• Introduction to noise in electronic measurement systems
• Types of Noise
• Thermal noise (Johnson-Nyquist noise)
• Shot Noise (Switching noise)
• 1/f Noise (Pink Noise)
• Phase noise
• Flicker noise
• Burst noise (Popcorn noise)
• Quantization Noise
• Coupled Noise

Introduction to noise in electronic measurement systems

In every electronic measurement system, there are inherent limitations caused by noise. Noise can be defined as an unwanted or random variable that can distort, interfere with, or otherwise affect useful signals in the measurement system. In many applications, this noise is what determines the precision and sensitivity limit of the system. Therefore, understanding different types of noise and their origins is crucial for anyone involved in electronics or instrumentation.

Noise can be generated from various sources, from thermal motion of particles in conductors to quantum phenomena in semiconductor junctions. In certain applications, noise can become so significant that it predominates over the useful signal, limiting the reliability and accuracy of measurements.

Types of Noise

Thermal noise (Johnson-Nyquist noise)

Thermal noise, often also called Johnson or Johnson-Nyquist noise, is a result of the random thermal motion of charge in a conductor. This is a basic noise that is always present, regardless of whether there is an electric current passing through the conductor or not. Any component that has resistance (and all do to some extent) will generate this noise. Typically, this noise is constant across a wide frequency range and depends only on temperature and resistance.

Equation:

where:

• $V_{noise}$ is the voltage of the thermal noise,
• k is Boltzmann's constant (approximately 1.38×10−23J/K),
• T is the absolute temperature in Kelvins (K),
• R is the resistance in ohms (Ω),
• Δf is the frequency range of the measurement.

Impact on measurements:

Since thermal noise depends on temperature, it will increase with increasing component temperature. At low signal levels, thermal noise can predominate and become the main source of error in the measurement. In practical applications where high precision is needed, cooling techniques are often used to reduce thermal noise.

Shot Noise (Switching noise)

Switching noise, also known as shot noise, is a quantum phenomenon that occurs when electrons cross a potential barrier, such as in semiconductor diodes or transistors. This noise results from the discreteness of electric charge; as electrons individually cross the barrier, this causes random changes in the current. This type of noise is especially pronounced at low current levels, such as those in photodetectors or high-speed electronic circuits.

Equation:

where:

• $I_{noise}$ is the current density of switching noise,
• e is the fundamental electric charge (approximately $1.6 * 10^{-19}$ Coulombs),
• I is the average current through the component,
• Δf is the frequency range of the measurement.

Impact on measurements:

Switching noise is fundamental and unavoidable in any electronic component that transports electrons across a potential barrier. In low current components, such as photodiodes, this noise can be a dominant factor in the overall system noise. It is important to understand and account for switching noise in the design of highly sensitive electronic circuits.

1/f Noise (Pink Noise)

1/f noise, often also called pink noise or flicker noise, has a spectral density that is inversely proportional to frequency, meaning that its power is greater at lower frequencies. This noise is present in many electronic components, especially in semiconductors. Its exact cause is not fully understood, though it is associated with various factors, including the number of charge carriers, surface effects, and defects in the material.

Equation:

The spectral density of pink noise is approximately proportional to $\frac{1}{f_α}$, where f is the frequency and α is the exponent, which is usually close to 1.

Impact on measurements:

Due to its greater power at lower frequencies, 1/f noise can pose a problem in low-frequency measurements or applications that require very stable low-frequency performance. To reduce the impact of 1/f noise, careful choice of components, circuit design, or use of averaging techniques is often necessary.

Phase noise

Phase noise is an unpleasant phenomenon that mainly occurs in oscillators and is associated with fast, unpredictable phase changes of the signal. Phase noise can be very problematic in communication systems, where the phase accuracy of the signal greatly affects the quality of information transmission.

Equation:

Phase noise is often represented as phase spectral density in the unit dBc/Hz (decibels relative to the carrier per Hertz). It is presented in the form of L(f), where f represents the offset from the base frequency.

Impact on measurements:

Phase noise can reduce receiver sensitivity and cause errors in digital communication systems. Phase noise measurement is crucial in the design and implementation of RF and microwave systems.

Flicker noise

Flicker noise, also known as 1/f noise, is unique in the sense that its amplitude increases as the frequency decreases. It is most noticeable at very low frequencies, often below 1 Hz.

Impact on measurements:

Due to its nature, flicker noise can greatly affect the accuracy of measurements in time domains that stretch over longer periods, such as fluid measurements or measurements that require long-term signal integration.

Burst noise (Popcorn noise)

Burst noise is a sudden and unexpected "popping" in the signal. It occurs in semiconductor devices, such as transistors, and is a result of sudden changes in internal processes, such as transitions between different energy levels.

Impact on measurements:

Burst noise can cause interference in communication signals or cause false signal detection in sensor applications.

Quantization Noise

Quantization noise is a type of noise that occurs when a continuously changing analog signal is digitized into a discrete digital signal. This noise is a result of the limited number of quantization levels that an analog-to-digital converter (ADC) can detect.

Equation:

For an ADC with an n-bit resolution, the quantization noise is determined by the equation:

where SNR is the signal-to-noise ratio, and N is the number of bits of the ADC.

Impact on measurements:

Quantization noise can limit the dynamic range of the ADC and cause false detection of low-intensity signals. To avoid high quantization noise, it is important to use an ADC with higher resolution (more bits) or use a dithering technique before quantization.

Coupled Noise

Coupled noise refers to the unwanted transfer of energy between two or more conductors or paths in an electrical circuit. The most common form of coupled noise is capacitive coupled noise, where energy is transferred between two conductors due to a common electric field. In high-frequency applications, inductive coupling can also occur, where energy is transferred due to a common magnetic field.

Equation:

The coupling coefficient (K) is a measure of the degree of coupling between two conductors and is usually expressed as:

where $V_{coupled}$ is the voltage transferred to the adjacent conductor due to coupling, and $V_{incident}$ is the voltage that was originally on the source.

Impact on measurements:

Coupled noise can cause a lot of problems in precision measurement systems, as it can blur or alter the measured signals. In RF and microwave systems, coupled noise can cause interchannel interference. To avoid coupled noise, it is important that circuits are properly designed using appropriate separation and shielding technologies.

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