Skip to main content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.


The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Flat Frequency Response in the Electronic Measurement of the Boltzmann Constant



Jifeng Qu, Horst Rogalla, Yang Fu, Jianqiang Zhang, Alessio Pollarolo, Samuel P. Benz


A new quantum voltage calibrated Johnson noise thermometer (JNT) was developed at NIM to demonstrate the electrical approach that determines the Boltzmann constant k by comparing electrical and thermal noise power. A measurement with an integration period of 19 hours and bandwidth of 638 kHz results in a relative offset of 1x10-6 from the current CODATA value of k, and type A relative standard uncertainty of 17x10-6. Closely matched noise powers and transmission-line impedances were achieved and resulted in a flat frequency dependence of the noise power ratio. Consequently, the quadratic fitting parameters of the ratio spectrum show flat frequency responses with respect to the measurement bandwidth. This flat response produces a dramatically reduced systematic error compared to that of the NIST measurement of k, in which the relative combined uncertainty was dominated by this error.
IEEE Transactions on Instrumentation and Measurement


Boltzmann constant, Correlation, Johnson Noise, Josephson junction arrays, Noise, Quantization, Thermometry
Created June 1, 2013, Updated November 10, 2018