52. Which of the following statements is/are true for a BJT with respect to its DC current gain β?

 

Q.52 Which of the following statements is/are true for a BJT with respect to its DC current gain β?

1. Under high-level injection condition in forward active mode, β will decrease with increase in the magnitude of collector current.
2. Under low-level injection condition in forward active mode, where the current at the emitter-base junction is dominated by recombination-generation process, β will decrease with increase in the magnitude of collector current.
3. β will be lower when the BJT is in saturation region compared to when it is in active region.
4. A higher value of β will lead to a lower value of the collector-to-emitter breakdown voltage.

Answer: Option A, C, D Solution

Answer

The correct answer is: (A), (C), and (D) are true. (B) is false.

(A) True

In a BJT operating in forward active mode, when the collector current becomes very large (high-level injection), the excess carrier concentration in the base becomes comparable to the base doping concentration.

This causes:

• Reduced emitter injection efficiency
• Increased recombination
• Deviation from ideal transistor action

As a result, the collector current no longer increases proportionally with the base current, and the DC current gain

β = IC / IB

starts to decrease at high collector currents. This phenomenon is known as β roll-off.

(B) False

At low-level injection, if the emitter-base junction current is dominated by the recombination-generation (R-G) process, then:

IC ∝ eVBE/VT

while

IB ∝ eVBE/(2VT)

because recombination current has an ideality factor of 2.

Therefore,

β = IC / IB ∝ eVBE/(2VT)

Since collector current increases with VBE,

β ∝ √IC

Thus, β increases with collector current, not decreases.

(C) True

In the active region,

β = IC / IB

is typically large (around 50–300).

In saturation, both the emitter-base and collector-base junctions are forward biased. Extra charge storage occurs and the collector current is no longer efficiently controlled by the base current.

The effective gain in saturation,

βsat = IC / IB

is much lower than the active-region gain.

Designers often use a forced gain of about 5–10 to ensure saturation, even when the active-region gain may be around 100.

(D) True

There is a well-known trade-off in transistor design:

• Higher β generally requires lighter base doping.
• A lightly doped base increases susceptibility to avalanche multiplication and punch-through effects.

An approximate relationship is:

BVCEO ∝ β-n

where n is a positive constant.

Therefore, as β increases, the collector-emitter breakdown voltage BVCEO decreases.

This is a standard breakdown-gain trade-off in BJTs.

Final Answer

(A), (C), and (D) are true.

Therefore, the correct choice is: A, C and D.

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