Math Problem Statement

Consider a BJT with an emitter injection efficiency of 0.9995 and a DC current gain (β) of 50. Calculate the base transport factor

0.99

0.98

0.95

1.01

Solution

The base transport factor (αT\alpha_T) in a Bipolar Junction Transistor (BJT) relates to how well the injected carriers are transported across the base without recombining. It is defined by the following relationship:

αT=ββ+1×Emitter Injection Efficiency(γ)\alpha_T = \frac{\beta}{\beta + 1} \times \text{Emitter Injection Efficiency} (\gamma)

Given:

  • β=50\beta = 50
  • Emitter Injection Efficiency (γ\gamma) = 0.9995

First, we calculate the transport factor:

αT=5050+1×0.9995=5051×0.9995\alpha_T = \frac{50}{50 + 1} \times 0.9995 = \frac{50}{51} \times 0.9995

Let's compute this value.

αT0.9804\alpha_T \approx 0.9804

Thus, the base transport factor is approximately 0.98.

Final answer: 0.98


Would you like more details or have any questions?

Here are 5 related questions to further explore the topic:

  1. How does the base width affect the base transport factor?
  2. What is the physical significance of emitter injection efficiency in a BJT?
  3. How does the base transport factor impact the overall performance of a BJT?
  4. How is the current gain β\beta related to the base transport factor and emitter injection efficiency?
  5. What are typical values of emitter injection efficiency in high-performance BJTs?

Tip: In high-gain BJTs, reducing base recombination helps improve both current gain and the base transport factor.

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Math Problem Analysis

Mathematical Concepts

Electronics
Semiconductor Physics
Bipolar Junction Transistors (BJT)

Formulas

Base Transport Factor (α_T) = (β / (β + 1)) * Emitter Injection Efficiency (γ)

Theorems

BJT Current Gain Theorem
Emitter Injection Efficiency Theorem

Suitable Grade Level

Undergraduate (Electronics/Physics)