Phase Tree: A Periodic, Fractional Flux Quantum Vernier for High-speed Interpolation of Analog-to-Digital Converters

A novel Josephson junction circuit is proposed which can rapidly track and record a magnetic flux signal to a small binary fraction of the flux quantum. This so-called "phase tree" circuit behaves periodically, recording the residue of the signal modulo the flux quantum in 2(p)ths of a flux quantum for a p-level binary tree. Signal quantization is accomplished by comparators which read the 2(p-1) circulating currents in the leaf-level branches, providing a total of 2(p) possibilities in the periodic code. The phase tree can therefore he used as a vernier, linear over a large number of periods because a single analog element determines the quantization levels once the network is properly biased. A system consisting of a conventional m-bit analog-to-digital converter (m approximate to 4- 7) and an auxiliary p-bit phase tree interpolator (p approximate to 2-5) can achieve at least (m + p - 1) bits without loss of bandwidth or sample rate.