 0.9925/1-0.9925 = 0.9925/0.0075 = 132.33

a1) for β = 60, α = 0.9836

a2) for β = 150, α = 0.9934

b1) for α = 0.9820, β = 54.56

b2) for α = 0.9925, β = 132.33

Explanation:

a1) for β = 60

α = β / (β+1)

α = 60 / (60+1)

α = 60/61

α = 0.9836

a2) for β = 150

α = 150 / (150+1)

α = 150 / (150+1)

α = 150/151

α = 0.9934

b1) for α = 0.9820

β = α / (1-α)

β = 0.9820 / (1-0.9820)

β = 54.56

b2) for α = 0.9925

β = 0.9925 / (1-0.9925)

β = 132.33