Preface ix Acknowledgments xi 1 Introduction 1 1.1 Motivation 1 1.2 Contents of the Chapters 3 References 8 2 Josephson Junctions 9 2.1 Josephson Equations 9 2.2 RCSJ Model 9 References 13 3 dcSQUID''s I - V Characteristics and Its Bias Modes 15 3.1 SQUID''s I-V Characteristics 15 3.2 An Ideal Current Source 19 3.3 A Practical Voltage Source 19 References 21 4 Functions of the SQUID''s Readout Electronics 23 4.

1 Selection of the SQUID''s Bias Mode 23 4.2 Flux Locked Loop (FLL) 23 4.2.1 Principle of the FLL 24 4.2.2 Electronic Circuit of the FLL and the Selection of the Working Point 25 4.2.3 "Locked" and "Unlocked" Cases in the FLL 28 4.

2.4 Slew Rate of the SQUID System 29 4.3 Suppressing the Noise Contribution from the Preamplifier 29 4.4 Two Models of a dc SQUID 29 References 31 5 Direct Readout Scheme (DRS) 33 5.1 Introduction 33 5.2 Readout Electronics Noise in DRS 33 5.2.1 Noise Characteristics of Two Types of Preamplifiers 34 5.

2.2 Noise Contribution of a Preamplifier with Different Source Resistors 37 5.3 Chain Rule and Flux Noise Contribution of a Preamplifier 39 5.3.1 Test Circuit Using the Same Preamplifier in Both Bias Modes 40 5.3.2 Noise Measurements in Both Bias Modes 42 5.4 Summary of the DRS 43 References 43 6 SQUID Magnetometric Systemand SQUID Parameters 45 6.

1 Field-to-Flux Transformer Circuit (Converter) 45 6.2 Three Dimensionless Characteristic Parameters, ? c, Γ, and ? L, in SQUID Operation 48 6.2.1 SQUID''s Nominal Stewart-McCumber Characteristic Parameter ? c 49 6.2.2 SQUID''s NominalThermal Noise Parameter Γ 52 6.2.3 SQUID''s Screening Parameter ? L 54 6.

2.4 Discussion on theThree Characteristic Parameters 55 References 56 7 Flux Modulation Scheme (FMS) 61 7.1 Mixed Bias Modes 61 7.2 Conventional Explanation for the FMS 63 7.2.1 Schematic Diagram of the FMS 63 7.2.2 Time Domain and Flux Domain 65 7.

2.3 Flux Modulation 66 7.2.4 Five Additional Notes 71 7.3 FMS Revisited 73 7.3.1 Bias Mode in FMS 74 7.3.

2 Basic Consideration of Synchronous Measurements of I s and V s 74 7.3.3 Experimental Synchronous Measurements of Δ i and VR s 75 7.3.4 Transfer Characteristics of the Step-Up Transformer 78 7.3.5 V (Φ) Comparison Obtained by DRS and FMS 80 7.4 Conclusion 81 References 82 8 Flux Feedback Concepts and Parallel Feedback Circuit 85 8.

1 Flux Feedback Concepts and History 85 8.2 SQUID''s Apparent Parameters 87 8.3 Parallel Feedback Circuit (PFC) 89 8.3.1 Working Principle of the PFC in Current Bias Mode 89 8.3.2 Working Principle of PFC in Voltage Bias Mode 94 8.3.

3 Brief Summary of Qualitative Analyses of PFC 97 8.4 Quantitative Analyses and Experimental Verification of the PFC in Voltage Bias Mode 99 8.4.1 The Equivalent Circuit with the PFC in Voltage Bias Mode 99 8.4.2 Introduction of Two Dimensionless Parameters r and Δ 101 8.4.3 Numerical Calculations 103 8.

4.4 Experimental Results 108 8.4.5 Noise Comparison and Interpretation 111 8.4.6 Two Practical Designs for PFC 114 8.5 Main Achievements of PFC Quantitative Analysis 116 8.6 Comparison with the Noise Behaviors of Two Preamplifiers 117 References 119 9 Analyses of the "Series Feedback Coil (Circuit)" (SFC) 121 9.

1 SFC in Current Bias Mode 121 9.1.1 Working Principle of the SFC in Current Bias Mode 121 9.1.2 Noise Measurements of a Weakly Damped SQUID (Magnetometer) System with the SFC 123 9.2 The SFC in Voltage Bias Mode 125 9.3 Summary of the PFC and SFC 127 9.4 Combination of the PFC and SFC (PSFC) 129 9.

4.1 PSFC Analysis Under Independence Conditions 129 9.4.2 PSFC Experiments and Results 132 9.4.3 Conclusion of the PSFC 136 References 137 10 Weakly Damped SQUID 139 10.1 Basic Consideration of Weakly Damped SQUID 139 10.2 SQUID System Noise Measurements with Different ? c Values 140 10.

3 Statistics of SQUID Properties 143 10.4 Single Chip Readout Electronics (SCRE) 147 10.4.1 Principle of SCRE and Its Performance 148 10.4.2 Equivalent Circuit of SCRE 149 10.4.3 Differences Between the Conventional Version of Readout Electronics with an Integrator and SCRE 152 10.

4.4 Two Applications of SCRE 153 10.5 Suggestions for the DRS 154 References 155 11 Two-Stage and Double Relaxation Oscillation Readout Schemes 157 11.1 Two-Stage Scheme 158 11.2 ROS and D-ROS 164 11.3 Some Comments on D-ROS and Two-Stage Scheme 168 References 169 12 Radio-Frequency (rf) SQUID 171 12.1 Fundamentals of an rf SQUID 171 12.2 Conventional rf SQUID System 176 12.

2.1 Block Diagram of rf SQUID Readout Electronics (the 30MHz Version) 176 12.2.2 rf SQUID System Noise in the 30 MHz Version 178 12.3 Introduction to Modern rf SQUID Systems 180 12.3.1 Magnetometric Thin-Film rf SQUID and a Conventional Tank Circuit with a Capacitor Tap 181 12.3.

2 Improved rf SQUID Readout Electronics 184 12.3.3 Tank Circuit Operating Up to 1 GHz with Inductive Coupling 188 12.3.4 Modern rf SQUID System 190 12.3.4.1 Microstrip Resonator 190 12.

3.4.2 Coplanar Resonator 192 12.3.4.3 Instability of rf Bias Current 194 12.3.5 Substrate Resonator 196 12.

3.6 Regarding the rf SQUID''sThermal Noise Limit 200 12.4 Further Developments of the rf SQUID Magnetometer System 201 12.4.1 Achievement of a Very Large ?V rf/ ? Φ in a Low-Impedance System 201 12.4.2 Multiturn Input Coil for a Thin-Film rf SQUID Magnetometer with a Planar Labyrinth Resonator 204 12.4.

3 Modern rf SQUID Electronics 208 12.5 Multichannel High- T c rf SQUID Gradiometer 211 12.6 Comparison of rf SQUID Readout with dc SQUID Readout 214 12.7 Summary and Outlook 215 References 218 Index 225.