Low-cost cross-correlation noise setup for measuring the Boltzmann constant and the elementary charge

TL;DR

This paper introduces a low-cost, compact experimental setup using cross-correlation noise measurement to accurately determine the Boltzmann constant and elementary charge, suitable for educational settings.

Contribution

It presents a novel, affordable noise measurement system employing dual-channel sampling and standard components for precise physical constant determination.

Findings

Achieved up to 1% relative accuracy in measuring kB and e.

Reduced background noise significantly through cross-correlation technique.

System is low-cost, robust, and ideal for educational laboratories.

Abstract

We present a low-cost experimental setup to measure the Boltzmann constant (kB) and the elementary charge (e) through thermal and shot noise, achieving relative accuracies of up to 1%. The system utilizes a cost-effective ADC module integrated with a carefully selected low-noise audio operational amplifier, resulting in a simple and compact circuit design that better satisfies experimental requirements. Furthermore, the approach employs a dual-channel sampling method to measure cross-correlation noise, thereby significantly reducing the uncorrelated background noise of the device and improving the signal-to-noise ratio. The noise measurement methodology offers an intuitive demonstration of microscopic fluctuations, making it a valuable teaching tool. In addition, the experimental setup employs standard electronic components, is low cost and robust, making it well-suited for widespread adoption in university and even high school laboratories.