Johnson Noise Explained

Johnson noise, often referred to as thermal noise, is a fundamental type of random electrical noise found in electronic circuits. It originates from the thermal agitation of charge carriers, primarily free electrons, within a conductive medium.

At any temperature above absolute zero ($T$ = $0$ K), electrons within a conductor possess kinetic energy due to heat. This energy causes them to move randomly in various directions. While current flow involves a net movement of electrons (drift velocity), the underlying thermal motion persists, leading to constant, small fluctuations in the electron density. These fluctuations generate random variations in voltage and current across the conductor.

The intensity of Johnson noise is directly influenced by several factors:

• Temperature ($T$): Higher temperatures increase the thermal energy of electrons, resulting in more vigorous random motion and thus higher noise levels.
• Resistance ($R$): Conductors with higher resistance exhibit greater Johnson noise.
• Bandwidth ($\Delta f$): The noise power is proportional to the range of frequencies considered (bandwidth).

The mean square noise voltage ($ \overline{v_n^2} $) across a resistor $R$ at absolute temperature $T$ within a bandwidth $\Delta f$ is given by the formula:

$ \overline{v_n^2} = 4 k R T \Delta f $

where $ k $ is the Boltzmann constant ($ \approx 1.38 \times 10^{-23} \, \text{J/K} $).

Understanding the Correct Option

Option 1 accurately defines Johnson noise: it is caused by thermal agitation of free electrons carrying current, which inherently leads to random fluctuations, or modulation, of the current. This aligns perfectly with the physical origin of thermal noise in conductors.

Differentiating Other Noise Types

Let's look at why the other options describe different phenomena:

• Option 2: Noise carried into a circuit through conductors
  This describes conducted noise or interference, which is typically external noise picked up by wires or transmission lines, rather than noise generated intrinsically within a component due to temperature.
• Option 3: Noise of an electromagnetic origin radiated into a circuit
  This refers to electromagnetic interference (EMI) or crosstalk. It originates from external sources like radio transmitters, electrical machinery, or switching circuits and is picked up by the circuit via electromagnetic fields. It is distinct from the internal thermal generation mechanism of Johnson noise.
• Option 4: Shot noise which results from emission of electrons across a pn junction
  This describes shot noise. Shot noise occurs due to the discrete nature of charge carriers (electrons and holes) crossing a potential barrier, such as in diodes or transistors. It arises from the random arrival times of these carriers, not from their thermal agitation within a resistive material.