Optimization of dc SQUID voltmeter and magnetometer circuits

Abstract

We calculate the signal-to-noise ratio in a dc SQUID system as a function of source impedance, taking into account the effects of current and voltage noise sources in the SQUID. The optimization of both tuned and untuned voltmeters and magnetometers is discussed and typical sensitivities are predicted using calculated noise spectra. The calculations are based on an ideal symmetric dc SQUID with % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaacqaHYoGycqGH9a% qpcaaIYaacbaGaa8htaiaa-LeadaWgaaWcbaacbiGaa4hmaaqabaGc% caGGVaGaeuOPdy0aaSbaaSqaaiaa+bdaaeqaaOGaeyypa0JaaGymaa% aa!3D23!\[\beta = 2LI_0 /\Phi _0 = 1\] and moderate noise rounding % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4baFfea0dXde9vqpa0lb9% cq0dXdb9IqFHe9FjuP0-iq0dXdbba9pe0lb9hs0dXda91qaq-xfr-x% fj-hmeGabaqaciGacaGaaeqabaWaaeaaeaaakeaaiiGacqWFOaakcq% WFtoWrcqWF9aqpcqWFYaGmcqaHapaCcaWGRbWaaSbaaSqaaiaadkea% aeqaaGqaaOGaa4hvaiaac+cacaGFjbWaaSbaaSqaaerbbjxAHXgaiu% GacaqFWaaabeaakiab-z6agnaaBaaaleaacaqGGaacbiGaaWhmaaqa% baGccqGH9aqpcaaIWaGaaiOlaiaaicdacaaI1aGaaiykaaaa!471A!\[(\Gamma = 2\pi k_B T/I_0 \Phi _{{\rm{ }}0} = 0.05)\], where Φ0 is the flux quantum, T is the temperature, L is the SQUID inductance, and I 0 is the critical current of each junction. The optimum noise temperatures of tuned and untuned voltmeters are found to be 2.8(ΩL/R)T and 8(ΩL/R)T (1 + 1.5α2 + 0.7α4)1/2/α2 respectively, where Ω/2π is the signal frequency, assumed to be much less than the Josephson frequency, and α is the coupling coefficient between the SQUID and its input coil. It is found that tuned and untuned magnetometers can be characterized by optimum effective signal energies given by (16k B TLE/α2 R)[1 + (1 + 1.5α2 + 0.7α2)1/2 + 0.75α2] and 2kB T iRiB/Ω2 L p respectively, where B is the bandwidth, R i is the resistance representing the losses in the tuned circuit at temperature T i and L p is the inductance of the pickup coil.