On the synthesis of quantum Hall array resistance standards

Quantum Hall effect (QHE) is the basis of modern resistance metrology. In quantum Hall array resistance standards (QHARS), several individual QHE elements, each one with the same QHE resistance (typically half of the von Klitzing constant), are arranged in networks that realize resistance values close to decadic values (such as 1 k Omega or 100 k Omega), of direct interest for dissemination. The same decadic value can be approximated with different grades of precision, and even for the same approximation several networks of QHE elements can be conceived. This paper investigates the design of QHARS networks by giving methods to find a proper approximation of the resistance of interest, and to design the corresponding network with a small number of elements; results for several decadic case examples are given. The realization of these networks with multiterminal QHE elements requires a new multiple bridge connection, here described.