In this paper we describe a superconducting chopper amplifier used as an instrument to measure the V(I) curve of multifilamentary superconductors. Experimental results are presented

Kate, H.H.J. ten

Klundert, L.J.M. van de

Overbeeke, F. van

English

van Overbeeke, F.

ten Kate, H.H.J.

van de Klundert, L.J.M.

University of Twente Research Information

IEEE TRANSACTIONS ON MAGNETICS, VOL. MAG-23, NO. 2, MARCH 1987 1413 A SUPERCONDUCTING  MODULATOR  FOR EXTREMELY SENSITIVE VOLTAGE MEASUREMENTS  ACROSS MULTIFILAMENTARY  SUPERCONDUCTING  WIRES F. van Overbeeke, H.H.J.  t en  Kate and L.J.M. van de Klundert, Twente University,  Dept. of Applied Physics,  P.O. Box 217, 7500 AE Enschede, the Netherlands. Abstract In   th i s   paper  we describe a superconducting chopper amplifier used as an instrument  to  measure t h e  V(1)  curve o f  multifilamentary  superconductors. Experimental  results are presented. Introduction For a number, o f   reasons   in te res t   has  emerged i n  s e n s i t i v e  and accurate measurement of the  - V ( I )  curve of multifilamentary  superconducting wires. On one  hand, information  can  be  obtained from it regarding  the quali ty  of  the  superconducting ' material and the  production  process, by ca l cu la t ing   t he   d i s t r ibu t ion  f u n c t i o n   o f   t h e   c r i t i c a l   c u r r e n t  from it [l];  on the  other hand, superconducting wires t h a t  w i l l  be used i n  h ighly  s tab le  magnet system which are opera ted  in  the  p e r s i s t e n t  mode;have  a.maximum cur ren t   t ha t  is not  determined by the   usua l   c r i te r ion   of  p = lo-' kx Qm, but  by a much more conservat ive  a lue  l ike Qq. If we take  a prac t ica l   wi re ,  for example  one  with a diameter of 0.6 mm operating a t  200 A,  t h i s  means t h a t  a vol tage  across  the  wire of  the order  of  1 nV/m should be detectable .  A t  room temperature DC vol tages   of   this   order   of  magnitude can be measured only  with  very  expensive equipment.  Furthermore,  the  thermovoltages  experienced in   t he   connec t ion   l i nes  between the  sample  and the  instrument are probably much grea te r ,   un less   the  experiment is performed on very long samples. For t h i s  reason, a measurement  system is prefer red  of  which the  f i r s t  stage of  amplification is loca ted   . a t   the  temperature  level  a t  which the experiment is performed, usua l ly  4'.2 K. An elegant   but   a lso  ra ther   expensive  solut ion to t h i s  problem is the  use  of  a SQUID sensor. However, a p a r t  from the   h igh   cos t ,   th i s   ins t rument   needs   to   be  located  in  an  electromagnetically  "clean"  environment, e s p e c i a l l y  i n  a weak magnetic f i e l d ,  It was decided not t o  accep t  t he  latter condition beforehand and t o  b u i l d  the  measurement  system' as cheap as poss ib le  and therefore   the   p r inc ip le 'o f  a chopper  amplifier  with a superconducting modulator was adopted. '1 The Instrument History The concept of a superconducting chopper amplifier was already  developed  in  the  1950's  independently by Templeton [2] and de Vroomen e t  a l .  [3]. Their modulators were tantalum or thallium wires, switched in and  out  of  the  superconducting state by  means of  an o s c i l l a t i n g  magnetic f i e ld .  In  o rde r  t o  ope ra t e  such  a system i n  t h e  h i g h  s t r a y  f i e l d  of a magnet, Edwards [4] b u i l t  a similar system  with  a  thermally  switched NbZr modulator. Each of  the  r ferenced  instruments was claimed to have a noise  leve l  of less  than 10 pV a f t e r  low-pass f i l t e r ing  wi th  a  time constant of less than 1 second. Description The l ay -ou t   o f \   t he   i n s t rumen t   i n  its e s s e n t i a l  form is sketched  in   Fig.  1. The taps  between  which a vol tage  has   to   be measured are connected t o   t h e  low- impedance s ide  of  a transformer via the superconducting modulator. By switching  the latter between t h e  r e s i s t i v e  and superconducting states, an AC vo l tage  is generated  on  the  transformer's   primary  side,   of which the  amplitude is propor t iona l   to   the  DC voltage U i .  I f  the  t ransformer  has  a ferromagnetic core, as is the  case in  our  ins t rument ,  i t  w i l l  behave as a r e l a t i v e l y  high  impedance, However in   the   case   o f   an   a i r -core  transformer, which we still  plan  to  apply  because it should  be  'usable  in  high  magnetic  fields,  care  should be   t aken   tha t   the   f fec t ive   input  impedance of  the system  does  not become too low. The transformer  has a high  winding r a t i o  ( lo2 - lo3 ) and is followed a t  room temperature by an AC a m p l i f i e r ,   f i l t e r  and  phase- s ens i t i ve  de t ec to r .  Because t h e  r e s i s t i v e  t r a n s i t i o n  o f  the  modulator is independent  ofthe sign  ofthe modulating  current,   in th rmally as well .as magnetically  activated  devices,   half   the r ference frequency  f,  can  be  used as the  modulating  frequency. A s  a r e s u l t ,   t h e  system is n o t   s e n s i t i v e   t o  interference of the modulating signal,  provided that i t  contains no even harmonics of fs/2. 7 I . '  I I bond-pass fiiter I I cryogenic part 1 Ac and 1 demoduia- 1 low-pass fitter tionl and DC amplification I Figure 1. Basic concept of a superconducting chopper amplifier. attenuator  1 : 10" and voltage source Figure 2. S.c. chopper amplifier used as a zero detector i n  a feedback system. Manuscript received September 30. 1986. 0018-9464/87/0300-1413$01.0001987 IEEE 1414 It can  be shown [5] tha t  t he  maximum RMS value of t h e  fs-component of the s igna l  U, is given by: (U2,RMS/Ui)max = 42  n, In, . (1) In  practice  the  gain  of  the  system  can  be a factor   2  smaller which i s  the pr ice  of  s table  operat ion of  the modulator. This  gain  being  neither  accurately known. n o r   i n  pract ice  very constant  as a function of the t ime, i t  is more convenient t o  use the  instrument as a zero d e t e c t o r  i n  a feedback  system,  as is shown in   F ig .   2 .  In  order  to  ealize  an  acceptable  performance, different  parameters  have  to be  weighed against   each o ther .  The feedback  system  of  Fig.  2 is s t a b l e   o n l y   i f  t he  open-loop  gain  meets  the well-known criteria from the  theory  of  control  systems,  l ike  the  Nyquist  c r i t e r i o n .  Because the  low-pass f i l t e r   a l r e a d y  introduces a phase s h i f t  of 9 0 ° ,  the  phase  shift   of modulated  low-frequency  signals  in  theb ndlpass f i l t e r  should be very limited in the relevant frequency range. For example, i t  was chosen t o  have f, = 85 Hz and t o  have an open-loop  gain  of 0 dB a t  o = 10 (s-l) (see Fig. 3 ) .  An extra  phase shif t  due to  the band-pass  f i l t e r  at wst10 of 30° was considered  acceptable, with os = 2n-fs.  Because  thsystem  should  be operated  in  n  electromagnetically  rather  noisy environment, an attenuation for 50 Hz s igna l s  of 60 dB was a l so   spec i f i ed .   Th i s   r e su l t s   i n a 4 th   o rder  Ghebyshev f i l t e r  with -3 dB poin ts  a t  wsf25 ( s - , ) .  The  problem is now that cross-products of 85 Hz and 50 Hz, f o r  example 170-250 or 255.350,  experience  only a small a t tenuat ion  and especially  the  former  one is clear ly   observed  i f   the   system is switched t o  a high gain such as U, / V i  = lo3 (see Fig.  2) .  The price  for   smaller   cross-products  is thus a smaller bandwidth of t h e   f i l t e r  which impl ies  tha t  0 dB open-loop  gain  has t o  be  chosen a t  a lower  frequency, with  the  resul t   of  a longer  response time of  the overall system. The realized system Modulator. The modulator  (Fig. 4 )  consis ts   ofmonofilament NbTi/Cu wire,  of which the  copper  matrix has  been  etched away over a length  of  approximately 5 mm. Close to   he  e t ched   pa r t  a b i f i l a r l y  wound insu la ted  manganin hea ter  wire is laid.  This  assembly is mounted between two pieces of  anodized  aluminium shee t ,  whereas  the r maining  space i s  f i l l e d   w i t h  S t y c a s t   r e s i n .   I n   t h i s  way a switch i s  created  with short  thermal time constants and having a r e s i s t a n c e  i n  the heated s i tuat ion of  the order  of  0.1-1 Q, which is high enough for our purpose. Transformer. It is our   f i na l  aim to   bu i ld  a system without an iron-core transformer. Because of the ease of manufacturing  however, our present  model has  been  provided with a f e r r i t e  po t - co re ,  which has  been placed a t  such a d is tance  from the  ,experiment  that s t r a y  f i e l d s  o f  t h e  magnet have no observed influence. It appears t o  behave sa t i s fac tor i ly   a t   c ryogenic  temperatures. The numbers of windings are n, = 5 and nz = 10.000. Both the primary and the secondary circui t  have  been wound with  superconducting wire. It may be advisable t o  wind the  secondary  coil  from a r e s i s t i v e  conductor i n   o r d e r   t o  damp o s c i l l a t i o n s  due t o  paras i t ic   capac i tances .  The natural   frequency  of  this transformer i s  about 4 kHz and has  been damped with a p a r a l l e l  r e s i s t o r  on the secondary side of 10 kQ. This r e s i s t o r  however is transformed to   the  pr imary  s ide with a f ac to r  4-106, which means tha t   the   t ransformer  O -540 Figure 3. AmpZitude  and phase diagrams  of t h e  open-Zoop  transfer  function. ,, matrix etched away anodized AI sheet iMonganln heater Figure 4. Lay-out of the  superconducting  moduZator. behaves as a r e s i s t o r  of 2.5 mP, which e f f ec t ive ly  reduces the gain given in eq.  (1) by a factor 2.  Room-temperature e lec t ronics .  The charac te r i s -  tics of  the  band-pass f i l t e r  have  been  outlined  in a previous  section. The ampl i f ie rs  and  demodulating c i rcui t  are a l l  buil t  with commercially available low- noise  components t o   ensu re   t ha t   t he   s ens i t i v i ty  and accuracy of the system'are completely determined by the  cryogenic   par t .  The output  voltage is t r ans fe r r ed   t o  the feedback at tenuator  via  an i so l a t ion  ampl i f i e r ,  so t h a t   t h e r e  is no  galvanic  ontact between e l ec t ron ic  system  and  sample. The a t tenuator  is a current   source feeding a current  proport ional  to  the output  vol tage to  a r e s i s t o r   o f  1 mQ t ha t   has  been mounted i n   t h e  c r y o s t a t   i n  series with  the  pr imary  c i rcui t   of   the  transformer. The gain of the whole system can be set t o  U, / U i  = 10% , lo6 , lo7 , lo8 or lo3 . The output  signal is f i l t e r ed   w i th  a time  constant  hat  can  be  chosen from 0.1 t o  10 seconds  and is then  recorded by a computer, a p l o t t e r ,  or another device. Applicat ion for  V(I) Measurement Experimental implications The use  of a high-sensi t ivi ty   instrument   implies  t ha t   ou r  measurements w i l l  a l so  be very   sens i t ive   to  no i se  tha t  is generated by the other equipment involved i n   t h e  experiment.  Furthermore,  the  steepness  of  the V ( 1 )  curve has important experimental implications. Voltages are measured along 1 m of wire. Even i f  t he  po ten t i a l  wires are la id   very  c lose  to   the  sample conductor, an induction coefficient of less than 0.2 pH is hardly  a t ta inable .   This  means t h a t  low-frequency r ipp le  of the sample current with a derivative of 1415 and  magnet are switched on, the latter increases  by a t  l e a s t  a f a c t o r  10. "his is mainly  due t o   t h e   c u r r e n t  source  of the magnet, which has a r e l a t ive ly   h igh  dr i f t .  Closing of  the pers is tent-mode switch el iminates  t h e  e f f e c t  of t h i s   d r i f t .  d I /d t  = 0.01 A/s is measured a s  a voltage of at  least 2 nV. Raising  the  current  with  a  constant ramp, a s  is frequently done i n  I,-measurements, is therefore  impractical  because  of  the small d I /d t   t ha t  would be allowed. The most appropriate way .is to   ad jus t   t he  cur ren t  success ive ly  to  a  number of  pre-chosen  values and t o  measure the  resulting  voltage  with  each  value. The current  source  should be able   to  maintain  the c u r r e n t   a t  a constant  value  with a high  precis ion , (bet ter   than lo-' over  several  minutes).  Apart from this,  the high-frequency ripple (remnants of the power frequency) should be as small as possible.  Although the  system is theore t ica l ly   no t   sens i t ive   for   these  s ignals ,  they may r e s u l t  i n  overloaded amplifiers, thus a f f e c t i n g  t h e i r  l i n e a r i t y .  The slope  of  the V ( 1 )  curve is much higher  than t h e  ratio V / I .  I n   t he   cu r ren t   i n t e rva l  where the  r e l a t i o n  V = IN applies ,   the   difference is a f ac to r  N, which means t h a t  a cu r ren t   d r i f t   o f q% is experienced  as  a voltage  drift   of  N*q%. A s  above, we conclude that use of a high-precision current source is imperative. I f   t h e  sample  wire is subjected  to  a magnetic f ie ld ,   as imilar   reasoning  appl ies   to   the  magnet ic-  f i e ld   con t ro l .   Dr i f t i ng  of  the  magnetic f i e l d  can  be in t e rp re t ed  as a  changing I/Ic. This w i l l  not  be mathematically worked out  here  for  reasons  of  l imited space,  but  obviously  eads  tohe  conclusion  that e i t h e r   t h e  magnet should  be  fed by a high-precision current  source as well ,  or it should be operated i n  t h e  pe r s i s t en t  mode. The l a t t e r  s o l u t i o n  was chosen i n  o u r  experiments. Lay-out of the experiment The experimental set-up is shown schematical ly  in  Fig. 5. The measurements a r e  performed on an MCA wire, 367 f i l .  NbTi:Cu=l:1.25,  having a diameter  of 0.2 mm. The wire is wound on a bobbin with a diameter of 60 mm, which f i t s   i n  a small Maxwell-type magnet generating a maximum magnetic field  of approximately 2 . 2  T. The potential   wires  are  connected  to  the  sample at  a dis tance  of  1 metre from each  other and are wound ca re fu l ly  on the  bobbin  together  with  the  sample. The compensation r e s i s t o r  is a narrow s t r i p  made of brass sheet.   with a r e s i s t ance  between the  measurement contacts   of 1 mQ at  4.2 K.  A l l  w i r ing   i nthe  measurement c i rcu i t ,  inc luding  the  pr imary  co i l  o f  the  transformer, is made with NbTi/Cu monofilament superconducting wire having a diameter of 0.2 mm. I n  order to  reduce  the  50 Hz r ipp le  of the  sample current, a low-pass f i l t e r  is rea l i zed  wi th  a  r e s i s to r  of 10 mQ and an inductance of  0.6 mH (see Fig. 5 ) .  Performance of the instrument The "dirty"  electromagnetic  environment  in which the  instrument is used  severely  deter iorates  its performance. Due t o   t h e   r e l a t i v e l y   h i g h  number of j o i n t s   i n   t h e  primary c i r c u i t  an offset   vol tage  of  several  nanovolts and a  low-frequency d r i f t  vo l t age  o f  200 pV peak, a f t e r   f i l t e r i n g   a t  T = 1 s, i s  not exceptional.  As soon a s   t h e  power supplies of  sample Figure 6. Measured voltage across the MCA wire as a function of the current. Horizontal scale: Sample current ( A ) ;  Vertical scales for the eurves from Lef t  to  right:  10 nV/div; 100 nV/div; 1 pV/div; 10 pV/div. 65 70 75 Figure 7. V(II curve of the MCA wire on a logarithmic scale. Horizontal scale: Sample current ( A ) ;  Vertical scale: Voltage across the sample ( V ) .  Figure 5. Experimental lay-out for the measurement of  V ( I )  curves. 1416 Results A typical  example  of a V(1)  curve  that  is  measured in  this  configuration  is  given  in  Fig. 6 The  applied DC field  Ba  was  set  to 1 T and  the  voltage  across  the sample  wire  was  measured  over 4 decades.  The measurement  system  showed  an  offset  voltage  of -6nV, whereas  the  offset  due  to  induction  by  the  current derivative  was  about +2nV. The two curves for the smallest voltages were measured  with  an  output  low-pass  time  constant Of 1. second, whereas the two others were obtained with T < 0.1 s. The  big  spikes  on  the  leftmost  curve  are  due to  movement  of  furniture  near  the  cryostat. If  these  curves  are  plotted  in a logarithmic  graph such 85 Fig. 7, it  is  seen  that  over  several  decades  in the  voltage  we  have V = IN with N 0 73. This  curve exhibits a smaller N value  for  lower  currents.  Although this  may  be  due  partly  to  incorrect  compensation  for offsets,  the  error  introduced  by  this  compensation  is not  big  enough  to  completely  account  for a smaller N. There  are  however  indications  that  the  occurrence  ,of asmaller N in the low-resistivity range should be expected  from  theoretical  considerations. The  distribution  function  of  the  critical  current of  this  wire  can  not  be  completely  determined  because of the  poor  cooling  of  the  sample,  which  results  in quenching  at a current  that  is  smaller  than Ic(lO'~* Qm).  At 1 T. this IC is 75.2 A. The distribution function is proportional to d2V/dIz and is  steeply  increasing  in  the  interval  that we have covered with measurements, as is shown by Fig. 8. A dip in this curve below IC. as was sometimes  observed  by  Warnes  et  al. [l], does  obviously not  occur.  Future  experiments  will  show  what  happens for  higher  currents  in a better-cooled  configuration. Conclusions A superconducting  chopper  amplifier  is a useful instrument to obtain V(1) curves of superconducting wires  over  many  decades  of  the  voltage. A sensitivity of  less  than 1 nV  can  be  attained,  if  noise  coming  from the  high-current  sources  that  are  involved  is sufficiently  eliminated.  Considering  results  that  were obtained earlier with a similar instrument, the sensitivity limit may be brought down one or two decades  more. Acknowledgements The  authors  wish  to  express  their  gratitude  to W.J.C.M. Vermeulen, E.J.H. van  Zon, D. ter  Avest  and B.J.'Oldehinkel  for  their  assistance  in  developing  the electronic  circuitry  and  performing  the  experiments. Figure 8. The distribution curve.of the c r i t i ca l  current a t  1 T .  References 1. W.H. Warnes and D.C. Larbalestier, "Analytical technique  for  deriving  the  distribution  of  critical currents  in a supercondupting  wire",. bpi. Phys. Lett., 48, 1403-1405,  1986. 2. I.M. Templeton,  "A  superconducting  modulator", J. Sci.  Instr., 32, 314-315,  1955. 3.  A.R. . de  Vroomen  and C. van  Baarle, "A sensitive 785-794 1957. superconducting 'chopper' amplifier", Physica, 23, 4. G.J. Edwards, "A simple  superconducting  chopper amplifier  for  use  in  magnetic  fields", J. Phys. E: Sci.  Instr., 4, 299-300, 1971. 5. F.  van  Overbeeke,  "DC-measurements  in  the  nanovolt and  picovolt  range",  internal  report,  Twente University, Applied Superconductivity Group, 1985 (in  Dutch). 

A superconducting modulator for extremely sensitive voltage measurements across multifilamentary superconducting wires

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A sensitive 785-794 1957. superconducting 'chopper' amplifier&quot;,

A simple superconducting chopper amplifier for use in magnetic fields&quot;,

A superconducting modulator&quot;,

Analytical technique for deriving the distribution of critical currents in a supercondupting wire&quot;,.

Overbeeke, &quot;DC-measurements in the nanovolt and picovolt range&quot;, internal report,

A superconducting modulator for extremely sensitive voltage measurements across multifilamentary superconducting wires

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