Calculating Equivalent Resistance Bjt High Resistance Emitter Follower

Calculating the equivalent resistance of a BJT high resistance emitter follower involves understanding the circuit's behavior and applying the appropriate formulas. This guide provides a step-by-step approach to determining the equivalent resistance, including the formula, assumptions, and practical applications.

Introduction

The emitter follower is a fundamental amplifier configuration that provides high input impedance and low output impedance. When the emitter resistor is high, the equivalent resistance calculation becomes more complex and requires careful consideration of the transistor's parameters.

This guide explains how to calculate the equivalent resistance of a BJT high resistance emitter follower, including the formula, assumptions, and practical applications. The interactive calculator on this page simplifies the process by allowing you to input the necessary parameters and obtain the result instantly.

Theory of Emitter Follower

The emitter follower is a common-emitter amplifier with the output taken from the emitter rather than the collector. This configuration provides several advantages:

High input impedance
Low output impedance
Voltage gain close to unity
Good current amplification

When the emitter resistor is high, the equivalent resistance calculation must account for the transistor's current gain (β) and the resistance values in the circuit.

Calculation Method

The equivalent resistance of a BJT high resistance emitter follower can be calculated using the following formula:

R_eq = (R_E * β) / (1 + β)

Where:

R_eq is the equivalent resistance
R_E is the emitter resistor value
β is the current gain of the transistor

This formula accounts for the transistor's current gain and the resistance values in the circuit, providing an accurate calculation of the equivalent resistance.

Note: The current gain (β) is typically provided by the transistor's datasheet. For this calculation, we assume β is known or can be measured.

Worked Example

Let's consider a practical example to illustrate the calculation:

Given:

Emitter resistor (R_E) = 10 kΩ
Current gain (β) = 100

Using the formula:

R_eq = (10 kΩ * 100) / (1 + 100) = 100 kΩ / 101 ≈ 990.1 Ω

The equivalent resistance of the emitter follower circuit is approximately 990.1 Ω.

Applications

The emitter follower configuration is widely used in various electronic circuits, including:

Audio amplifiers
Buffer stages
Voltage followers
Signal level shifters
Impedance matching circuits

Understanding the equivalent resistance calculation is essential for designing and optimizing these circuits.

FAQ

What is the difference between a common-emitter and emitter follower?

The common-emitter amplifier has the output taken from the collector, while the emitter follower has the output taken from the emitter. This configuration provides high input impedance and low output impedance, making it suitable for buffer stages and voltage followers.

How does the emitter resistor value affect the equivalent resistance?

The emitter resistor value (R_E) directly affects the equivalent resistance. A higher emitter resistor value will result in a higher equivalent resistance, as shown in the formula R_eq = (R_E * β) / (1 + β).

What is the significance of the current gain (β) in the calculation?

The current gain (β) is a critical parameter that determines the transistor's ability to amplify current. A higher β value will result in a higher equivalent resistance, as it affects the denominator (1 + β) in the formula.