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

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.