Calculate Voltage Gain for Follower

Voltage gain is a fundamental concept in electronics that measures how much an amplifier increases the amplitude of an input signal. For follower circuits, which are a type of amplifier, calculating voltage gain helps engineers understand signal amplification characteristics. This guide explains how to calculate voltage gain for follower circuits, including the formula, assumptions, and practical applications.

What is Voltage Gain?

Voltage gain (A_v) is a dimensionless ratio that compares the output voltage (V_out) of an amplifier to its input voltage (V_in). It's calculated as:

A_v = V_out / V_in

Voltage gain measures how much an amplifier increases the amplitude of a signal. A gain of 1 means the output equals the input, while gains greater than 1 indicate amplification. Follower circuits typically have a voltage gain close to 1 because they're designed to maintain signal levels while providing other benefits like impedance matching.

Follower Circuit Basics

Follower circuits are a type of amplifier configuration that provides several advantages over other amplifier types:

High input impedance (minimal current draw from the source)
Low output impedance (good for driving loads)
Voltage gain close to 1 (minimal signal distortion)
Phase inversion (output is 180° out of phase with input)

The most common follower circuit is the emitter follower (for bipolar junction transistors) or the source follower (for field-effect transistors). These circuits are widely used in audio amplifiers, signal buffers, and impedance matching applications.

Calculating Voltage Gain

For follower circuits, voltage gain can be calculated using the following formula:

A_v = R_L / (R_L + R_in)

Where:

R_L = Load resistance
R_in = Input resistance of the follower circuit

This formula assumes the follower circuit is ideal (no current flows into the input) and that the load resistance is much larger than the input resistance. In practical circuits, you may need to account for additional factors like transistor parameters and bias conditions.

For emitter followers, R_in is typically the parallel combination of the transistor's β (current gain) times R_E and R_B.

Example Calculation

Let's calculate the voltage gain for a follower circuit with:

Load resistance (R_L) = 10 kΩ
Input resistance (R_in) = 1 kΩ

Using the formula:

A_v = 10 kΩ / (10 kΩ + 1 kΩ) = 10 / 11 ≈ 0.909

This means the circuit amplifies the input signal by approximately 0.909, or 90.9% of the input voltage. The slight reduction from 1 is due to the finite input resistance of the follower circuit.

FAQ

What is the difference between voltage gain and current gain?: Voltage gain measures how much an amplifier changes the amplitude of a signal, while current gain measures how much it changes the current. Follower circuits typically have voltage gain close to 1 and current gain greater than 1.
Why do follower circuits have voltage gain less than 1?: Follower circuits have finite input resistance, which causes some voltage division between the input resistance and the load resistance, resulting in voltage gain slightly less than 1.
What are the practical applications of follower circuits?: Follower circuits are used as signal buffers, impedance matching circuits, and in audio amplifiers where maintaining signal levels is important.
How does temperature affect voltage gain in follower circuits?: Temperature can affect transistor parameters like β, which can slightly change the input resistance and thus the voltage gain. For precise applications, temperature compensation may be needed.