Theory of a UHF pumped double SQUID

A theoretical analytical analysis is presented which describes the behavior of a UHF pumped double SQUID (a traditional UHF SQUID in which a DC SQUID is used instead of the weak link) for the bias frequency omega(B) much greater than omega(c)/[2(gamma + 1/4)] max(beta, 1), where beta is the hysteresis parameter, omega(c) is the cutoff frequency, and gamma is the ratio ofinductances of the UHF and DC loops. The output signal, transfer function and noise characteristics are computed and the system is optimized from these points of view. Thus, this, in particular, is believed to be the first comprehensive and thorough analytical investigation of a UHF pumped SQUID having an arbitrary value for the hysteresis parameter beta and operating al the now-typical frequency of omega(B) approximate to omega(c) or omega(B) approximate to beta omega(c) (to my knowledge there is no such an approach for a traditional one-junction system nor for a double two-junction SQUID).