Voltage-flux-characteristics of asymmetric dc SQUIDs

We present a detailed analysis of voltage-flux V(/spl Phi/)-characteristics for asymmetric dc SQUIDs with various kinds of asymmetries. For finite asymmetry /spl alpha//sub I/ in the critical currents of the two Josephson junctions, the minima in the V(/spl Phi/)-characteristics for bias currents of opposite polarity are shifted along the flux axis by /spl Delta//spl Phi/=/spl alpha//sub I//spl beta//sub L/ relative to each other; /spl beta//sub L/ is the screening parameter. This simple relation allows the determination of /spl alpha//sub I/ in our experiments on YBa/sub 2/Cu/sub 3/O/sub 7-/spl delta// dc SQUIDs and comparison with theory. Extensive numerical simulations within a wide range of /spl beta//sub L/ and noise parameter /spl Gamma/ reveal a systematic dependence of the transfer function V/sub /spl Phi// on /spl alpha//sub I/ and /spl alpha//sub R/ (junction resistance asymmetry). As for the symmetric dc SQUID, V/sub /spl Phi// factorizes into g(/spl Gamma//spl beta//sub L/)/spl middot/f(/spl alpha//sub I/,/spl beta//sub L/), where now f also depends on /spl alpha//sub I/. For /spl beta//sub L//spl lsim/5 we find mostly a decrease of V/sub /spl Phi// with increasing /spl alpha//sub I/, which however can only partially account for the frequently observed discrepancy in V/sub /spl Phi// between theory and experiment for high-T/sub c/ dc SQUIDs.