Step 1: Understanding Leakage Current in BJTs:
Leakage current in a Bipolar Junction Transistor (BJT) is a small, temperature-sensitive current that flows when the transistor is ideally in the "off" state. Leakage current is defined differently based on the transistor's configuration:
\( I_{CEO} \): Collector-to-Emitter leakage current with an open base (Common Emitter configuration).
\( I_{CBO} \): Collector-to-Base leakage current with an open emitter (Common Base configuration).
These leakage currents are interconnected via the transistor's current gain parameters.
Step 2: Formula for Leakage Current Relationship:
The relationship between common emitter leakage current (\( I_{CEO} \)) and common base leakage current (\( I_{CBO} \)) is:
\[ I_{CEO} = (\beta + 1) I_{CBO} \]
Here, \(\beta\) represents the common emitter DC current gain. We are given \( I_{CEO} \) and \(\beta\) to determine \( I_{CBO} \).
Step 3: Calculation Process:
1. Given values:
Common emitter leakage current, \( I_{CEO} = 300 \, \mu A \).
Common emitter current gain, \( \beta = 130 \).
2. Rearrange the formula for \( I_{CBO} \):
\[ I_{CBO} = \frac{I_{CEO}}{\beta + 1} \]
3. Substitute and compute:
\[ I_{CBO} = \frac{300 \, \mu A}{130 + 1} \]
\[ I_{CBO} = \frac{300}{131} \, \mu A \]
\[ I_{CBO} \approx 2.290 \, \mu A \]
Step 4: Concluding Result:
The calculated common base leakage current is approximately 2.29 \(\mu\)A. The closest option is 2.28 \(\mu\)A.