Phase tree: a periodic, fractional flux quantum vernier forhigh-speed interpolation of analog-to-digital converters

A Josephson junction circuit that can rapidly track and record a magnetic flux signal to a small binary fraction of the flux quantum is proposed. 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 that 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 be 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 (ADC m≈4-7) and an auxiliary p-bit phase tree interpolator (p≈2-5) can achieve at least m+p -1 bits without loss of bandwidth or sample rate