Resistance Standards Based on Fractal-Like Star-Mesh Transformations
Paper Authors: Dean G. Jarrett, Albert F. Rigosi
Presenter: Albert Rigosi
National Institute of Standards and Technology
Gaithersburg, MD 20899
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 (QHARS). Using fractal-like, or recursive, features
of the framework allow 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. This element count
is several orders of magnitude smaller than what would be required in an array with elements
exclusively in series.
These measurements seek to validate the mathematical framework one may use for minimizing the
resistor values needed in a recursive star-mesh design to achieve a particular high-valued
resistance. Reported here are calibration results of high resistance standards of 100 MΩ, 1 GΩ and
10 GΩ using a recursive star-mesh QHARS. Ultimately, the validation of this framework is important
for highlighting the untapped potential of more complex resistance networks for use in metrology.
Keywords: dual source bridge; star-mesh transformation; quantum Hall eect; wye delta
transformation; resistance standards
Target audience: Anyone with a background in physics, mathematics, or electrical engineering
Learning objectives:
1. To understand the core concept of a mathematical framework for optimizing resistor networks to
achieve high resistance values.
2. To identify the potential benefits of using fractal-like or recursive features in resistor network
design for achieving high resistances with lower-valued components.
3. To recognize the potential of this framework for reducing the number of quantum Hall elements
needed in quantum Hall array resistance standards (QHARS) to achieve high resistances compared
to traditional series arrays.
4. To learn the significance of validating this mathematical framework for advancing metrology,
particularly in exploring more complex resistance networks.
