Why Are Things the Way They Are? by G. Venkataraman
By G. Venkataraman
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1. JOSEPHSON WEAK-LINK DEVICES 27 FIG. 11a. Complex response of the rf voltage Vi in Fig. 10 for ß < 1 and a variable applied field Φχ°. junction conductance and capacitance. Without going through the details of the derivation, the voltage across the resonant circuit at the fundamental frequency, correct to the first order in Lic/Φο, is M Vx = |Z|/isin(co< - δ) + 2 — ic\Z\Jx L\ X [2τ/L\l/2\Z\hl k y . / Λ 4-JcoB*«n(--2·--) (51) where Ζ(ίω) = ( 1 / Ä L + ùàCx + lAcoLx)-1 = \Z\eiS (52) and h is the amplitude of the rf bias current at ω.
20), or with no rf bias, the Josephson coupling energy averaged over an rf cycle varies as cos 0O, and so acts as a constraint to reduce the amplitude of the phase fluctuations. If β » 1 and the size of the loop is such that kBT « |Φο2/£> for J o (0i) = 0, 0o will be constrained to the neighborhood of zero or π. On the other hand, with zero bias, 0O will be constrained to the neighborhood of zero if kBT « Φ 0 4/2π. The latter case, which was discussed in detail by Burgess (1967), is analogous to a particle trapped in a minimum of a periodic potential, where thermal energy is less than the height of the barriers between minima.
Operation of practical oscillators The output, at radio frequencies, of a resistive loop oscillator can be detected with the circuit shown in Fig. 15. This is the same as Fig. 10, with 1. 37 JOSEPHSON WEAK-LINK DEVICES the omission of the rf bias and the addition of a constant bias current J0 through the resistance R. If a « 1, that is, if the detector frequency ω0 is much greater than 27τ4Α/Φο, and also if β > 1, then the current oscillation in the loop is essentially a sawtooth in time (Fig. 16) accompanied by voltage pulses of area somewhat less than Φ0 across the link.