The Variation in the effective width of a base in a Bipolar Junction Transistor is due to a variation in the a

Question

The Variation in the effective width of a base in a Bipolar Junction Transistor is due to a variation in the applied _____.

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The correct answer is Option C: base to collector voltage. The variation in the effective base width of a BJT, known as the Early Effect or Base Width Modulation, occurs due to changes in the reverse-biased collector-base junction depletion region width. As the $V_{CB}$ increases, the depletion layer extends further into the base region, effectively narrowing the neutral base width.

Step-by-Step Solution & Concepts:
The variation in the effective base width of a BJT, known as the Early Effect or Base Width Modulation, occurs due to changes in the reverse-biased collector-base junction depletion region width. As the $V_{CB}$ increases, the depletion layer extends further into the base region, effectively narrowing the neutral base width.

Working Principle: In a BJT operating in the active region, the collector-base junction is reverse-biased. Increasing the magnitude of $V_{CB}$ increases the width of the depletion region, given by $W_{dep} \propto \sqrt{V_{CB}}$. Since the base is typically more lightly doped than the collector, the depletion region expands primarily into the base, reducing the distance between the emitter-base and collector-base junctions. This reduction in effective base width $W_{eff}$ increases the concentration gradient of minority carriers, leading to an increase in collector current.

Key Formulas: $W_{eff} = W_B - W_{dep}$ — represents the effective base width where $W_B$ is the metallurgical base width.; $I_C = I_{S} \cdot e^{\frac{V_{BE}}{V_T}} \left(1 + \frac{V_{CE}}{V_A}\right)$ — the Ebers-Moll model modification showing the dependency on $V_{CE}$ and Early voltage $V_A$.

Key Points: The Early effect leads to a finite output resistance in the BJT output characteristics.; Higher doping in the base region can reduce the severity of the Early effect.; The collector current $I_C$ becomes dependent on the collector-emitter voltage $V_{CE}$ due to this modulation.; The point where all output characteristic curves intersect on the $V_{CE}$ axis is called the Early voltage ($V_A$).

Advantages: Useful for modeling non-ideal behavior in small-signal analysis.; Provides a parameter ($V_A$) for designing stable bias circuits.

Disadvantages: Causes finite output conductance, limiting the gain of BJT amplifiers.; Reduces the output impedance of the transistor.

Applications: Designing high-gain common-emitter amplifiers.; Modeling transistor behavior in integrated circuit design software like SPICE.

Additional Info: The Early voltage $V_A$ is typically in the range of 50V to 100V for standard BJTs.. Option A is incorrect because $V_{CE}$ is the aggregate of $V_{CB} + V_{BE}$, and the primary depletion widening effect is localized to the $V_{CB}$ junction.. Option B is incorrect as collector current is a result, not the cause of the depletion width variation.. Option D is incorrect as the emitter current is primarily controlled by the forward-biased emitter-base junction voltage $V_{BE}$.

Answer: C is correct — The variation in effective base width is caused by the change in the width of the depletion region at the reverse-biased collector-base junction, which is controlled by the base to collector voltage.

Exam Tip: Always remember that in BJT analysis, $V_{BE}$ controls the carrier injection while $V_{CB}$ controls the effective base width through the Early effect.

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Option A: emitter to collector voltage

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Option B: collector current

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Option D: emitter current

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