Noise Fundamentals by Teachspin

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Noise Fundamentals

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Introduction

noise

Detect and quantify Johnson noise, the ‘Brownian motion’ of electrons
Deduce Boltzmann’s constant, k_B, from the temperature dependence of Johnson Noise
Observe and quantify shot noise in order to measure the fundamental charge ‘e’
Configure front-end low-level electronics for a variety of measurements
Investigate ‘power spectral density’ and ‘voltage noise density’ of signals, and their V²/Hz and V/√Hz units
Apply Fourier methods to digitally process noise signals into noise densities
Explore amplification, filtering-in-frequency, squaring, and averaging-in-time
Develop skills applicable across the breadth of measurement science

TeachSpin's Noise Fundamentals is a set of tools for teaching and learning about electronic noise. The noise present in all electronic signals limits the sensitivity of many measurements. That, in itself, would be reason enough to motivate learning how noise can be quantified. But electronic noise can be much more than a nuisance, or a limit -- in the famous phrase of Landauer, sometimes ‘noise is the signal’. In fact, there are at least two cases in which the measurement of noise can give the values of fundamental constants.

By concentrating on the processing and measurement of Johnson noise and shot noise, TeachSpin’s Noise Fundamentals allows students to determine both Boltzmann’s constant, k_B, and the magnitude of the charge on the electron, ‘e’.

Johnson noise is the fluctuating emf which arises spontaneously in any resistor at absolute temperature T > 0. Nyquist’s prediction is that the mean square of this emf obeys < V²(t) > = 4 k_B T R Df, where Df is the bandwidth over which noise is measured. This result allows Boltzmann’s constant k_B to be measured.

Shot noise is a measure of the fluctuations observed in certain currents, due to the granularity imposed on them by the quantization of charge. In this case, Schott’s prediction is that a dc current i_dc will be accompanied by fluctuations obeying another mean-square relation, < [δi(t)]²> = 2e i_dc Df. This result allows the magnitude of the fundamental charge e to be measured.

Noise from either of these sources, and many more, can be observed because of the modular, and user-configurable, arrangement of our electronics. The transparent signal-flow layout of our apparatus makes it very clear how noise is quantified in practice, since the processes of amplification, filtering-in-frequency, squaring, and averaging-in-time can be understood separately and in detail. The result is a method for quantifying noise, and noise densities, that students can actually understand. This generates a portable set of skills applicable across the breadth of measurement science.

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