# Johnson and Shot Noise. First Draft

Abstract

Two sources of noise, Johnson noise and shot noise, are investigated in this experiment. The Johnson noise which is the voltage fluctuations across a resistor that arose from the random motion of electrons. It was measured across different resistances and at different bandwidths at room temperature, resulting in a calculation of the Boltzmann constant of $$1.46 \cdot 10^{-23} \textrm{ m}^2 \textrm{ kg} \textrm{ s}^{-2} \textrm{ K}^{-1} \pm2.5 \cdot 10^{-21} \textrm{ m}^2 \textrm{ kg} \textrm{ s}^{-2} \textrm{ K}^{-1}$$ and $$1.46 \cdot 10^{-23} \textrm{ m}^2 \textrm{ kg} \textrm{ s}^{-2} \textrm{ K}^{-1} \pm2.6 \cdot 10^{-21} \textrm{ m}^2 \textrm{ kg} \textrm{ s}^{-2} \textrm{ K}^{-1}$$. The shot noise occurs due to the quantization of charge, and was measured by varying current in the system, with which we calculated the electron charge of $$1.64 \cdot 10^{-19} \pm 7.0 \cdot 10^{ -22}$$. They agree quite well with the accepted values of $$1.38064852 \cdot 10^{-23} \textrm{ m}^2 \textrm{ kg} \textrm{ s}^{-2} \textrm{ K}^{-1}$$, and $$1.64 \cdot 10^{-19} \textrm{C}$$ for the Boltzmann constant and electron charge respectively. Errors are discussed.

Please compare your description of Johnson Noise and Shot Noise below in your Aims and Introduction Sections with the short description I provided you in the getting started instructions for this lab (reprinted below):

By measuring Johnson noise — the fluctuating voltage that arises due to the random walk motion of electrons in a resistor (even when current isn’t flowing through it) —- as a function of temperature and frequency “bandwidth”, we can determine Boltzmann’s constant $$k_B$$, the fundamental constant connecting temperature $$T$$ to energy $$k_B T$$.

By measuring Shot noise — the fluctuations in a measured current of electrons due to quantization of charge — we can determine the fundamental unit of charge $$e$$ (the charge on an electron).

Who would have thought you could discover fundamental physics from simple “noise?” That’s pretty neat!

Notice how this version tries to provide a description of

1. what Johnson noise and Shot noise are

2. what we need to measure (and as a function of what variables)

3. and what we aim to determine from the measurement (for example, values for fundamental constants of physics $$k_B$$ and $$e$$)

.

Do you think your classmates in PHY350 would understand these three points from your paper, as written? If not, you need to rewrite your paper in a way that they can.

Do you understand these 3 points yourself? If not, your responsibility is to review the physics — I recommend reviewing the introductions to sections 1 and 3 of your teachspin manual! — and make sure you do! Then, rewrite the paper to make it clear you understand what you were doing (and why).