Stability factors are defined as the rate of change of _____ with respect to the ____, keeping both the base c

Question

Stability factors are defined as the rate of change of _____ with respect to the ____, keeping both the base current and the current gain β constant.

Examoogle · Accepted Answer

The correct answer is Option C: collector current; collector base leakage current. Stability factors, denoted by $S$, are defined as the rate of change of collector current $I_C$ with respect to the reverse leakage current $I_{CBO}$, while keeping base current $I_B$ and current gain $\beta$ constant. This measure quantifies how sensitive the transistor bias point is to temperature-induced variations in leakage current.

Step-by-Step Solution & Concepts:
Stability factors, denoted by $S$, are defined as the rate of change of collector current $I_C$ with respect to the reverse leakage current $I_{CBO}$, while keeping base current $I_B$ and current gain $\beta$ constant. This measure quantifies how sensitive the transistor bias point is to temperature-induced variations in leakage current.

Working Principle: In a BJT, the leakage current $I_{CBO}$ is highly temperature-dependent. Since $I_C = \beta I_B + (1 + \beta) I_{CBO}$, any change in temperature increases $I_{CBO}$, which in turn increases $I_C$ (thermal runaway). The stability factor $S = \frac{dI_C}{dI_{CBO}}$ describes the multiplier effect of this leakage variation on the collector current.

Key Formulas: $S = \frac{dI_C}{dI_{CBO}}$ — Definition of the stability factor; $I_C = \beta I_B + (1 + \beta) I_{CBO}$ — General BJT collector current equation; $S = \frac{1 + \beta}{1 - \beta(\frac{dI_B}{dI_C})}$ — Generalized stability factor formula

Key Points: A lower value of $S$ represents a more stable operating point.; The ideal value of the stability factor $S$ is $1$.; Thermal runaway occurs if the circuit is not designed to keep $S$ within reasonable limits.; BJT biasing circuits like Voltage Divider Bias are used specifically to minimize the stability factor.

Advantages: Provides a quantitative metric to compare different biasing circuits.; Essential for designing reliable amplifiers that operate across wide temperature ranges.

Disadvantages: Does not account for $\beta$ variations directly (other factors like $S'$ and $S''$ are used for $\beta$ and $V_{BE}$).

Applications: Transistor bias circuit design; Temperature-compensated amplifier stages

Additional Info: For a common-emitter fixed bias circuit, $S = 1 + \beta$.. Options A, B, and D are incorrect as they invert or swap the dependent and independent variables of the partial derivative definition.

Answer: C is correct — Stability factors are defined as the rate of change of collector current with respect to the collector base leakage current, keeping both the base current and the current gain $\beta$ constant.

Exam Tip: Remember that in any stability analysis, the goal is to keep $I_C$ constant; thus, $I_C$ is always the dependent variable (in the numerator of the derivative).

Examoogle · Answer

Option A: collector base leakage current; emitter current

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Option B: emitter current; collector base leakage current

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Option D: collector base leakage current; collector current

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