I t - » TRANÍvACTKWS 1>N INSTRI-MFNTATION ΑΝΠ MHASl'RFMl·:^T. VOL IM V .̂ NO 4. DHCl-MBlíR I98f»

Test Results of an Automatic Calibration System for AC-DC Thermal Voltage Converters and AC

Voltage Sources C H U - M I N F U . A R T C O H E E . A N D K L A U S B . J A E G E R

Ábstntci—\n autonuitic calibmtioii system has been developed for testia^ ac-dc thermal voltage converters (TVC's) and ac voltage sources. Precision, repeatability. and svi^ematic errors are investi­gated ttsiog the daU gathered from 100 mV to 1000 V over a frequency range 10 Hz to 1 MHi . The ac<-<k difference of a TVC is determined by the least-square fit to the charactrristic equation Ε = Μ") ^ith ac and dc inpaU. A mathematicAi formalism incorporating the systematic errors and the »c-óc difference, or deviation, caused by the ac input source is developed for data analysis.

I. I N T R O D U C T I O N

AU T O M A T I C s y s t e m s for ca l ibra i ing a c - d c t h e r m a l vo l t age c o n v e r t e r s ( T V C s) have been d e v e l o p e d by

N B S {!]. [ 2 ] . T h e use o f T V C ' s for cu r ren t and v o l t a g e m e a s u r e m e n t s h a s been d i scus sed in the l i t e ra tu re l 3 ] - [ 5 ] . In this p a p e r a new s y s t e m is presented w h i c h m o n i t o r s the ou tpu t s o f the r e fe rence JVC and that o f an u n k n o w η ( T V C unde : t e s t ) , and d e t e r m i n e s their a c - d c d i f ferences S imul taneous ly . E a c h ind iv idua l difference is d e t e r m i n e d by the ac and the d c cha rac te r i s t i c cu rves o f the T V C o b ­ta ined th rough the l ea s t - squa re fit of the m e a s u r e m e n t s to the equa t ion

TVCr TVCu

(1)

whe re Ε is t he ou tpu t t h e r m a l E M F of the T V C . V i s the co r r e spond ing input v o l t a g e , and k and η a r e p a r a m e t e r s CO be d e t e r m i n e d by the fit, A ma thema t i ca l fo rma l i sm is deve loped to re la te the u n k n o w n to the r e f e r ence a n d the devia t ions c a u s e d by t h e inaccuracN of the ac s o u r c e and the ca l ib ra t ion s y s t e m .

T h e bas ic idea b e h i n d the d e v e l o p m e n t of the a u t o ­ma ted sys t em is to t ake advan t age of the ava i l ab i l i ty of precis ion d ig i ta l v o l t m e t e r s and p r o g r a m m a b l e ac a n d dc sources and to avo id bu i l d ing soph i s t i ca t ed e l ec t r i c cir­cui ts for the s y s t e m . U s i n g a c o m p u t e r , w e h a v e in te­gra ted the m e a s u r e m e n t p r o c e s s and the da t a ana lys i s in to one c a h b r a i i o n s y s t e m , wh ich has e l im ina t ed r ead i n g and ca lcu la t iona l h u m a n e r r o r s comple t e ly . F u r t h e r m o r e , it is capable of gene ra t ing stat is t ical ly significant results wi thin a r easonab le a m o u n t of t i m e a n d with l i t t le o p e r a t o r at­t endance .

.Manuscript received March 25, 1986. The authors arc with Primary Standards Laboratory. Lwkheed Missiles

and Space Companv, Sunnvvalc, CA 94088-3503. lEEELoj, .>iumber 8610602.

Fig. 1. Definition of the ac-dc difference.

D a t a repor ted in th is p a p e r inc lude both the la tes t r e ­sul ts gene ra t ed by the n e w c o m p a r a t o r a n d those f rom the c o m p a r a t o r o f an o l d e r ve r s ion [6 ] . H o w e v e r , t h e f o r m e r cons t i tu tes the bu lk of the d a t a .

Π . C A L I B R A T I O N M E T H O D [6]

A. Definition of AC-DC Difference

F o r a the rmal vo l t age c o n v e r t e r / ( T V C / ) , t h e a c - d c difference at Vj is def ined by the equa t ion

(2)

w h e r e Va and V,i a re the input ac and dc vo l tages that p r o ­d u c e the s a m e t h e r m a l E M F from / (as d e p i c t e d in F i g . 1).

B. Determination of AC-DC Difference

C u s t o m a r i l y ( e . g . , [1] a n d [2]) the a c - d c d i f ference of an u n k n o w n T V C u is d e t e r m i n e d by measu r ing the q u a n ­tity

Ε a - E, (3)

for the re ference T V C r , o r for both u and r . H e r e n^ is the e x p o n e n t ( see Π ]) o f a T V C with dc inpu t , a n d a n d E¿ a re E M F ou tpu t s of the T V C with ac and dc inpu t , r e spec t ive ly .

0 0 1 8 - 9 4 5 6 / 8 6 / 1 2 0 0 - 0 3 9 6 S 0 1 . ( J ( ) ^ ; 1986 I E E E

Ρυ ff al.: TfvST RESULTS OF AUTOMATIC CAMBRA HON SYSThM W7

'"out

^out

yin (h)

Fig. 2. (a) Characteristic curves and measurement sequence, (b) Charac­teristic curve measurement, least-square fits, and the * "measured" ac-dc difference.

In this p a p e r the a c - d c difference is ca l cu l a t ed from the leas t - square fitted ac a n d dc charac te r i s t ic c u r \ ' e s , each o f wh ich is ob t a ined by fitting e m e a s u r e d da ta to (1 ) . A s ingle ac~dc d i f ference m e a ement at a rest point ( i . e . , at a cer ta in f r equency for a ed nomina l vo l t age K,. of a T V C ) is de r ived f rom four s t ies of r ead ing pai rs Eoui)^ w h e r e V^n and £out a re the input vo l t age to and out ­put E M F of t h e T V C . T h e V,^ is swi tched in the o rde r

{AC\, D C - F , DC-R. AC2) ( 4 )

w h e r e AC\ and AC2 s t and for the ac inpu t , a n d D C - F and DC-R m e a n dc wi th fo rward and reversed po la r i t i e s . E a c h of these four se r ies o f (Κ^^, E^^J,^) pa i rs t r aces a long the co r r e spond ing cha rac t e r i s t i c curves as ske t ched in F i g . 2 ( a ) . T h e reg ion c o v e r e d by these four se r ies (of read ing pairs) is e n l a r g e d as s h o w n in Fig , 2 ( b ) . N o t e that input vo l tages o f all ser ies a re s tepped up f rom the s a m e va lue V,, and wi th the s a m e s t ep s i z e . The sol id do ts indica te the measu red r ead ing p a i r s , and the c rosses and the squa res the ave rages o f the t w o dc series and the t w o ac se r i e s , r e spec t ive ly .

T h e ' ' m e a s u r e d a c - d c d i f f e r ence" is ca lcu la t ed us ing the l eas t - square fitted charac te r i s t ic c u r v e s ( l abe led as DC [LSQF] and AC [LSQF] of the a v e r a g e s s h o w n in F ig ,

2(b ) ) . T h e fits g i v e the exponen t η and its s t andard e m i r An. T h e la t te r is u s e d a s a reject ion cr i ter ion (see Sect ion I I I -C for de t a i l s ) .

# 1 Φ2

SOURCE r AC SOURCE

± ± C O N T R O L L E R

KEYBOARO M A S S S T 0 R A i 3 £ PLOTTER

Fig. 3 . Auiomauc calíbraiíon sysiem for 2i£-<k iramfor ^usiáaFái ¡asá sources.

T h e * 'measu red a c - d c d i f f e r e n c e ' ' is t he b a s i c infor­m a t i o n used in the da ta a n a l y s i s . H o w t h e a c - d c differ­e n c e o f an u n k n o w n T V C u is d e t e r m i n e d wi l l be d i s ­c u s s e d in Sec t i ons III and I V .

I I I . T H E A U T O M A T I C C A L I B R A T I O N S Y S T E M A N D I T S

OPER.ATION

T h e a u t o c o m p a r a t o r d i s c u s s e d in th i s p a p e r , a s dep ic ted in F i g . 3 , is bas ica l ly the s a m e a s tha t p r e s e n t e d in {6]. In the la t ter s y s t e m , the c o m p u t e r ins t ruc ted a s c a n n e r t o do t he swi tch ing of the inpu t v o l t a g e s o u r c e s . U s i n g an ac vo l t age sou rce with isola ted o u t p u t fea ture in the new s y s t e m , the sw i tching is n o w a c c o m p l i s h e d by ins t ruc t ing the v o l t a g e sou rces d i rec t ly . C o n s e q u e n t l y , t h e s canne r has b e e n e l imina t ed in the n e w s y s t e m . H o w e v e r , this modi f ica t ion h a s no effect o n h o w the m e a s u r e m e n t s are d o n e .

T h e t w o T V C ' s shown in F i g . 3 a re p l aced in a w o o d e n box a s ind ica ted by t he do t t ed l i nes . A me ta l l i c screen is inse r t ed b e t w e e n the inner fiberglass in su la t ion and the ex te rna l w o o d e n wal ls of the b o x . T h u s t h e Sox has bo th the t h e r m a l insula t ion and e lec t r i ca l s h i e l d i n g . T h e func­t ions o f different parts of the s \ s i e m are d e s c r i b e d in the fo l lowing th ree s tages of o p e r a t i o n .

A. Input

T h r o u g h the keyboard w e inpu t t h e fo l lowing infor­m a t i o n to start the measurement:

1) t h e ident i f icat ion of t h e T V C o n e a c h s ide of the c o m p a r a t o r ;

2 ) n o m i n a l input vo l t age 3) a c in ru t f requencies F.: 4 ) total n u m b e r of v o l t a s e s t eps p e r charac te r i s t ic c u n e

5) input v o l t a g e s t ep s ize in dV V (/?^., in p p m of 6) n u m b e r o f read ings p e r s t ep A V : 7) s tabi l i ty l imit on r ead ings (S^, 5 n V s : a measun?-

m e n t re ject ion cr i te r ion o n the s t a n d a r d e r r o r o f the e x p o n e n t η {λη) from the LSQF—stc Sec t ion I I I - A for de t a i l s ) : and

8) n u m b e r o f ' ^ m e a s u r e m e n t s ' * p e r T V C a r r a n g e m e n t p e r test po in t Λ',„.

Each " m e a s u r e m e n t " p r o d u c e s o n e set o f fitted a c a n d dc charac te r i s t i c c u r s e s for the t w o T V C ' s . T h e r e are t w o

398 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-35, NO. 4, DECEMBER 1986

T V C a r r a n g e m e n t s , be fo re a n d after s w i t c h i n g the s ides for the t w o T V C ' s .

B, Measurement

T h e con t ro l l e r does the fo l lowing in the m e a s u r e m e n t s t age .

I ) Based on the k e y b o a r d inpu t , c a l cu l a t e s the initial vo l tage

K ^ V n - {Ny ~ 1) · K„ . Ryll (5a)

and instructs t h e vo l t age s o u r c e s to s t ep u p

= I / , + m · /?, · V, (5b)

whe re

m - 0 , 1, 2 , · · · (/V, - 1).

2) Swi tches the input v o l t a g e sou rces in the o rde r of (4)

iACX. DC-F, DC'R. ACl)

for N„ t imes . ( N o t e : the ACl se r ies of the wth ' ' m e a ­s u r e m e n t ' ' wil l be used a s t h e AC\ se r ies o f the (m l ) th ' ' m e a s u r e m e n t . " )

3) C h e c k s t he .stability l imi t (on read ings ) S, and in­structs the n a n o v o l t m e t e r s t o t ake r ead ings (after the S, test has been passed each t i m e ) .

4 ) Stores the E M F o u t p u t of the T V C ' s in the m a s s s torage uni t ( M S U ) .

5 ) Ins t ructs t h e vo l t age s o u r c e s to start from I ' , a t a new le.st point .

6 ) S tops t ak ing m e a s u r e m e n t s w h e n da ta for all the F , ' s h a v e been co l l ec ted .

7) Manua l ly swi t ches the t w o T V C ' s and p roceeds the measu remen t p roces s f rom Π to 6 ) . T h e n s tops tak ing m e a s u r e m e n t s .

C. Data Analysis

W h e n the da ta for bo th T V C a r r a n g e m e n t s a re ava i lab le in M S U , the d a t a ana lys i s c a n b e g i n . T h e con t ro l l e r d o e s the fol lowing du r ing the d a t a ana lys i s s t a g e .

1) Re t r ieves the data from the M S U . 2) Per fo rms data ana lys i s that i nc ludes :

a ) Ca l cu l a t e s the η v a l u e s of the charac te r i s t i c c u r \ e s of bíMh T V C ' s t h r o u g h l ea s t - squa re fits, the individ­ual ' m e a s u r e d " a c - d c d i f fe rences , the i r relative a c -dc dif ference, a n d s a m p l e s tandard dev ia t ions ( S S D ' s ) of these q u a n t i t i e s .

H o w the " m e a s u r e d " a c - d c differences of a reference s tandard r (6,) and that of a n u n k n o w n T V C u (δ„), and the i r re lat ive difference (ό^/) , a re ob t a ined is depic ted in F i g . 4 . N o t e that the η v a l u e s a re au toma t i ca l l y ca lcu la ted in he re . But , it is not so by t h e conven t i ona l m e t h o d ( i . e . , measu r ing the relat ive di f ference d i r ec t l y ) . T h e η va lues and the S S D ' s (of fi, δ^, ó.,, a n d ό.,,) a re exce l l en t c h e c k s for the qual i ty of the ca l i b r a t i on tes t .

b ) Rejec ts p o o r m e a s u r e m e n t s . T h e s t andard er ror (Δ.»ί) of the exponen t η is u sed as re jec t ion cr i te r ion . Any

Fig. 4. Individual and relative ac-dc diflfercnces.

m e a s u r e m e n t has a An g r e a t e r t han a cer ta in l imi t is re jec ted . D e p e n d i n g o n the f r equency , the l imi t ing va lue of An r anges a n y w h e r e b e t w e e n 0 .1 to 1.0.

c) I n c o φ o r a t e s the i n fo rma t ion ob t a ined f rom bo th T V C a r r a n g e m e n t s to p e r f o r m the ana lys is u s ing the ma themat i ca l f o rma l i sm d e v e l o p e d in the nex t s ec ­t ion .

3) Ins t ructs the p r in te r t o pr in t out the resul ts of the a n a l y s i s . T h e t ime requ i red for " o n e m e a s u r e m e n t " at a test point is about 9 - 1 0 m i n w h e n seven input v o l t a g e s t eps and 5 n V / s of D V M r e a d i n g stabil i ty are u s e d .

IV . T H E M A T H E M A T I C A L F O R M A L I S M FOR D A T A

A N A L Y S I S

In prepara t ion for the d i s c u s s i o n of the resu l t s , w e in­t roduce the t e r m i n o l o g y , n o t a t i o n s , and the bas ic equa ­t ions to be used for da ta a n a l y s i s .

A. The AC-DC Difference

I. A Single Measurement: A s ingle a c - d c difference m e a s u r e m e n t for a T V C / c a n be exp res sed as

( ó j , = δ, -¥ Ca + es + Cr (6)

w h e r e δ, is the t m e v a l u e , e^ is the e r ro r caused by the inaccuracy of the ac s o u r c e , a n d e^ and £V a re the s y s t e m ­at ic and random e r ro r s , r e spec t ive ly . T h e subsc r ip t a re­fers to a par t icular ac s o u r c e a. T o s implify the d e v e l o p ­m e n t of the fomia l i sm , the e r r o r c a u s e d by the inaccu racy o f the d c source h a s b e e n in ten t iona l ly left out in ( 6 ) . N o t e that its con t r ibu t ion to the tota l e r ro r can easi ly b e deter ­m i n e d and be i n c o φ o r a t e d in t he co r rec t ion to the a c - d c difference d e t e r m i n a t i o n .

2. A Sample of Measurements: By tak ing the a v e r a g e o v e r a sufficiently la rge s a m p l e , (6) r educes to

a n d

<δ,>, = δ, -f e, ^ (es\

<er>^ = 0 .

(7a)

(7b)

FU et al.: TEST RESULTS OF AUTOMATIC CALIBRA!ION SYSTEM 399

S * i (in % or ppm)

Fig. 5 . Systematic and random errors in an ac-dc difference distribution.

T h e t e r m s <oa>^ and <^;.>^ are the m e a n v a l u e of the m e a s u r e d ' ' a c - d c dif ference of / and tha t of t h e r a n d o m

e r r o r , r espec t ive ly . T h e i n t e φ r e t a t i o n of t h e s e equa t ions is d e p i c t e d in F i g .

5 . T h e wid th of the d i s t r ibu t ion gives the p rec i s ion of the m e a s u r e m e n t s . T h e S S D is a direct m e a s u r e of the w i d t h . In Sec t ions V a n d V I w e shal l use S S D for the d i s cus s ion o f p rec i s ion .

3, The ''Right'* and the "Lefi^' Differences: W h e n T V C / is p laced on the right side of the c o m p a r a t o r , the m e a n va lue of i ts a c - d c difference is g iven by

S imi la r ly

<6^>f = δ, + + (es)^

(8a)

(8b)

(ir, % Of ßpm)

Fig. 6. Systematic and random errors and the left and right ac-dc differ­ence distributions.

T h e r e l a t i ons desc r ibed by (11) a r e dep ic ted in F i g . 6 . T h e a n t i s y m m e t r i c a l par t of the sys temat i c e r r o r m e a s u r e s t h e s e p a r a t i o n be tween the right a n d the left m e a n va lue a s wel l a s t h e i r d i s t ances from the ave rage va lue (def ined by (1 I c ) ) . T h e t e rm on the right-hand s ide of (1 l a ) is the offset o f t h e a v e r a g e f rom the t m e a c - d c difference 6j.

B. Determination of the Difference of an Unknown TVC

1. Relative AC-DC Difference: C o n s i d e r a r e f e r ence s t anda rd r o n the left and an u n k n o w n T V C u o n t h e right. E l i m i n a t i n g e^ b e t w e e n (9a) and ( 9 b ) , o n e o b t a i n s t h e a c -d c di f ference of u r e la t ive to r as g iven b e l o w :

a s uni t / is p laced on the left s ide . E q u a t i o n s (8a ) and (8b) can b e wr i t ten in the fo rm

<5 , > f = δ, + + (el\ + {et\ (9a) w h e r e

and

w h e r e

and

<δ,>ί- = δ, + e, + (el)i -

{ei\ - ies), = (es)l

(9b)

(lOa)

(I Ob)

and

Oa)^ = <^a>u - <δ.>'

= δ„ ~ δ, + D l + Si

D l = {ehu ~ iel)r

(12)

( I 3 a )

( I 3 b )

S i m i l a r i y , if w e swi tch s ides for u and r ( i . e . , w h e n u is on the left s ide and r is on the right s ide ) , w e h a v e t h e re la t ive di f ference

T h e t e r m s ( ^ 5 ) , and ies)i a r e referred to as the s y m m e t r i c a l and the an t i symmet r i ca l pa r t of the sys temat ic e r ro r for /. T h e y are indeed proper ly n a m e d , s ince o n e n o t e s that the an t i symmet r i ca l part mus t vanish if one requ i res that m e a n v a lu e s of the right and the left differences (<δ^>f and <óa>f) o f / are equa l w h e n the sys tem is s y m m e t r i c .

E q u a t i o n s (9) and (10) fo rm the bas i s for t h e da t a ana l ­y s i s . So lv ing for e^ + el a n d e^ in t e rms of the m e a n va lue a n d the t rue va lue of t h e a c - d c difference, o n e ob ta ins

(11a)

( l i b )

<δ.>ίί = <δ.>ί; - <δ,>?

= δ„ - δ;. + DI - Sur- (14)

e, + e's = AvidJi - δ,

eí = i «δ.>Γ - <δ.>ί')

E q u a t i o n s (12 ) and (14) g ive the relat ive a c - d c differ­ences for t he t w o different T V C a r r a n g e m e n t s in t e rms of the a c - d c di f ference of individual T V C ' s and c o m b i n a ­t ions o f s y s t e m a t i c e r ro r s . T h e y a r e general r e la t ions a p ­p ly ing t o a n y two T V C ' s .

2. The AC-DC Difference of the Unknown u: R e a r r a n g i n g (12) and (14) , w e ob ta in the a c - d c di f ference of the u n k n o w n u for the t w o different T V C a r r a n g e m e n t s as fo l lows :

w h e r e and

^ι^<δ,>. = \ «δ ,> f 4- <δ,>ί). ( l i e )

δα = δ^ -r iha)^^ - DI - si

δ, - δ, + iKYfr - O l + S

(15a)

(15b)

4 0 0 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-35, NO. 4, DECEMBER 1986

By c o m b i n i n g t he t w o p rev ious equa t ions , w e h a v e

δ . = 5r + i * l<8a> RL + <δ.>ίί] ~ Dl, (16)

( k n o w n ) ( m e a s u r e d ) (es t imated)

N o w w e h a v e r educed the re la t ion for d e t e r m i n i n g the a c -d c d i f ference o f the u n k n o w n u t o one quant i ty D^r t o b e e s t i m a t e d . U s i n g t w o k n o w n s t andards r' a n d r o n e c a n u s e (15) a n d (16) to e s t ima te t h e values o f Df^ and 5^^.. By def ini t ion ( 1 3 b ) , t h e la t ter c a n also be ca l cu l a t ed w i th ( l i b ) . E q u a t i o n s (15) and (16) a r e the genera l r e l a t i ons to be u sed to d e t e r m i n e the a c - d c difference o f an u n k n o w n T V C w.

C. Calibration of an AC Source

U s i n g (9) and (11a ) one can expres s the i n a c c u r a c y of an a c sou rce a s fo l lows :

^ = = - δ, - [ ( 4 ) , + iet)^] ( I 7 a )

7 7 = ^« = <^^>ί' ~ δ, - [(el), - (e^),] (17b)

77 = ^o- Av(dJ, - 0, - (el)^ (18)

w h e r e / is a k n o w n T V C . Equa t i on (18) can a l s o be o b ­ta ined by c o m b i n i n g (17a) and (17b) . T h e i n a c c u r a c y is exp re s sed in t e r m s o f the ra t io o f ΔΚ^ to the n o m i n a l d c vo l t age of the test . T h e sys temat i c e r rors in t h e a b o v e equa t ions h a v e to b e p r e d e t e r m i n e d . H o w e v e r , if e^ is k n o w n t h e n o n e can d e t e r m i n e the inaccuracy o f an u n ­k n o w n sou rce a' by

ea^ - e,= <δ,.>Γ - ( ó ,> f (19a)

(19b)

w h e r e / c a n be an u n k n o w n T V C . Equat ion (19) is de r ived from ( 1 7 ) .

V . R E S U L T S

D a t a r epor t ed in th i s sec t ion conta in all the m e a s u r e ­m e n t s t a k e n in the last 18 m o n t h s . D u r i n g that t i m e dif­ferent t y p e s and leng ths of c a b l e s , different c o n n e c t o r s and d ig i ta l v o l t m e t e r s , and e v e n different a c s o u r c e s h a v e been u s e d . N u m e r o u s tes ts and i m p r o v e m e n t s h a v e b e e n m a d e for t h e au toma t i c ca l ibra t ion sys tem. H o w e v e r , even wi th m a n y modi f ica t ions , bas ica l ly the s y s t e m is o f the same t y p e . T o t ake a c ons e rva t i ve v iewpoin t , in s t u d y i n g each o f t h e quant i t i es in t roduced in this p a p e r , w e a l w a y s use all t he da ta ava i l ab le inc lud ing the wors t c a s e . In a b r o a d e r s e n s e , it e n h a n c e s the statistical s ign i f icance o f the s tudy o f th is n e w au tomat i c ca l ibra t ion s y s t e m . In t he fo l lowing d i s c u s s i o n , excep t fo r one case ( r epea t ab i l i t y . Sec t ion V - B ) , w e shal l not separa te the da ta o b t a i n e d in different s t a g e s . Th i s m e a n s tha t the l imits of all the q u a n ­t i t ies q u o t e d in this p a p e r shou ld be rather c o n s e r v a t i v e .

A s a r e m i n d e r , t h e da ta p resen ted here w e r e t aken at

100.0

1 FREQUENCY (Hz)

V/A 1 Sid Dev. =0 .5-6 ppm \:^ΐΣ\ 1 Sid Dev.i1~10 ppm

1 Std Dev. = 3-60 ppm

1 Std Dev. - 30-100 ppm

to be tested

1 Std Dev. =^160-550 ppm

Fig. 7. One S S D of the relative ac-dc difference.

test po in ts that are c o m m o n l y r equ i r ed for ins t rument ca l ­ib ra t ions . F o r major i ty o f the d a t a , m e a s u r e m e n t s w e r e not m a d e in the ideal s i tua t ions . W h e n the appl ied vo l t age is m u c h l o w e r than the nomina l v o l t a g e o f the T V C ' s o r the full r ange o f the vo l t age s o u r c e (espec ia l ly at the u p ­pe r l imi t ing f requency of t h e s o u r c e ) , t h e sys t em d o e s not per form as wel l as it is expec t ed t o . T h u s la rge unce r t a in ­t ies resul t , e . g . , at 100 m V and a r o u n d 1 M H z .

T h e da ta p resen ted in this p a p e r c o v e r a vo l t age r a n g e from 100 m V to 1000 V . At 4 V o r b e l o w , the T V C ' s used a re j u s t t he rma l e l e m e n t s . A b o v e 4 V , t h e T V C ' s a lways cons is t of a the rma l e l e m e n t a n d a range res is tor . T h e fo l lowing are the g roups of s a m p l e s used in the d i s ­cuss ion b e l o w .

G r o u p A : vo l t age from 100 m V to 1000 V , f requency from 10 H z to 1 M H z , and ten m e a s u r e m e n t s p e r T V C a r r a n g e m e n t at each test po in t .

G r o u p B : at 0 .5 V and 2 0 k H z , w i th 5 0 m e a s u r e m e n t s per data po in t . ^

G r o u p C : 6 0 0 V at 2 0 and 5 0 k H z , wi th 5 0 m e a s u r e ­ments p e r da ta point .^

F o r G r o u p s Β and C , there m a y b e m o r e than o n e da t a point for a T V C a r r a n g e m e n t at a tes t po in t .

A. Precision

U s i n g G r o u p A w e obta in the d i s t r ibu t ion of 1 S S D va l ­ues of t he rela t ive a c - d c d i f ferences ( (12) o r (14)) as shown in F i g . 7 . A b o v e 3 9 0 m V a n d u p to 1000 V , the largest shaded area in the figure h a s t he bes t 1 S S D va l ­u e s , app rox ima te ly 0 . 5 - 6 . 0 p p m . H o w e v e r , the major i ty of the da t a points in this a rea l ie a r o u n d 2 - 2 . 5 p p m . T h e h igh- f requency region (500 k H z to 1 M H z ) h a s the la rges t 1 S S D va lues ( 3 - 6 0 p p m ) . B e l o w 3 9 0 m V and d o w n to

' -Part of this group of measurements was taken with the comparator of the earlier design | 6 ] .

FU et al.: TEST RESULTS OF AUTOMATIC CAUBRAHON SYSTEM 401

Δ 300 mV O 1 V • 900 V

• O.S V Χ 3.B V

4

Ίο 50 ισ* ^ 1 0 * 10* 10* ίο* FREQUENCY (Hz)

κι. RL RL Fig. 8. Repeatability: Δ<6,>ί? = | « δ . > ! ; ) 2 - «ö ,>t f ) . i .

100 m V , t he 1 S S D v a l u e s a re a r o u n d 3 0 - 1 0 0 p p m b e ­tween 10 H z and 100 k H z , a n d 1 6 0 - 5 5 0 p p m be tween 100 k H z to 1 M H z .

B. Repeatability

In F ig . 8 w e p lo t as a funct ion o f f r equency the abso lu te va lue of t h e d e v i a t i o n b e t w e e n t w o m e a n re la t ive differ­ences of the s a m e k i n d at 3 9 0 m V , 0 . 5 V , 1.0 V , 3 . 9 V , and 600 V . H e r e a f t e r w e sha l l refer to th i s dev ia t ion a s Δ . T h e da ta a re t a k e n f rom al l t h r e e g r o u p s A , B , a n d C when.f ; t he re is m o r e t h a n o n e set o f m e a s u r e m e n t s o f a relat ive a c - d c d i f ference a v a i l a b l e . T h e e r r o r bars s h o w the combined t h r e e s t a n d a r d d e v i a t i o n s . T h e e r ror is e s ­t imated at th ree t i m e s o f t h e s q u a r e roo t of t he sum of t he squares of 1 S S D ' s o f t he m e a n re la t ive differences f rom the two sets of m e a s u r e m e n t s , o r

Error = 3[(1 S S D of M, )^ 4- (1 S S D oí M^fY'^ (20)

w h e r e Μχ and Mi r e fe r t o t h e m e a n v a l u e s of the s a m e relat ive difference o b t a i n e d f rom t w o se ts of m e a s u r e ­m e n t s , set 1 a n d se t 2 , r e spec t ive ly .^ Only the largest er­ror at each frequency is plotted.

Based on the d a t a s h o w n in F i g , 8 , w e o b s e r v e the fol­lowing .

1) T h e va lue of Δ i s l e s s t h a n 10 p p m b e l o w 2 0 0 k H z and a round 2 0 0 p p m o r less b e t w e e n 2 0 0 k H z and 1 M H z , T h e main con t r i bu to r s to t h e l a rge Δ v a l u e s in the h igh -frequency reg ion a r e d a t a p o i n t s f rom 0 , 5 and 3 ,9 V , In both cases the Δ v a l u e s w e r e e v a l u a t e d u s i n g data t aken at t imes sepa ra t ed b y at l eas t e igh t m o n t h s . In add i t ion , they w e r e t a k e n e i t h e r a t o r n e a r t h e u p p e r l imit ing fre­quency a n d at 5 0 p e r c e n t o r l e s s of the ftiU range of t he a c source . T h e n , a f t e r r e m o v i n g da t a f rom 0 , 5 and 3 , 9 V in the h igh- f requency r e g i o n , all the res t o f the data po in t s in F ig , 8 (excep t o n e po in t at 1 M H z a n d 390 m V ) l ie be low 10 p p m . A g a i n the e x c e p t i o n a l c a s e was t aken a t

^Part of this group of measurements was taken with the comparator of the earlier design [6],

t h e u p p e r l im i t i ng f requency and l e s s than 5 0 percen t of t he full r ange < 1.0 V ) o f the s o u r c e . In o r d e r to m a k e a m o r e definite s t a t e m e n t in t he h igh - f r equency reg ion , re ­p e a t e d n e w m e a s u r e m e n t s h a v e t o b e m a d e the re ,

2) Er rors of m a n y o f the Δ ' 8 ( e spec ia l ly above 2 0 0 k H z ) are s m a l l e r than the v a l u e o f Δ ' 5 t h emse lves . T h i s ind ica tes tha t in t hose cases the re w a s a significant c h a n g e in t h e s y s t e m b e t w e e n t imes w h e n t h e t w o samples w e r e t a k e n . T h e c h a n g e s d u e to modi f ica t ions of the sys t em c a u s e d the m e a n re la t ive dif ferences t o shift significantly (wi th respec t to the t h r e e s tandard dev ia t i ons ) but h a d lit­t le effect on the p rec i s ion .

C. Asymmetry

T h e a s y m m e t r y o f t h e ca l ib ra t ion s y s t e m is defined by the a n t i s y m m e t r i c a l par t of t h e s y s t e m a t i c e r ror (^5)/ ( l i b ) . I dea l l y , w h e n a T V C i is s w i t c h e d from the left s ide to the right s ide , o r v ice v e r s a , t h e m e a n va lue o f its m e a s u r e d a c - d c difference s h o u l d shift b y twice the a m o u n t of (^5 ) , . T h e la t ter v a n i s h e s if the sys t em ( inc lud­ing t h e t w o TVC*s) is per fecdy s y m m e t r i c . F i g . 9(a) and (b) s h o w s t h e ^ 5 va lues of the t w o T V C ' s present in the s a m e test run a s a funct ion of f r equency at 390 m V to 1000 V a n d at 100 m V , r e spec t ive ly . O n l y the la rges t er­ror a t each f requency is p lo t t ed .

In F i g , 9 ( a ) , t he d a t a poin ts t e n d to be d is t r ibuted n e a r ze ro but o n the nega t ive s ide o f 6 5 , H o w e v e r , in m a n y c a s e s the v a l u e s of t he t w o T V C ' s f rom the same test run h a v e app rox ima te ly equa l m a g n i t u d e and a re of oppos i t e s i gns . T h e m a g n i t u d e o f the a s y m m e t r y is abou t 5 p p m or less be low 5 0 0 k H z , and 120 p p m o r less at 1 M H z , In F i g . 9 (b) t h e a s y m m e t r y is nega t i ve at all f requenc ies , and has a m a g n i t u d e of 6 0 p p m o r l e s s b e l o w 5 0 0 k H z , and 350 p p m o r l ess at 1 M H z ,

D, Offset

T h e offset o f the ca l ibra t ion s y s t e m is defined by Ca -f (^s)i as g iven in (11a ) . F i g . 10 s h o w s the offset as a func­t ion of f r equency for da ta from 0 . 5 , 1.0, 3 . 9 , 10, 3 5 , 100 , 6 0 0 , and 1000 V . The error bars indicate the largest er­ror at each frequency. The offset l i es in the range of —120 to -h 160 p p m b e t w e e n 10 H z a n d 6 0 k H z , and in the r a n g e of - 1 2 0 to 4-500 p p m above 5 0 k H z u p to 5 0 0 k H z . S o m e of t h e s p r e a d i n g of the data po in t s a r e d u e to modif ica t ions d o n e o n t h e c o m p a r a t o r s at d i f ferent t i m e s . Signif icant shifts o f t h e offset, fo r e x a m p l e , t h e da ta po in t s at 2 0 , 5 0 , and 100 k H z f rom 3 . 9 ν and 3 5 V , a r e ma in ly caused by the c h a n g e of t he input ac s o u r c e . T h i s t ype of shift can eas i ly b e u n d e r s t o o d in t e rms o f

and S'^r'r^

B a s e d o n the data from s u b g r o u p s of G r o u p s A and C , w h e r e the a c - d c differences o f b o t h T V C ' s present in a test run a r e a v a i l a b l e , p a r a m e t e r s (16) and 5^v (15) h a v e b e e n ca l cu la t ed . T h e abso lu t e va lue of aga ins t f requency at 1, 3 , 9 , 3 5 , 100 , 6 0 0 , a n d 1000 V is p lo t ted in F i g , 1 1 , In the fo l lowing d i s c u s s i o n w e shall s imply use D and S t o d e n o t e the p a r a m e t e r s .

402 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT. VOL. IM-35, NO. 4, DECEMBER 1986

(a)

80

40

1 0

«< Vi '40

'80

'120

-160

•

lOOmV

/ I r : ]

i 1 L —

: : [ Γ

L

i 1 L —

1 0 10^ 10^ 10^ 10

I

\ )

400

200

0

'200

•400

- 6 0 0

'800

10^

FREQUENCY (Hz)

(b) Fig. 9. (a) Asymmetr>' of the calibration system between 390 mV and 1000

V. (b) Asymmetry of the calibration system at 100 mV.

0) + (if-

.1 I o U C 3 9 i/

\ X ro V ^ 600 V

35 V © TOGO V "7 fOO V

^ J

10^ 10^

FREQUENCY (Hz)

Fig. 10. Offset {e^ + €¡).

10^ 2XtO^

T h e S v a l u e s a r e usua l ly of the o r d e r o f a f ew par t s p e r mi l l ion o r l e s s , e x c e p t a t 1 M H z w h e r e o n e v a l u e is c l o s e to 27 p p m . T h e v a l u e o f D va r ies f rom less than 1 u p to a r o u n d 6 0 p p m . T h e r e is a t e n d e n c y that it ge t s l a r g e r n e a r t h e u p p e r f r equency l imi t s of t he ac s o u r c e a t different vo l t ages ( e . g . , 1 M H z b e l o w 100 V , 100 k H z at 100 V , a n d 5 0 k H z at 6 0 0 V ) . O n e m a y n o t e tha t the S d e p e n d s on ly o n the m e a s u r e d q u a n t i t i e s . H o w e v e r , D d e p e n d s on bo th the m e a s u r e d quan t i t i e s and the va lues of t he a c - d c di f ferences o f t he t w o k n o w n T V C ' s . T h e l a t t e r , e v e n t h o u g h t r a c e a b l e t o N B S , w e r e d e t e r m i n e d by different ca l ib ra t ion l a b o r a t o r i e s o v e r a t i m e span of m o r e t han ten y e a r s . It is i n t e n d e d tha t the D v a l u e s wil l b e r eeva lua t ed

wi th t w o sets of T V C ' s , bo th o f w h i c h a re t o be ca l ib ra ted by N B S .

E . The Exponent η

T h e measured ind iv idua l a c - d c di f ferences a r e c a l cu ­la ted us ing the l e a s t - squa re fits t o ( 1 ) . H e n c e the e x p o n e n t η mus t a lways b e d e t e r m i n e d first. F r o m the da ta of G r o u p s Β and C w e o b s e r v e tha t t h e m e a n v a l u e of of a T V C differs no t m o r e t h a n 1.25 p e r c e n t b e t w e e n t w o s a m p l e s , even t h o u g h different c o m p a r a t o r s w e r e e m ­p l o y e d . Therefore the value of the exponent n„ and its S S D can be used as initial indicators to see whether the cali­bration system is functioning properly. T h e y a l s o can tell

FU e! al.: TEST RESULTS OF AUTOMATIC CALIBRATION SYSTEM 403

o IV • »001^

X ».»v ^ «oov Δ 361^ ·1000ν

r

ι f<M>

f.O

a i

c 5 f<M>

f.O

a i

f<M>

f.O

a i

f<M>

f.O

a i

FREQUENCY (Hz)

Fig. 11. Estimate of the absolute value of Df,.

X ' 7.4 1SSD-.0183

Ü

ω

1.630 1.638 1.646 1.610 1 6 5 0 1 690

> 24,

0 1 SSD=.O048

( > / o )

1SSD-.0 190

I

1.690 1.700 1.7 10 1.670 1.710 1 750

Fig. 12. The exponent η without RFIS.

t he qual i ty o f the m e a s u r e m e n t s . T o i l lus t ra te the po in t , the e x p o n e n t s a n d for b o t h T V C ' s u n d e r the same fixed a r r a n g e m e n t a r e plot ted in F i g s . 12 and 1 3 . T h e only difference i n t h e ca l ibra t ion s y s t e m s for t he t w o figures is tha t the D V M at t h e left for F i g . 12 w a s r ep laced by a m e t e r w i t h R F in ter ference s h i e l d i n g ( R F I S ) fo r F i g . 13 . T h e data h a v e b e e n fitted t o G a u s s i a n s as s h o w n b y the c u r v e s . T h e c h i - s q u a r e o f the fit a n d the v a l u e of 1 S S D of each s a m p l e a r e g iven in the subf igures . B o t h t he chi-squa re a n d t h e S S D show c o n s i d e r a b l e i m p r o v e m e n t in F i g . 13 . L o w e r ch i - squa re impl i e s tha t the s a m p l e ag rees be t t e r w i t h t h e ' * r a n d o m n e s s " a s s u m p t i o n , a n d tha t the errors can be broken down loosely in the manner as de­picted in Fig. 6. T h e smal ler S S D v a l u e s in F i g . 13 sim­ply m e a n b e t t e r p r e c i s i o n .

V I . C O N C L U S I O N

W i t h t h e n e w a u t o m a t i c s y s t e m w e h a v e p r o d u c e d sta­t is t ical ly s igni f icant data to d e t e r m i n e the p r e c i s i o n and the repea tab i l i ty o f m e a s u r e m e n t s . T h e 1 S S D dis t r ibut ion s h o w n in F i g . 7 we l l represents the p rec i s ion of the sys­t e m as con f i rmed by samples o t h e r t h a n G r o u p A . Excep t

1.694 1 702 1.7 10 1.670 1 7 10 1 750

Fig. 13. The exponent η with RFIS.

for t w o small v o l t a g e - f r e q u e n c y regions w h i c h are to b e tes ted , the 1 S S D v a l u e o v e r a vo l tage r ange o f 3 9 0 m V to 1000 V is a b o u t 0 . 5 - 1 0 p p m be tween 10 H z - 5 0 0 k H z , and 3 - 6 0 p p m a b o v e 5 0 0 k H z u p to I M H z . A t 100 m V the 1 S S D va lue is m u c h h ighe r . It is abou t 3 0 - 1 0 0 p p m b e t w e e n 10 H z a n d 100 k H z , a n d 1 6 0 - 5 5 0 p p m from 100 k H z to 1 M H z . Repea t ab i l i t y in t e rms o f the m e a n v a l u e of the re la t ive d i f ference of t w o T V C ' s is a b o u t 10 p p m o r less b e t w e e n 10 a n d 2 0 0 k H z , and 2 0 0 p p m o r l e s s ab o v e 2 0 0 k H z u p to 1 M H z (see Sect ion V - B for a d e ­tai led d i s c u s s i o n ) .

T o d e t e r m i n e t h e a c - d c difference of an u n k n o w n T V C , one c a n use e i t h e r (15) o r ( 1 6 ) . The only quan t i t y tha t needs t o b e e s t i m a t e d is D in ( 1 6 ) , s ince the v a l u e of S in (15) c a n readi ly b e ca l cu l a t ed b y using ( l i b ) . W i t h t w o k n o w n T V C ' s w e h a v e e s t i m a t e d the va lue o f D . I t va r i e s app rox ima te ly f rom —60 to 4 - 6 0 p p m . T h e m a g n i t u d e in ­c reases with f r e q u e n c y . As d i scussed ear l ie r , b e t t e r e s t i ­ma te s on D and S wi l l b e d o n e in the n e a r fu tu re .

F ina l ly , wi th t h e a u t o m a t e d sys t em w e are a b l e t o g e n ­erate sufficient d a t a for e x a m i n i n g var ious a s p e c t s of t he m e a s u r e m e n t s s u c h a s the r a n d o m n e s s of the m e a s u r e ­men t s of a s a m p l e ( s ee Sec t ion V - E ) and the i n c o n s i s t e n c y in the m e a n v a l u e s of t he re la t ive difference ( s ee Sec t ion V - B ) . Careful e x a m i n a t i o n o f these aspects s h o u l d g u i d e us to fur ther i m p r o v e the s y s t e m .

R E F E R E N C E S

[1] E. S. Williams and J. R. Kinard, '*A dual-channel automated compar­ator for ac-dc difference measurements," in Proc. Precision Electro­magnetic Meas. Conf., 1984, pp. 191-192; also/££"£ Trans. Instrum. Meas., vol. lM-34. no. 2, pp. 290-294, June 1985.

[2] K. J. Lentner. D. R. Flach, and B. A. Bell, "An automated ac/dc thermal voltage converter and ac voltage calibration system," Nat. Bur. Stand., Rep. NBSIR 84-2973, Nov. 1984.

(3] F. L. Hermach, ** A C - D C transfer instruments for current and voltage meas. ," ¡RE Trans. Instrum., pp. 235-240, Dec. 1958.

14] F. L. Hermach, "AC-DC comparators for audio-frequency current and voltage measurements of high accuracy," IEEE Trans. Instrum. Meas., vol. IM-25, no. 4, pp. 489-494, Dec. 1976.

[5] E. S. Williams, "The practical uses of ac-dc transfer instruments," Nat. Bur. Stand., Tech. Note 1166, Oct. 1982.

[6] C. Fu, A. Cohee, and K. B. Jaeger, "Preliminary results from a semi-automated comparator for testing the ac-dc transfer standards," in Proc. NCSL Workshop and Symp. Conf., 1985, pp. 113-131.