2015 Winter School on Superconductivity @ HPSTAR Low-T c dc SQUID System Yi Zhang 张懿 Peter Grünberg Institute (PGI-8), Forschungszentrum Jülich (FZJ), D-52425 Jülich, Germany Shanghai Institute of Microsystem and Information Technology (SIMIT), Chinese Academy of Sciences (CAS), 200050-Shanghai, P. R. China
Joint Research Institute Founded on 23.10.2015
SQUID Applications SQUID 芯片读出电路低温技术
Contents What is a SQUID? SQUID Readout Electronics Noise Matching between SQUID and Preamplifier A Practical SQUID System Conclusion
What is a dc SQUID?
dc SQUID is... Superconducting QUantum Interference Device (SQUID) I 1 J I 2 I JJ 1 Φ JJ 2 V I dc SQUID = Superconducting Loop + Josephson Junction = Φ = nφ 0 Superconducting Loop: Flux Quantization 0 2 10-15 Wb + Josephson Junction: Josephson Tunneling SQUID is a superconductive ring interrupted by two Josephson junctions. It combines two physical phenomena, flux quantization and Josephson tunneling.
Basic Knowledge Who understands Ohm s law, knows dc SQUID, too. Ohm s law: V = I R
I-V Characteristics -Two typical elements I V I V Resistors Diode
0 : 2 10-15 Wb I-V Curve of SQUID I-V curves of a dc SQUID depend on the magnetic flux and are divided into superconductive region and resistive region. I V I I Resistive region I c = n 0 Superconductive region Resistive region I c V = (n+0.5) 0 Superconductive region V
Specificity of I-V Curve For example: = 3.25 10-12 Wb. / 0 = 1.625 10 3 (0.625 0.5) 0 = 0.125 0 (1/4) 0 (3/4) 0 0 (1/2) 0 1 0 I c (5/4) 0 I (7/4) 0 (3/2) 0 2 0 = n 0 = (n+0.5) 0 (9/4) 0 = (2n+1)/4 0 (11/4) 0 (5/2) 0 3 0 V (13/4) 0 (7/2) 0 SQUID I-V Curves are limited by two states, =n 0 and =(n+0.5) 0, and periodically changed with increasing (decreasing) flux. The period denotes a flux quantum 0.
dc SQUID is... SQUID is a I I c = n 0 V two terminal passive similar to a resistive sensor = (n+0.5) 0 SQUID is operated in the resistive region. R d element. for measuring the change of a magnetic flux.
SQUID Bias Circuits -- On the Basis of Ohm s Law I i V A R d V R d Current bias mode: An ideal current source connects SQUID to readout V( ) at I = constant. Voltage bias mode: An ideal voltage source connects SQUID to readout i( ) at V = constant.
SQUID Signal Readout voltage bias mode working point -- Two Projections i I I swing V b V/ = ( i/ ) R V swing d 3 0 Relation between both bias modes: 2 0 0 0 @ working point 2 0 0 2 0 I b working point I b, V b : two bias lines V V working point Current bias mode
SQUID Readout Electronics V - characteristics will be linearized. V V out of SQUID system
Piezo-element (jacking force) V Negative Feedback V Jack -- for linearization W 0 V V 0 W 0 Working point V feedback @max. V/ W W W
Flux Locked Loop (FLL) -- in current bias mode I b - V in =0 M G R f i G is automatically adjusted. Requirement: G open _ + V out V SQUID Flux Change Voltage Change V out = V in G V/ Current Vout Change i = V out / R f Compensation Flux - = i M FLL FLL: V out is proportional to (linearized)
Flux Modulation Scheme (FMS) -- a standard readout technique C ac Swing 1:n FMS standardized in 1967 Input: Transformer + Output: Integrator Our recent analysis shows that FMS works in mixed bias mode, thus further reducing ac swing at transfomer primary winding.
Direct Readout Scheme (DRS) s : SQUID intrinsic noise M f V/ Φ 4.2 K SQUID I b V + Amplifier V - I f preamp R f Problem: R Integrator C V out preamp = [ V preamp / ( V/ )] > S
Noise Matching between SQUID and Preamplifier in Direct Readout System M f V/ Φ Amplifier I b V + SQUID V - I f R f Integrator C R V out
SQUID System Noise 2 system = 2 SQUID + 2 preamp. : SQUID intrinsic noise Our goal is to reach ( V/ Ф) the minimum of system V: Preamplifier noise Traditional notion: The readout electronics noise contribution should be suppressed below the SQUID intrinsic noise.
Noise Analysis in DRS δф system2 = δф s2 + δф preamp 2 2 V in δф s : SQUID intrinsic noise In current bias mode: δф preamp2 = [V n2 +(I n R d ) 2 ] /( V/ Ф) 2 Each preamplifier has two noise sources, V n and I n. The five parameters decide δф system.
Five Parameters -- influencing System Noise V n I n V/ s R d Preamplifier property Matching? SQUID property
Preamplifier Candidates V - V+ V n 0.9 nv/ Hz AD797 V out I n 2 pa/ Hz Operational amplifier Preamplifier (V n, I n ): V - V + V+ 83 Ω V- T4 27 k V n 0.35 nv/ Hz T3-B T2-B T1-B T1-A T2-A T3-A 150 Ω 10 nf V- 1.5 k Parallel Connected Bipolar Transistors (PCBT) I n 1.5 k V n V out I n 5 pa/ Hz 6 SSM2220 V n PCBT I n PCBT = (1/ 6) V n AD797 = 6 I n AD797 R s V n total voltage noise: V n2 = (I n R d ) 2 + V n 2 V out
Total Voltage Noise V n at different R s (R d ) AD 797 V n V n is dominated by V n. At R s = 50 Ω, I n R s influences V n in f < few Hz. Vn, preamp.=[v 2 n +(I n R s )2 ] 1/2 10 1 10 0 10-1 10-2 10 1 10 0 10-1 10-2 Vn Vn, preamp. PCBT n 10 V n n 50 10-1 10 0 10 1 10 2 10 3 10 4 Frequency [Hz] V n is dominated by I n R s. At R s = 50 Ω, I n R s completely determines V n in the whole frequency range.
Five Parameters -- influencing System Noise V n I n V/ s Preamplifier property Matching? SQUID property R d
RCSJ Model of SQUID R J L s /2 L s /2 C C β c = 2 I c CR J2 / 0 R J Steward- McCumber parameter β c In order to obtain different ß c, we change R J @ I c C const.
Three Parameters at Different β c -measured R d, V/ and estimated noise s s, R d and V/ increase with increasing β c. β c 0.1 0.4 3.5 17 R d [ ] 3.5 10 25 50 V/ [μv/ф 0 ] 30 110 350 600 s [µ 0 / Hz] (L s = 350 ph) V n [nv/ Hz] Required preamplifier noise Impossible Almost impossible Possible 1 2 4.2 7 Easy 0.02 0.16 0.5 3 preamp = 0.7 s V n = 0.7 s ( V/ ) Zeng J, Zhang Y, et al., Appl. Phys. Lett. 103, 122605 (2013)
Noise Matching c δф s2 Noise matching: δф preamp2 δф = [V n2 +(I n R d ) 2 ] /( V/ Ф ) 2 preamp2 = V n2 /( V/ Ф) 2 I n of AD797 can be neglected due to its large V n. s preamp Fortunately, the large I n contribution of PCBT can be PCBT reduces V n, but increases I n, suppressed by a Current Feedback Circuit (CFC). thus increasing I n R d and worsening Φ preamp. G.F. Zhang, Y. Zhang, et al., doi:10.1016/j.physc.2015.03.009
Suggestion -- for selecting Preamplifier and SQUIDs β c 0.4 1 3.5 17 V/ [μv/ф 0 ] 110 200 350 600 s [µ 0 / Hz] (L s = 350 ph) Noise matching: 2 2.5 3.5 7 AD797 for c 3 strongly Intermediately PCBT for weakly damped damped damped 1 with CFC c? PCBT AD 797 employed preamplifier
A Practical SQUID System
A Commercial Electronics -- in flux modulation scheme Back view Front view
Single Chip Readout Electronics Our concept: PI P, remove the integrator c 3 SCRE (DRS) AD797 P the simplest DRS Chang K, Zhang Y, et al, A simple SQUID system with one operational amplifier as readout electronics. Supercond. Sci. Technol. 27 (2014) 115004 (4pp)
Test of SCRE 6 μφ 0 Hz Test frequency (khz) R f = 1 M Ω BW =3.8 khz Slew rate (Φ 0 /μs) 1 0.8 10 0.9 100 1 500 2 1000 2 94 kω 30 khz 1.44 kω 2.7 MHz High bandwidth and slew rate can be easily achieved with SCRE
Applications (I) Magnetocardiography (MCG) R f = 1 M Ω Demonstration for biomagnetism
Applications (II) x y z Electric Actuator --Unshielded ULF MRI System @ SIMIT 1.5 m Slider Sample SQUID Permanent Magnet(PM) pair PM pair G xx Electric Actuator B applied LHe Cryostat B z = B c +B earth (26 μt) = 0; G xy & G xz B 0 = B earth// + B applied = 130 μt; 3D Gradient Coils B p = 0.65 T B 1 B c
Four-channel 3D MRI -- G = 47 T/m SQUID 44 mm 3 = 22 mm 50 mm 2 nd -order gradiometer 1 42 2 Pepper mm 4
Applications (III) Transient Electro-Magnetic (TEM) 15km 测区地理位置
Measurement Field 200 米 200 米 发射机 300 nt 80 ms Secondary field 超导接收机
TEM Profile Depth [m] Coil of Jilin University SQUID 0 17 km The SQUID detection depth is clearly larger than 1000 m.
Depth [m] TEM Profile of Shallow Layer Coil of EM 67 0 17 km SQUID SQUID TEM 测量实用化之日, 便是我退出江湖 ( 金盆洗手 ) 之时 Using SQUID, the shallow layer of < 100 m is detectable.
Conclusion (I) Three novel paradigms: 1) We expand the hysteresis-free range ( c >1). 2) We should aim at preamp s (not preamp < s ). 3) We change the feedback controller from PI to P (remove the integrator), thus obtaining the simplest SQUID system (SCRE). Concept for SQUID systems: 1) Intermediately damped SQUID ( c 1) + PCBT (preamplifier) + CFC yields a high performance. 2) Weakly damped SQUID ( c 3) + SCRE forms the simplest SQUID system with an acceptable system for many applications.
Conclusion (II) --a practical dc SQUID system Simplicity Stability Convenient to manufacture User-friendliness Robustness Acceptable system noise Single Chip Readout Electronics (SCRE) with a weakly damped SQUID the simplest SQUID system Albert Einstein: Everything should be made as simple as possible, but not simpler.
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