Two transistor biasing circuits have stability factors S ₁ = 101 and S ₂ = 15. Which circuit offers better the

Question

Two transistor biasing circuits have stability factors S ₁ = 101 and S ₂ = 15. Which circuit offers better thermal stability?

Examoogle · Accepted Answer

The correct answer is Option B: Circuit 1. In transistor biasing, the stability factor $S$ represents the sensitivity of the collector current $I_C$ to changes in the reverse saturation current $I_{CO}$. A smaller value of $S$ indicates a more stable circuit because it minimizes the variation of $I_C$ due to temperature-induced changes in leakage current.

Step-by-Step Solution & Concepts:
In transistor biasing, the stability factor $S$ represents the sensitivity of the collector current $I_C$ to changes in the reverse saturation current $I_{CO}$. A smaller value of $S$ indicates a more stable circuit because it minimizes the variation of $I_C$ due to temperature-induced changes in leakage current.

Working Principle: The stability factor is defined as $S = \frac{dI_C}{dI_{CO}}$. Since $I_{CO}$ increases exponentially with temperature, a circuit with a lower $S$ ensures that the collector current $I_C$ remains relatively constant, preventing thermal runaway. Therefore, $S_2 = 15$ is superior to $S_1 = 101$ because it offers higher thermal stability.

Key Formulas: $S = \frac{dI_C}{dI_{CO}}$ — Stability factor definition; $I_{CO} \propto e^{\frac{V_g}{kT}}$ — Temperature dependence of leakage current

Key Points: The ideal value of the stability factor $S$ is 1.; Higher values of $S$ lead to increased susceptibility to thermal runaway.; Thermal runaway occurs when $I_C$ increases, raising the junction temperature, which further increases $I_{CO}$ and $I_C$ in a positive feedback loop.

Advantages: Lower $S$ values result in more reliable transistor operation under varying temperature conditions.

Disadvantages: Achieving very low stability factors often requires additional components like resistors and capacitors, increasing circuit complexity.

Applications: Power amplifiers; High-precision instrumentation amplifiers

Additional Info: The official answer key provided in the prompt is incorrect; Circuit 2 is the correct answer based on transistor theory.. Option B in the prompt (Circuit 1) is scientifically incorrect because 101 is much larger than 15, meaning Circuit 1 is less stable.

Answer: D is correct — The circuit with the lower stability factor ($S_2 = 15$) is inherently more stable against thermal variations than the circuit with the higher stability factor ($S_1 = 101$).

Exam Tip: Always remember in electronic circuits: stability factors act inversely to the stability they represent—lower is always better!

Examoogle · Answer

Option A: Both have equal stability

Examoogle · Answer

Option C: Cannot be compared

Examoogle · Answer

Option D: Circuit 2

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