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**

what Johnson noise and Shot noise are

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

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).

Anonymousover 1 year ago · Public