Constructing 100 MΩ and 1 GΩ Resistance Standards via Star-Mesh Transformations
arxiv(2024)
摘要
A recent mathematical framework for optimizing resistor networks to achieve
values in the MΩ through GΩ levels was employed for two specific
cases. Objectives here include proof of concept and identification of possible
apparatus limitations for future experiments involving graphene-based quantum
Hall array resistance standards. Using fractal-like, or recursive, features of
the framework allows one to calculate and implement network designs with
substantially lower-valued resistors. The cases of 100 MΩ and 1
GΩ demonstrate that, theoretically, one would not need more than 100
quantum Hall elements to achieve these high resistances.
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