Optimizing the slew rate of SQUID system

ELSEVIER

Physica C 341-348 (2000) 2719-2720 www.elsevier.nl/locate/physc

Optimizing the Slew Rate of SQUID System EX. Xie, D.E He, T. Yang, E Ma, R.J. Nie, L.Y. Liu, S.G. Wang, S.Z. Wang, Y.D. Dai Mesoscopic Physics National Laboratory and Department of Physics, Peking University, Beijing 100871, China* We study optimization of the slew rate of SQUID (Superconducting QUantum Interference Device) systems both theoretically and experimentally. Considering the total equivalent noise flux input in the SQUID, both for SQUID electronics with one pole and for electronics with two poles and one zero, we get new formulas for slew rate and find the optimum bandwidth for the maximum slew rate. For SQUID electronics with one pole, the optimum bandwidth and corresponding maximum slew rate are both proportional to S~1. While for systems with two poles and one zero, the optimum bandwidth and corresponding maximum slew rate are proportional to S®~ and S. 2 respectively. The SQUID sensors and a multi flux quanta electronic simulator are used in the experiment and the results are in good agreement with analysis. Because of their unmatchable magnetic field sensitivity, SQUID (Superconducting QUantum Interference Device) systems are now used in fields like bio-magnetic measurement, nondestructive material evaluation (NDE), and geological exploration. In the later two fields, a high slew rate is required for lock-in operation of the SQUID system to detect large signal without shielding. A two poles and one zero response system111 can improve slew rate. But there is still lack of analysis on optimizing a given flux noise level SQUID system. This work determines the relationship between noise, bandwidth and slew rate and studies the optimization of slew rate of SQUID systems both theoretically and experimentally. There is a maximum attainable bandwidth for SQUID systems working in flux-locked loop mode. The root mean square (RMS) value of total flux noise is:

where Att~o~rd2, ,o~ is the bandwidth of the system responsettl. The crest factor of Gaussian type noise is 3.890 with 0.01% of the time peak is exceeded. 121 For steady lock-in of the system,-peak-to-peak equivalent noise should not exceed about 2/3 of 0o/4 empirically,131 where the flux quanta O0=2.07x10 ~5 Wb. Taking these factors into consideration, we get: 0)c max ~

' When

(I)02' 1 18ZtS. 3.892 S~lt2=lxl0500/~/Hz,

=

we

get

maximum

bandwidth BWmax(le-5)=ah,max/2r~ 12MHz. Because the feedback of integrated system noise will deteriorate slew rate, we should revise slew rate formulas. For an one pole response system and a two poles one zero system, the maximum slew rate formulas without noise feedback are: SR~=o~cO0/4 and SR~=t, OzlO)et{oO0/4 respectively. [l] Revised formulas should be: SRm~ = (1- N)coc~0/4

O.i (~o,¢.)(co)deo) 1/2

(2)

(1)

* Work supported by Chinese National R&D Center for Superconductivity 0921-4534/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. Pll S0921-4534(00)01410-6

2720

EX. Xie et aL/Physica C 341-348 (2000) 2719-2720

SRm~x = O - N ) °)~c°z' D°

Co

(3)

4

]

J

i

J

t

where N is the contribution of integration of noise: ~lOS=

coc

N=ot

S . l/z

2zrBWm~x(le-5) 1 0 _ s ¢ 0 / . ~ z

(4) 10s

ot is for adjustment according to experiment. Differentiating (3), we can get optimum bandwidth BWopt, and according maximum slew rate SRmax,opt for both types of systems. We use several SQUIDs with different noise levels and a multi quanta electronic SQUID simulator [4] to verify the above theoretical prediction. For an one pole response system, firstly we measure a given bandwidth system with different test frequencies and prove that the slew rate is a constant in the predicted range. []] We then change system bandwidth by changing the integration capacitor of the SQUID control electronics. The result is shown in Figure 1. The flux noise is SoVZ=6.6xl0SD0/Hz v2. Squares are experimental data and the dotted line is the fitted curve. We can clearly see that there is an optimum bandwidth for a maximum slew rate. Next, we choose SQUIDs with different noise levels and adjust the system bandwidth for maximum slew rate. In order to test the rather low noise situation, we use a SQUID simulator in the experiment. The result is shown in Figure 2. The asterisks are the SQUID . . . . . .

~

10 4

0.0

,

,

.

,

•

,

,

,

.

,

.

2 . 0 x 1 0 "5 4 . 0 x 1 0 "5 6 . 0 x 1 0 "5 8 . 0 X 1 0 "s 1 . 0 X 1 0 "4 1 . 2 x 1 0 -4

Flux Noise (.o/rtHz) Figure 2: M a x i m u m slew rate vs.

flux noise of an one pole SQUID simulator data. Fitting the above experimental data, we get: BWopt=3.3 x 103/So (I/z) with SR~x,opt=2.8 x 1 0 " 4 / S . ( ¢ d s ) for the one pole system. The analysis for the two poles and one zero system shows that: BWopt=7.7 x 10a/so (Hz) and corresponding SRmax.opt=7.3x 10"9/¢th/So2 (D0/s). In summary, after considering the total equivalent noise flux input in the SQUID, both for SQUID electronics with one pole and for electronics with two poles and one zero, we get new formulas for the slew rate and find the optimum bandwidth for maximum slew rate. The SQUID sensor and a multi flux quanta electronic simulator are used in the experiment and the results are in good agreement with analysis.

i. . . . .

6 x i 0 4-

REFERENCES

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[ 1] C.Rillo,D. Veldhuis, and J. Flokstra, IEEE Trans. Instru. Meas.,Vol IM-36,3,770(1987) [2] C.D.Motchenbacher, Low Noise Electronics Design, New York: Wiley, 1973 [3] D.Drung, H. Matz, and H.Koch, Rev. Sci. Instrum., 66,3008(1995) [4] EX.Xie, S.G.Wang, and Y.D. Dai, Low Noise SQUID Simulator, accepted by Chinese Low Temp. Phys.

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31104 .

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=

Bandwidth(Hz) Figure 1: Slew rate vs. Bandwidth of

an one pole response SQUID system