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INTEGRATION OF SQUID 1/f NOISE AND ITS
APPLICATION TO A SUPERCONDUCTING
GYROSCOPE
J. Anderson, B. Cabrera
To cite this version:
INTEGRATION OF SQUID l/f NOISE AND ITS APPLICATION TO A SUPERCONDUCTING GYROSCOPE
J.T. Anderson and B. Cabrera
W.W. Hansen Laboratories of Physios, Stdnford University, Stanford, California 94305, USA
Abstract.- SQUID noise in the 1/f noise region was integrated for 140 hours in a narrow frequency band centered on 0.017 Hz, and the theoretical minimum detectable energy of
1.3 x 10_33J was demonstrated. We use this result to determine the angular readout sensi-tivity of a superconducting gyroscope.
INTRODUCTION.- SQUID magnetometers exhibit increa-sing noise power at low frequencies /l/ which tends to rise as f /f, typically beginning in the range 10-2 Hz < f < 1 Hz. The integrability of SQUID
noise in the 1/f region to improve sensitivity is essential to the attainment of high angular resolu-tion in the gyroscope described below, but it has sometimes been erroneously claimed that 1/f noise cannot be integrated. Sensitivity to a dc signal is not improved for integration times longer than approximately 1/f because of the greater contri-bution from low frequency noise power to the result, but for an ac signal in the 1/f region, the
expec-ted benefits of integration can be accrued. The experiment described below will demonstrate that point.
EXPERIMENT.- An S.H.E. /2/ TSQX SQUID, operated with S.H.E. model 330X electronics, was used for
this experiment. With its input shorted, the SQUID was placed in an ambient field of 3 x 1 0- 7 gauss. The output noise of the magnetometer was passed through a 3 pole filter at 0.1 Hz, amplified by 964, digitized at 5 second intervals, and recorded on magnetic tape for 140 continuous hours. A 7.1 x
10- 6 <j>o rms calibration signal'at 0.017 Hz was injected into the SQUID rf coil; it was nearly an order of magnitude below the noise at the filter output.
ANALYSIS.- The data was analysed using power spec-tra determined via the fast Fourier spec-transform. The example shown in figure 1 was made by averaging 49
individual 1024 point periodigrams.
For white noise, the minimum detectable erergy <5E at frequency f is SE = S(f)Af, where S(f)
is the spectral density of the noise. It is not obvious a_ priori that when integrating noise in the 1/f region for times as long as 140 hours that either the noise is integrable to the expected 6E, or that instrumentation effects will not limit the process.
The minimum Af for an FFT power spectrum is 1/TD where T„ is the record length. For T„ = 140 hours, Af = 1.98 x 10"6 Hz. At the calibration si-gnal position, S(f) = 6.8 x 10- J/Hz that one hopes to find SE : 1.35 x 10-33J.
The spectrum of figure 2 is an expanded re-gion around the calibration signal and has Af = 1.98 x 10-6 Hz. The accepted criterion for a 1:1 signal to noise ratio is that the signal equals Fig. 1 : Low frequency SQUID noise spectrum with
calibration signal.
JOURNAL DE PHYSIQUE Colloque C6, supplément au n" 8, Tome 39, août 1978, page C6-1210
Résumé. Le b r u i t d'un SQUID dans l a bande où i l e s t proportionnel à l ' i n v e r s e de l a f r é -quence ( 1 / f ) a é t é i n t é g r é pendant 140 heures dans une é t r o i t e bande de fré-quence c e n t r é e sur 0,017 h e r t z . Le s e u i l d ' é n e r g i e théoriquement d é t e c t a b l e , de 1,34 x 1 0 - *3j o u l e , a é t é
démontré. Nous u t i l i s o n s ce r é s u l t a t pour déterminer l a s e n s i b i l i t é a n g u l a i r e d'un gyros-cope supraconducteur.
t h e s t a n d a r d d e v i a t i o n , SD, o f t h e n o i s e . The under- l y i n g s t a t i s t i c a l d i s t r i b u t i o n f o r t h e d a t a of f i - g u r e 2 s h o u l d b e a c h i - s q u a r e w i t h 2 d e g r e e s o f freedom 131 f o r which t h e mean e q u a l s t h e s t a n d a r d d e v i a t i o n . The sample mean and s t a n d a r d d e v i a t i o n a r e 1 . 3 x J and 1 . 2 x J r e s p e c t i v e l y . F i t t i n g t h e c h i - s q u a r e c u r v e t o a f r e q u e n c y h i s t o - gram of t h e d a t a g i v e s a mean of 1.2 x Thus t h e minimum d e t e c t a b l e e n e r g y i s 6E : 1 . 3 x 5.
1
I
I
I
-31
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F i g . 2 : Noise e n e r g y a t each f r e q u e n c y sample i n expanded spectrum.
SUPERCONDUCTING GYROSCOPE READOUT.- Shown schema- t i c a l l y i n f i g u r e 3 i s a gyroscope a n g l e r e a d o u t 141 f o r a n e a r t h - o r b i t i n g t e s t o f G e n e r a l R e l a t i v i t y 151. The gyroscope i s a 3 . 8 cm d i a m e t e r q u a r t z s p h e r e c o a t e d w i t h s u p e r c o n d u c t i n g niobium, and c o o l e d t o % 1.5 K . When t h e gyroscope s p i n s , t h e superconduc t i n g c o a t i n g g e n e r a t e s a m a g n e t i c f i e Id e x a c t l y a l o n g t h e s p i n a x i s , t h e London moment 161 which i s g i v e n by HL = 7.14 x 10-I' f t e s l a ( 4 . 1 ) where f , t h e r o t a t i o n f r e q u e n c y , w i l l b e approxima- t e l y 200 Hz. MAGNETOMETER INPUT COIL READOUT LOOP
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MAGNETOMETER The r e a d o u t c i r c u i t i s a c o n t i n u o u s supercon- d u c t i n g p a t h , and f l u x from t h e gyroscope t h r e a d i n g t h e r e a d o u t l o o p g e n e r a t e s a c u r r e n t i n t h e c i r c u i - t r y p r o p o r t i o n a l t o s i n e . The s p a c e c r a f t w i l l r o l l , a t % 1 rpm, a b o u t a n a x i s t h a t i n i t i a l l y c o i n c i d e s w i t h t h e s p i n a x i s o f t h e g y r o s c o p e . I f t h e s p i n a x i s t i p s from t h e p l a n e of t h e l o o p , an a c c u r r e n t a t t h e r o l l r a t e and p r o p o r t i o n a l t o s i n e w i l l f l o w i n t h e r e a d o u t c i r c u i t , t r a n s f e r r i n g e n e r g y t o a SQUID magnetometer.
The e x p e c t e d a n g u l a r s e n s i t i v i t y i s c a l c u l a - t e d a s f o l l o w s . For a r e a d o u t l o o p c l o s e t o t h e gyroscope, t h e rms f l u x t h r e a d i n g t h e r e a d o u t c i r - c u i t i s , u s i n g e q u a t i o n ( 4 . 1 ) , $T = 5.05 x 10-l1 f ~ r i s i n e ( 4 . 2 ) whererG
i s t h e gyroscope r a d i u s . The rms r e a d o u t c i r c u i t c u r r e n t IR i sIR = bT/(LR + Ls) ( 4 . 3 )
where LR and LS a r e r e s p e c t i v e l y t h e r e a d o u t l o o p and SQUID i n p u t c o i l i n d u c t a n c e s . For maximum e n e r - gy t r a n s f e r , L e q u a l s LS. The e n e r g y c o n t a i n e d i n R t h e SQUID i n p u t c o i l i s 1 ES = - L I* 2 S R ' ( 4 . 4 ) Combining e q u a t i o n s ( 4 . 2 1 , ( 4 . 3 ) and (4.4) s e t t i n g E. = 6E = 1.3 x 5 , and t a k i n g LR = 0.3uH, t h e a p p r o p r i a t e v a l u e f o r t h e p r e s e n t gyroscope dimen- s i o n s , g i v e s 0 = 4.9 x r a d . The d e s i g n g o a l min f o r t h e R e l a t i v i t y e x p e r i m e n t i s 9 < 5 x lo-' min r a d o v e r a maximum a n g u l a r r a n g e of
2
50 a r c - s . CONCLUSION.- I n t e g r a t i o n f o SQUID l / f n o i s e i n a narrow f r e q u e n c y band away from dc p r o c e e d s a sthough t h e n o i s e were w h i t e , and t h u s SQUID s e n s i - t i v i t y i s d i r e c t l y c a l c u l a b l e from i t s n o i s e power c u r v e . A s e n s i t i v i t y of 1.35 x J h a s been de- m o n s t r a t e d , t h e e q u i v a l e n t of 1 m i l l i a r c - s f o r t h e gyroscope r e a d o u t d e s c r i b e d .
ACKNOWLEDGEMENTS.- The a u t h o r s thank R. G i f f a r d and
J. H o l l e n h o r s t f o r t h e i r a s s i s t a n c e i n s e t t i n g up t h e n o i s e measurements, and g e n e r a l d i s c u s s i o n s con- c e r n i n g power s p e c t r u m a n a l y s i s .
R e f e r e n c e s
/ I / C l a r k e , J., SQUID S u p e r c o n d u c t i n g Quantum I n t e r f e r e n c e Devices and T h e i r A p p l i c a t i o n s , e d . Hahlbolm, H.D. and Lcbbig, H. (Walter d e G r u y t e r , New York) 1977, pp. 213.
/ 2 / S.H.E. C o r p o r a t i o n , 4174 S o r r e n t o V a l l e y Blvd., San Diego, CA 92121. / 3 / Whalen, A.D., D e t e c t i o n o f S i g n a l s i n Noise (Academic P r e s s , New York)
1971, p . 108.
/ 4 / Hendricks, J.B., IEEE T r a n s . Magn. MAG-11 (1975) 712, and Anderson, J . T . and E v e r i t t , C.W.F., IEEE T r a n s . Magn. MAG-13 (1977) 377.
/5/ E v e r i t t , C.W.F., E x p e r i m e n t a l G r a v i t a t i o n , e d . B e r t o t t i , B. (Academic P r e s s , New York) 1973, pp. 331.
