BJT Beta Calculation from Alpha

This guide explains how to determine the current gain, beta ($\beta$), for a Bipolar Junction Transistor (BJT) in a common emitter configuration, using the provided alpha ($\alpha$) value.

Alpha and Beta ($\alpha$, $\beta$) Parameters

In BJT theory, alpha ($\alpha$) represents the common-base current gain, which is the ratio of collector current change to emitter current change ($\alpha = \Delta I_C / \Delta I_E$). Beta ($\beta$) signifies the common-emitter current gain, the ratio of collector current change to base current change ($\beta = \Delta I_C / \Delta I_B$). Both are critical parameters for analyzing transistor behavior.

Formula for Beta Calculation

A direct relationship exists between $\alpha$ and $\beta$. The formula used to calculate $\beta$ when $\alpha$ is known is:

\beta = \frac{\alpha}{1 - \alpha}

Understanding this formula is key for converting between these two common measures of transistor gain.

Given Alpha Value

The question provides the following value for alpha:

• $\alpha = 0.995$

Beta Calculation Steps

Follow these steps to calculate beta ($\beta$):

1. Use the formula:

   \beta = \frac{\alpha}{1 - \alpha}

2. Substitute the value of $\alpha$:

   \beta = \frac{0.995}{1 - 0.995}

3. Calculate the denominator:

   1 - 0.995 = 0.005

4. Perform the division:

   \beta = \frac{0.995}{0.005}

5. Simplify and find $\beta$:

   \beta = 199

Final Beta Value

The calculation shows that the beta ($\beta$) value for the BJT is 199. This matches the first option provided in the question.