Chapter 18: Electronics (Numerical Problems)

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Chapter Overview & SLOs

What is the fundamental relationship between currents in a junction transistor? The emitter current (I_E) is always the sum of the base current (I_B) and the collector current (I_C), expressed as I_E = I_B + I_C. This is the fundamental current relationship for all bipolar junction transistors (BJTs).

How is transistor current gain (β) defined? Current gain β (beta) is the ratio of the collector current to the base current: β = I_C/I_B. It represents how much the input signal is amplified by the transistor.

What is α (alpha) in transistor terminology? α is defined as the ratio of the change in collector current (ΔI_C) to the change in emitter current (ΔI_E): α = ΔI_C/ΔI_E. α is always less than 1 (typically 0.95-0.99).

What is the relationship between α and β? The relationship between α and β is derived as follows:

• β = α/(1 - α)
• α = β/(β + 1)

Important unit conversions:

• 1 μA (micro-Ampere) = 1 × 10⁻⁶ A
• 1 mA (milli-Ampere) = 1 × 10⁻³ A
• Always convert to Amperes (A) before calculations to avoid decimal errors.

Example 1 - Finding collector current: Given I_E = 5.82 mA, I_B = 120 μA. First convert to Amperes: I_E = 5.82 × 10⁻³ A, I_B = 120 × 10⁻⁶ A = 0.12 × 10⁻³ A. Then I_C = I_E - I_B = 5.82 mA - 0.12 mA = 5.7 mA.

Example 2 - Finding current gain β: Given I_B = 600 μA = 600 × 10⁻⁶ A = 6 × 10⁻⁴ A, I_C = 30 mA = 30 × 10⁻³ A = 3 × 10⁻² A. β = I_C/I_B = (3 × 10⁻²)/(6 × 10⁻⁴) = 50.

Example 3 - Finding α from current changes: Given ΔI_E = 4 mA, ΔI_C = 3.5 mA, α = ΔI_C/ΔI_E = 3.5/4 = 0.875.

Example 4 - Finding β from α: Given α = 0.875, β = α/(1 - α) = 0.875/(1 - 0.875) = 0.875/0.125 = 7.

Summary of formulas:

| Formula | Description | |---------|-------------| | I_E = I_B + I_C | Transistor current relationship | | β = I_C/I_B | DC current gain (beta) | | α = ΔI_C/ΔI_E | AC current gain (alpha) | | β = α/(1 - α) | Alpha to Beta conversion | | α = β/(β + 1) | Beta to Alpha conversion |

These notes are strictly aligned with the Student Learning Outcomes (SLOs) for the FBISE 2026 annual examination.

• How do we calculate the collector current ($I_C$) when emitter and base currents are known? For a transistor with $I_E = 5.82\text{ mA}$ and $I_B = 120\ \mu\text{A}$, the collector current is found by rearranging the formula to $I_C = I_E - I_B$, resulting in $5.7\text{ mA}$.
• How is the current gain ($\beta$) determined from DC values? If a transistor has a base current of $600\ \mu\text{A}$ and a collector current of $30\text{ mA}$, the gain is calculated as $\beta = (30 \times 10^{-3}) / (600 \times 10^{-6}) = 50$.
• How do we find the value of $\alpha$ from current changes? Given a change in emitter current of $4\text{ mA}$ and a change in collector current of $3.5\text{ mA}$, the gain $\alpha$ is $3.5 / 4 = 0.875$.
• How is $\beta$ calculated from the $\alpha$ value? Using the relationship $\beta = \alpha / (1 - \alpha)$, an $\alpha$ of $0.875$ leads to $\beta = 0.875 / (1 - 0.875) = 0.875 / 0.125 = 7$.

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