SQUID Readout Electronics and Magnetometric Systems for Practical Applications
Description
This book builds a bridge for scientists and engineers to fill potential know-how gaps for all working on SQUID systems and their practical applications. Key words such as readout electronics, flux quantization, Josephson effects or noise contributions will be no obstacle for the design and application of simple and robust SQUID systems.
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Persons
Yi Zhang received his Ph.D. in 1990 from the University of Gießen, Germany. His research at the Forschungszentrum Jülich is dedicated to the fabrication and application of SQUIDs. He has been awarded various Professor titles at the University of Peking, Shanghai Jiao Tong University, Tongji University and SIMIT CAS, and from Jilin University. In 2001, he worked at the University of California, Berkeley, in Prof. John Clarke's group, and was a co-author of the "SQUID Handbook", edited by John Clarke and Alex. I. Braginski (WILEY-VCH). He has contributed to more than 150 publications with about 2000 citations, and is one of the leading scientists for SQUID research worldwide. Several of his papers were cited in the book "100 Years of Superconductivity", edited by Horst Rogalla and Peter H. Kes (CRC Press).
Hui Dong received her Ph.D. in 2011 from SIMIT CAS. 2008 - 2010 she was a visiting student at Forschungszentrum Jülich, Germany, and a visiting scholar at the University of California, Berkeley. She is currently Associate Professor at SIMIT CAS. Her research interests include SQUID system optimization and applications of ultra-low field magnetic resonance imaging (ULF MRI). She has authored and co-authored about 30 scientific publications, and she holds 8 patents.
Guofeng Zhang received his Ph.D. in microelectronics and solid state electronics from SIMIT CAS in 2012. From 2009 - 2011 he was a visiting Ph.D. student at the Forschungszentrum Jülich, before becoming Assistant and in 2015 Associate Professor at SIMIT CAS. His research interests include SQUID design and fabrication, and SQUID applications in biomagnetism, geophysics and related areas. He has authored and co-authored about 20 scientific publications, and he holds 5 patents.
Hans-Joachim Krause received his Ph.D. in Physics from RWTH Aachen, Germany in 1993. He initiated the Non-destructive Evaluation Group at Forschungszentrum Jülich, working on projects with industrial partners for the development of SQUID systems for the magnetic testing of aircraft parts, pre-stressed concrete bridges and other structures. In summer 2011, he was a Visiting Professor at Université Pierre et Marie Curie, Paris, France. Currently, he leads the Magnetic Sensing Group in Jülich, focusing on SQUID sensors, magnetic biosensing, low field nuclear magnetic resonance, magnetic immunoassays and magnetic nanoparticle actuation. In 2017, he was appointed Professor of Physics at the University of Applied Sciences, Aachen, Germany. He has co-authored more than 150 scientific publications with over 1500 citations.
Content
1.1 Motivation
1.2 Contents of the chapters
2 JOSEPHSON JUNCTIONS
2.1 Josephson equations
2.2 RCSJ model
3 DC SQUID'S I-V CHARACTERISTICS AND ITS BIAS MODES
3.1 SQUID's I-V characteristics
3.2 An ideal current source
3.3 A practical voltage source
4 FUNCTIONS OF THE SQUID'S READOUT ELECTRONICS
4.1 Selection of the SQUID's bias mode
4.2 Flux locked loop (FLL)
4.2.1 Principle of the FLL
4.2.2 Electronic circuit of the FLL and the selection of the working point
4.2.3 "Locked" and "unlocked" cases in the FLL
4.2.4 Slew rate of the SQUID system
4.3 Suppressing the noise contribution from the preamplifier
4.4 Two models of a dc SQUID
5 DIRECT READOUT SCHEME (DRS)
5.1 Introduction
5.2 Readout electronics noise in DRS
5.2.1 Noise characteristics of two types of preamplifiers
5.2.2 Noise contribution of a preamplifier with different source resistors
5.3 Chain rule and flux noise contribution of a preamplifier
5.3.1 Test circuit using the same preamplifier in both bias modes
5.3.2 Noise measurements in both bias modes
5.4 Summary of the DRS
6 SQUID MAGNETOMETRY SYSTEM AND SQUID PARAMETERS
6.1 Field-to-flux transformer circuit (converter)
6.2 Three dimensionless characteristic parameters, beta-c, Gamma, and beta-L, in SQUID operation
6.2.1 SQUID's nominal Stewart-McCumber characteristic parameter beta-c
6.2.2 SQUID's nominal thermal noise parameter Gamma
6.2.3 SQUID's screening parameter beta-L
6.2.4 Discussion on the three characteristic parameters
7 FLUX MODULATION SCHEME (FMS)
7.1 Mixed bias modes
7.2 Conventional explanation of the FMS
7.2.1 Schematic diagram of the FMS
7.2.2 Time domain and flux domain
7.2.3 Flux modulation
7.2.4 Five additional notes
7.3 FMS revisited
7.3.1 Bias mode in FMS
7.3.2 Basic consideration of synchronous measurements of Is and Vs
7.3.3 Experimentally synchronous measurements of Delta i and VRs
7.3.4 Transfer characteristics of the step-up transformer
7.3.5 V(Phi) comparison obtained by DRS and FMS
7.4 Conclusion
8 FLUX FEEDBACK CONCEPTS AND PARALLEL FEEDBACK CIRCUIT
8.1 Flux Feedback Concepts and its History
8.2 SQUID's apparent parameters
8.3 Parallel Feedback Circuit (PFC)
8.3.1 Working Principle of the PFC in Current Bias Mode
8.3.2 Working Principle of PFC in Voltage Bias Mode
8.3.3 Brief Summary of Qualitative Analyses of PFC
8.4 Quantitative analyses and experimental verification of the PFC in voltage bias mode
8.4.1 The equivalent circuit with the PFC in voltage bias mode
8.4.2 Introduction of Two Dimensionless Parameters r and ¿
8.4.3 Numerical calculations
8.4.4 Experimental Results
8.4.5 Noise Comparison and Interpretation
8.4.6 Two practical designs for PFC
8.5 Main achievements of PFC quantitative analysis
8.6 Comparison with the noise behaviors of two preamplifiers
9 ANALYSES OF THE "SERIES FEEDBACK COIL (CIRCUIT)" (SFC)
9.1 SFC in current bias mode
9.1.1 Working principle of the SFC in current bias mode
9.1.2 Noise measurements of a weakly damped SQUID (magnetometer) system with the SFC
9.2 The SFC in voltage bias mode
9.3 Summary of the PFC and SFC
9.4 Combination of the PFC and SFC (PSFC)
9.4.1 PSFC analysis under independence conditions
9.4.2 PSFC experiments and results
9.4.3 Conclusion of the PSFC
10 WEAKLY DAMPED SQUID
10.1 Basic consideration of weakly damped SQUID
10.2 SQUID system noise measurements with different ßc values
10.3 Statistics of SQUID properties
10.4 Single chip readout electronics (SCRE)
10.4.1 Principle of SCRE and its performance
10.4.2 Equivalent circuit of SCRE
10.4.3 Differences between the conventional version of readout electronics with an integrator and SCRE
10.4.4 Two applications of SCRE
10.5 Suggestions for the DRS
11 TWO-STAGE AND DOUBLE RELAXATION OSCILLATION READOUT SCHEMES
11.1 Two-stage scheme
11.2 ROS and DROS
11.3 Some comments on D-ROS and two-stage scheme
12 RADIO-FREQUENCY (RF) SQUID
12.1 Fundamentals of an rf SQUID
12.2 Conventional rf SQUID system
12.2.1 Block diagram of rf SQUID readout electronics (the 30 MHz version)
1
Introduction
1.1 Motivation
Superconducting QUantum Interference Devices (SQUIDs) are well known because they are the most sensitive sensors for measuring magnetic flux. In magnetometry, a SQUID with a field-to-flux transformer circuit (converter) construct is a magnetometer with high field sensitivity in the range of fT/VHz (one millionth of the earth's magnetic field). Therefore, the study of SQUID systems has never stopped.
Many books and reviews have elaborated on the SQUID principle and SQUID magnetometric systems as well as SQUID applications, e.g. "Superconductor Applications: SQUIDs and Machines" edited by B. B. Schwartz and S. Foner [1], "Physics and Applications of the Josephson Effect" edited by A. Barone and G. Paterno [2], and the NATO proceedings "SQUID Sensors: Fundamentals, Fabrication and Applications" edited by H. Weinstock [3]. In particular, "The SQUID Handbook," edited in 2004 by John Clarke and Alex I. Braginski comprehensively summarizes SQUID's theory and practice since SQUIDs have been discovered [4]. Hence, this book has become the new "bible" for researchers in the field. Furthermore, the review of "SQUID Magnetometers for Low-Frequency Applications" by Tapani Ryhänen et al. presented a novel formulation for SQUID operation and SQUID magnetometers for low-frequency applications, taking into account the coupling circuits and electronics [5].
Structurally, a direct current (dc) SQUID is a superconducting ring interrupted with two Josephson junctions. Predicatively, SQUIDs have very rich physical meanings, e.g. the Aharonov-Bohm effect, flux quantization, Meissner effect, Bardeen-Cooper-Schrieffer (BCS) theory, and the Josephson tunnel effect. However, starting from the view of electronic circuits, our first question is on what a dc SQUID is. In magnetometry, a dc SQUID should be regarded as a resistor-like element where its dynamic resistance is modulated by the flux F threading the SQUID's loop. In the readout technique, the dynamic resistance of the SQUID, Rd(F) = ?V/?I, i.e. the derivative of the voltage with respect to current, is the fundamental readout quantity, which is embodied in the current-voltage (I-V) characteristics of the SQUID. Here, the changing I-V characteristics are limited by two curves at the integer (upper limit) and half-integer (lower limit) of the flux quantum F0, which reflect the quantity of magnetic flux in the SQUID loop. There is already abundant "know-how" to read out a resistor R. For example, one can measure a voltage V across R with a constant current flowing through R or measure a current I through R when a constant voltage V is connected to R in parallel. A dc SQUID can either be operated at constant current by measuring the voltage across it (called current bias mode) or at constant voltage by measuring the current through it (called voltage bias mode). In either bias mode, only the SQUID's V(F) or I(F) characteristics emerge. Similar to the change in I-V characteristics with the flux, V(F) and I(F) are also modulated by F. In brief, the essence of all three SQUID characteristics is recording the SQUID's dynamic resistance changes, Rd(F).
Generally, a SQUID system consists of the SQUID sensor and its readout electronics. The small SQUID signal leads to difficulty in reading out the SQUID's signal without additional noise contributions from the readout technique. Conventionally, one hopes to suppress such noise contribution below the intrinsic SQUID noise dFs. In other words, the measured system noise almost reaches dFs.
The main noise source in readout electronics is the preamplifier, which possesses two independent noise sources: the voltage noise Vn and the current noise In. Both of these noise sources are innate to the amplifier chip and cannot be changed. In order to compare these two noise contributions in a SQUID system, both types of electronic noise should be translated into a flux noise, dFe, in units of F0/VHz with SQUID's transfer coefficient of ?V/?F or ?I/?F. In fact, the original SQUID parameters including the transfer coefficients are also innate to the particular SQUID and cannot be changed. However, the SQUID's apparent parameters at the input terminal of the preamplifier can be modified. Over the past half century, people have developed different readout schemes, where the electronic noise dFe is suppressed by increasing the apparent transfer coefficients once a preamplifier is selected. Indeed, the modification of the apparent parameters is the main thread running through the book. Here, we will change the perspective to discuss the optimization of the SQUID system noise, i.e. how to match the SQUID parameters with the readout electronics.
According to the type of superconducting material used, SQUIDs can be divided into two groups: the low-temperature superconducting (LTS) SQUID, also called low-Tc SQUID, usually operated at 4.2 K (liquid helium temperature); and the high-temperature superconducting (HTS) SQUID, also called high-Tc SQUID, usually operated at 77 K (the liquid nitrogen temperature). The LTS material is typically niobium and HTS material is yttrium barium copper oxide (YB2Cu3O7-x).
However, according to the working principles, the dc SQUID mentioned above is completely different from the radio frequency (rf) SQUID, which is a superconducting ring interrupted with only one junction. To read the signal from an rf SQUID, it is inductively coupled to an rf tank circuit, which connects to the readout electronics.
In this book, LTS (low-Tc) dc SQUID and HTS (high-Tc) rf SQUID systems, which are often used in magnetometry, will be highlighted. We will share our experiences and lessons, mostly from our own works, with readers, college students, and graduates in physics and engineering who have an interest in SQUID techniques, e.g. how to set up a simple SQUID system for themselves.
1.2 Contents of the Chapters
The book is organized into 12 chapters, where most of the content (from Chapters 2-11) is about the dc SQUIDs, and only the last chapter is related to rf SQUIDs. However, the dc SQUID bias reversal scheme [6], the 1/f noise study [7,8], and the special readout scheme for the nano-SQUID [9,10] are not included.
Chapter 1: This chapter is devoted to our motivation above and the subsequent chapter contents - why did we write this book, and what is it about?
Chapter 2: Because the Josephson junction (JJ) is the key element of SQUIDs, Josephson's equations should be first introduced. Then, JJs are analyzed with the resistively and capacitively shunted junction (RCSJ) model, thus introducing two important parameters: the Stewart-McCumber parameter ßc and the thermal rounding parameter G. To observe the features of JJs, one often uses the I-V characteristics, where the hysteresis behavior depends on the values of both ßc and G. Actually, the I-V characteristics describe the changing dynamic resistances Rd of the JJ, i.e. Rd = ?V/?I. It was experimentally verified that the value of Rd depends not only on the junction shunt resistor RJ but also on the junction critical current Ic. Generally, JJs without hysteresis are suitable for SQUID operation. In fact, one habitually transforms the parameters ßc and G of the JJ into SQUID operation.
Chapter 3: For readout electronics, the dc SQUID is regarded as dynamic resistance Rd(F) modulated by the flux threading into the SQUID loop. The SQUID's I-V characteristics can be divided into three regions, and the SQUID is operated in the flux-modulated region (II). In fact, the behavior of Rd(F) is embodied in a SQUID's I-V characteristics. To measure a resistance Rd, one can impress a known current (current bias) into a SQUID and observe the voltage across the SQUID's dynamic resistance Rd. Alternatively, one can apply a constant voltage to the SQUID (voltage bias) and measure the current passing through Rd. Owing to the small Rd ~ 10 O of the SQUID, an ideal current bias mode for SQUID operation can easily be realized. In contrast, an ideal voltage bias mode can hardly be achieved, as will be shown in the course of the chapter.
Chapter 4: Almost all SQUID readout electronics developed over the past half century have a common feature: they establish a so-called flux-locked loop (FLL) to realize linearization of the output voltage Vout(F) of the readout electronics; i.e. Vout is proportional to the flux change F. In this chapter, the principle and...
