Collector Current In Active Region When Transistor Acts As Amplifier Calculator

Formula Used:

\[ i_c = i_s \times e^{\frac{V_{be}}{V_t}} \]

Saturation Current (i_s):

Voltage across Base Emitter Junction (V_be):

Threshold Voltage (V_t):

Collector Current (i_c):

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1. What is the Collector Current Formula?

The collector current formula \( i_c = i_s \times e^{\frac{V_{be}}{V_t}} \) describes the relationship between collector current and base-emitter voltage in a bipolar junction transistor operating in the active region. This exponential relationship is fundamental to transistor amplifier operation.

2. How Does the Calculator Work?

The calculator uses the collector current formula:

\[ i_c = i_s \times e^{\frac{V_{be}}{V_t}} \]

Where:

\( i_c \) — Collector Current (A)
\( i_s \) — Saturation Current (A)
\( V_{be} \) — Voltage across Base Emitter Junction (V)
\( V_t \) — Threshold Voltage (V)
\( e \) — Napier's constant (approximately 2.71828)

Explanation: The formula shows that collector current increases exponentially with base-emitter voltage, with the saturation current and thermal voltage determining the scale and slope of this relationship.

3. Importance of Collector Current Calculation

Details: Accurate calculation of collector current is essential for designing transistor amplifier circuits, determining operating points, analyzing gain characteristics, and ensuring proper biasing for linear operation.

4. Using the Calculator

Tips: Enter saturation current in amperes, base-emitter voltage in volts, and threshold voltage in volts. All values must be positive and non-zero for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is saturation current (i_s)?
A: Saturation current is the reverse leakage current of the base-emitter junction when the transistor is in cutoff mode. It's typically very small (nanoamperes to picoamperes range).

Q2: What is threshold voltage (V_t)?
A: Threshold voltage, also known as thermal voltage, is approximately 25-26 mV at room temperature and is given by \( V_t = \frac{kT}{q} \), where k is Boltzmann's constant, T is temperature in Kelvin, and q is electron charge.

Q3: When is this formula applicable?
A: This formula applies when the transistor is operating in the active region, where the base-emitter junction is forward biased and the base-collector junction is reverse biased.

Q4: What are typical values for these parameters?
A: Saturation current typically ranges from 10^-12 to 10^-15 A, base-emitter voltage is usually 0.6-0.7V for silicon transistors, and thermal voltage is about 25mV at room temperature.

Q5: How does temperature affect the calculation?
A: Temperature affects both saturation current and thermal voltage. Saturation current doubles approximately every 10°C, while thermal voltage increases linearly with temperature.