II. Applications of the Josephson Effect

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R. Gross, A. Marx, and F. Deppe © Walther-Meißner-Institut (2001 - 2013) 4.1.3 Operation and Performance of dc-SQUIDs for given S V (f): maximize H and L: 1. bias current: I ¸ I c : largest modulation of hVi(F ext ) 2. flux bias: close to (2n+1) F 0 /4 3. junction critical current: coupling energy E J À k B T simulations show: I c ¸ 5¢I th ´ 5¢2¼k B T/F 0 @ 4.2 K: I c ¸ 1 ¹A 4. loop inductance: should be large but: thermal noise flux (k B TL) 1/2 ¿ F 0 define thermal inductance: L th I th = F 0 /2 simulations: L · 0.2¢L th @ 4.2 K: L · 1 nH define: 5. screening parameter: ¯L = 2I c L/© 0 < 1 no hysteresis in hVi(F ext ) small L, but large area choose ¯L » 1 small I c ≈ 1 ¹A @ 4.2 K L · 1 nH 6. Stewart-McCumber parameter: ¯c < 1 no hysteresis in IVC (external shunt) choose ¯c ' 1 for large voltage output AS-Chap. 4 - 20
R. Gross, A. Marx, and F. Deppe © Walther-Meißner-Institut (2001 - 2013) 4.1.3 Operation and Performance of dc-SQUIDs AS-Chap. 4 - 21 • detailed numerical simulations: ²(f) minimum for ¯L » 1, ¯c ' 1 at (2n+1)F 0 /4, at max. voltage modulation (≈I c R N ) then: • small signal analysis in white noise regime (@ optimal point): T, C J c , ! p
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II. Applications of the Josephson Effect

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