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If the value of the common base current gain (α) is 0.98, then the value of the common collector current gain (γ) is ___________.
0.02
98
49
50
50
The common collector current gain, denoted by γ, is defined as the ratio of emitter current to base current. It is mathematically related to the common base current gain α by the expression γ=1−α1.
The common collector current gain, denoted by γ, is defined as the ratio of emitter current to base current. It is mathematically related to the common base current gain α by the expression γ=1−α1.
α=IEIC — Common base current gain
γ=1−α1 — Relationship between γ and α
In a Bipolar Junction Transistor, the emitter current IE is the sum of base current IB and collector current IC. Given α=IEIC, we derive γ=IBIE. Since IB=IE−IC, we substitute IC=αIE to get γ=IE(1−α)IE=1−α1.
The parameter γ is also known as the emitter-follower gain.
For a typical BJT where α is close to unity, γ results in a very large value.
The value of γ is always greater than 1.
High input impedance
Low output impedance
Voltage gain is less than unity
Primarily used as a buffer
Impedance matching circuits
Voltage buffers
Calculation: γ=1−0.981=0.021=50.
Option A (0.02) represents (1−α). Option B (98) is incorrect as it confuses α with β calculations. Option C (49) corresponds to the common emitter gain β=1−αα.
D is correct — Using the formula γ=1−α1, substituting α=0.98 gives 0.021=50.
Remember that γ=1+β, where β is the common emitter current gain. If α=0.98, then β=0.020.98=49, thus γ=1+49=50.
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