A New Design AC-DC Measuring Instrument Citation Pullen, Keats A., Jr. (1939) A New Design AC-DC Measuring Instrument. Bachelor's thesis, California Institute of Technology. doi:10.7907/cpa2-9290. https://resolver.caltech.edu/CaltechTHESIS:12132024-223457473 Abstract No abstract. Item Type: Thesis (Bachelor's thesis) Subject Keywords: (Electrical Engineering) Degree Grantor: California Institute of Technology Division: Engineering and Applied Science Major Option: Electrical Engineering Thesis Availability: Public (worldwide access) Research Advisor(s): Unknown, Unknown Thesis Committee: Unknown, Unknown Defense Date: 1 January 1939 Record Number: CaltechTHESIS:12132024-223457473 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:12132024-223457473 DOI: 10.7907/cpa2-9290 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 16924 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 17 Dec 2024 00:00 Last Modified: 17 Dec 2024 00:19 Thesis Files PDF - Final Version See Usage Policy. 14MB Repository Staff Only: item control page

SENIOR T~IBSI S A NEW JESIGtJ AC-DC i-:EASUR [ rm INSTRU1V~NT Electrical Engineering De partment Presented by Keats A. Pullen Jr. CALIFORNIA DffTTTUTE OF TiX~HN OLOGY I() 39 Eub.iect, m&.jor or minor PB.ge Introduction 1 Ba:::ic ?r inci nle 1 Develonrr.ent DC f-.C 7 nperntinv ChF...rctcteristics l e, DC 14 Equivalent oper a tin r circuit Theory lb 16 Effect of ~ize on stn~itivity 17 Fffect of le ,1 ka ge flux on sensl ti vi ty 18 AC c-unrr.e ter 19 DC fiel d ~istribution fources or Error Gener,31 Vo 1 trr:e t (ff 1 11 a t trnP. t er DC models Further r evelonrr:ent 1 DC in:c" truments AC in s trument ~-. Conclusion Index to Appendix PO I. J\ :sfe w De si gn J; C-DC :••'easur ing Tn!3trume n t This pa pe r will cover ratn r compl e t e ly a ll wor k done in the d evelo pme nt, both 1T c1 ctic,,. l ;:md theoretic '-;,l, \e ve lo pme nt, o ;:Y er n ting c h c,.,r ac t er istic s , t he ory, s ources of e rror in the d iffe r en t t y ··e s, r:l.i r • ction s i n 1,•hich de ve lo pment must b~ con t i nued , ~ n~ conclu s ion. 3 as :L c ?rLn c iDlE:' The or i ~inal idea ~a s a c qu i r ed fr om t he s tudy of t he '<elv in cur ren t b ;:. l ;:n c e a.n o.. De L2 3 iv0°s b a tt e r y . The a mp l y ex pl ai n ed by illu s tr a t ion 1. The s e b ~l a nc cs shO"'· r c: th( r l o," s en sit i vity in Actual ope ration. They ar e r Pt ~ r li ke l y t o h s ve Flo. 40.-Kelvin current balance. h i gh ' lo s s es in the for m of Fi gure 1. e -~1 ay current s i,,-he n the y a re us e cl on Al t E? rna ting c ur 2en ts. t t consists of a fl oa tinf b a tte r y 1"hi c h h P.s a c o :i_l of V'.1 ire connecte '3. to its plite~-- Bringinr; the mr ,gn e t up to the coil will cause the coil either to encomp2ss t he mE:grn-, t, or to turn around and 8 ncompass it. If one takes the st~t ionar y coils oh the Kelvin b a lance, and re places them with a rinc of iron, to 1':hich 1:2gn!: tism Fi gure ~~ is app lie~ either externally or int(· rnally, one c an caus e the mow: aole coils to e x peri e nce a turning couple if they 2.re properly connected . This conm, ::::tion is such thr t the one coil experie nc es a forc L t e n d ing to carry it to the cente r of the pi e c~ of iron, ~n ~ the othe r one r.. for ce tryinz to ym s h i t ~e lf off the i r·on. This is th8 b a sic principle under lyine; trw instrumE.nt. Develonment Pll of the ori gina l de v e lo p~ent ~ark ~es ri one ~ ith di. rect current rr: odels. The first rnethorl trier:1 ''' : : s the use of a.n exte rrn ,l rrn.f,nE:' t to excite the iron ring on which the coils move d. This of course vm s ins nired by the pr ese nt D0 fa.rs e nval Fi gure ::., DESIGNED /9.JT KEA TS PULL.EN . P(ILLE'N IMSTRl/MEIVT 3. instruments. The genera l l a yout is shown in fi gur e ;-s. The two coils are c=irranged as shown in the r:irint, with a fr &me of brass wir e c,1..rrying the:: po L1tc~ r, pivots, s prings, e tc. The rin g was of soft iron, being excited by ::m external magn8t. It was foun d tha t the d i s t d1 ce of the r.'l rJ.gnet fro v: t he f :-ccs of the rine V"c' S r,.:;_ the r i.rr:portant. Y'/1P. n th(➔ magnet WEtS placed n ,, ;:tr to the ring, the sensi tivity was rathto r low. If, on t he otne r hand, the s pe. cing v\i ere about thr ee qm:rte r s of a n inc h on e,: ch polP. , the sen s itivity tu:cnF:d out to b e r ,. thc r high . The first ss t of coil s fit clos e l y to the rine . When a. pcdr of coils hb.. ving a consider ably 1 , r ger crossect ion was rn;:,.de ~n,J instolle'3 , thE~ s 1- nsitivity 0 -:.v as founri to be v ,_ ry l o\'' cornp,.red to tl1e value shown under t ~1c prev ious test. ':'ht::, of C')Ur '.'·e me;:n t th;::,t the flux vims l eu vi rn.,. the r inc and turnl n c be c k A. lon g it, thto reby p(.,rr:iittinr; the flux to esc r\!k pr, ss1n e t hrough the c o ils in such ,:1 mannt::, r th;.. . t they on. PJ' E; u cted Various type s of flux conc 0-:nt.c~.: tors wer e t l: s ted ~ ith the magn e t to see if a pp lying the flux ov~r a v e ry s ma ll are a of ths e n d of t he rin g se gme nt would ch~ng e sensitiv t:.· . to. It w~: s f ound th,: t this ri .i 1l not ,; 'vrk. ':.' .i th thr eE: hundr c·d ohms in the rr,oving a.s s0mbl~- , In 4. and this grcivi ty return, sensi ti vi ty of a,jout r, h1..;ndred microamperes full scale ;,'i &S 2. chieved. Th, t v:;:,s 1-., ith thE ~gap to magnet di.sta.nce of tri.r c E: q .&rtf:r;::. of c-n inch. The megn~ t u 2cd in the experiments wa s rather weak, being of ordinary tungston steel, and being _pretty thoroughly dem;::,,gnetized E:i. t the time it ·?ras used. The flux d~nsi ty being used was prob 1_~bly not more th&n three or four gauss. This would le,ld one to sus cect thE; t fairly good sens i ti vi ty should be obt~.• inable. ,,·he n this form of thE instrum·, nt WF:, s de ve loped as fur as wo. s Tlractical, th(:' possibility of an internal magnet for the exci t, ,. tion of the instrument Vic.:.s consider t; d. A schematic diagram of this No 6 PR.11yc1PLt OF oPEQAnON £,vc,N£tR1No RestA!lCM DC PULLEN hvsTRuHt f'fT cA(r£c H Et.urR ICAL D RAWN t9J B CAuF. /Ns r. T£c ,- particular model is shown in f.i.gure 4. Figure 4. A s pecial magnet vrn.s designed by the author and made by Indiana Steel Products Company. in:, talled. P.. r,ither heavy moving ass c moly was built and ~prings used were strong e nough to hold the r,eriod to about a second ;c,nd a hfalf. could have been built with about & !he moving F..ssembly quarter the weight it haa, so the oeriod could hnve been h a lved. Aft e r attem pts mRde to u se ir on ba l a ncinr scre~s r e sulte d in s, lnr~e ouantitief of attraction b• in~ in evidenc~, br&~s 2-5cxl/~ bf l;..nc ine: sere -~ over the m ving coils ·,,ere u~ed . The actuEl structurr1l asserr:.bl:y can be sr_ en from th . dic:p;:rmnatic and TJhotof!r~, hie vir_;\' r shorn hL:re . The method of assembly is v6~Y similc-.r to that of thL previous rr.odel . ·The c1dditjon of the xci ted ring re sul tr-~ in P ver: p-reFt increF~e of sen~itivity. flux is beinp- used rruch more efficiently . Yigure 5 . tn even more efficient nu~i n hF~ been mavnPts, rn, etinr in the center of th(• E!rca on ..,nich thE coil noves . 11 ~ I [, t S Finll'E L. M They ,.rt mounted so that they hPV8 their ~~rnetic fields onDosing cr c h other , ~ith tht result tnat her~ th f lux crosses tht center of the rinv insts~rl of roinu thlou~~ the iron. 'The rracnetic flux out·nut c1lonv the n;:;vnet is 2nproxinF.tely con~tant for 6. different 8.ir g&.ps and paths, so that all t::-w 111;.x from the magne t~, , a~suming they L-.re J ala.nc cd , ·will be useful flux. 'there is of course a dr:,m0.gm, ti zing effect e n the magnets ~he re they have long a irgans , but expe riwnts indicate th; .. t with the cnoice o.:f' proper rnagm-, t m,, ter iE.ls, va.lue. thi .' can be h e ld t:, a suff icic ntly smB.11 ThG node l shown in the photo,;~:ranh 1:-.e n t on a journey to '-Tevib:::-k, ?Tew ,Jersey r-,nrl b ctCk ,' ithout indicating 0 any appreci&ble change in s e nsitivity . not be checked exF-.ctly, EtS Diffsrenc 0~ could it ·<i 'r.:s irr,po ssible to compm'e Bgainst the '. arr,.e me ter RS was used for CcLlib re tin g . 0 AftE:r thi s original rrodel ·vrns ·o uilt, the structure of the in~ trume nt '::;::. s given cEir-eful con~d dt:r a tion to s.ee ho it could oe r edesi ?,ncd for more ruggedncsE; . In the model shrr~n the support fo r th~ ffieter itself ~Rs by ~ey of the assembly carryin g the pivots an d springs. Obviously this ·would put the s 1 , pport ,~ssLmoly un'.:l.e r str a in 1'.; i th ver y good possibilities, th,- t it v'ould gt"t s ~rung in the cour se of use. As the m~fn~t is the heaviest pa.rt of the thing, the lof:ic2 l i thin~ to do is to place the sup ports on the m~vnet, an4 have i.t hold t r 18 r •:. st. J,. rn uch i.mproved i si.rn is shown in f icure 7. J;ctuc:; lly, the F'igurE, 7 . 7. supr;ort pins should go complr,tc ly th.rough thE, rrn=:gnet for one to get the IJ1r'i x irru1n of rigi ity. J\1so the mounting brc:ckets should be rli1ced next the mrrnct. .'\'.'Ork on the F:.O{:'net .As further r-:oiol ?oulcl h:se rn"cessit;ter:l lrTge expenoitures for experi.!rent,'Jl ru'gnPts, s:ince the funds "'ere not availRble, "M)rk w:l th thf:~ r::;c r::, .P' rn·t rr:odel ,··us temporarily discontinued. JaturHily, tne next 2 0lication to come to mind •':as oossible use on F!ltern;::; tins curren-zs. rne2furerr.ents CtTE f:incl rather e;:, sily mc• de on ex,jerirr:Pnb ,l designs for AC structures, it 0x: .2 dhcidc,5 thr;t rather care!ul investigation of the effect of the many veriables nresent in the instrument on thE-.? r,ct1.'::il sensitivity shoulr:;, be c,rrierl out. stampings of nurpose. f:-, A lc:Tge quantity of rinp; conveniE-:nt si.ze ,·.•,,: re~ acquircc; for this After the edges of the rinr-s hc,.d been ::: moothed off to hcln cut d01rn the erld;v current los~:e:=-, t, number of stEicks of thE-c=e rin~~s '"'ere riven differ,:mt leni:;ths of airgans, ro the efff',ct of this lLnrrth on the sensitivity anrl scele '.'listribution coul l be 'ietcrrn.i'1c,·L 1 'I'he :-:ictua.l rn thod of rn2kLig these detern':;.n;:,_tion'." v1 : . : , rs follov 1 ~0 : A c lnm0inp dev ide we. s built "' 'hich '.·:oul 1 holo the vEr ious r:lnF'~, in ;:, securE':, position, ·,;, nile an alt8rnc,ting curi'c-mt of aoout a half En r::rr:obre w2.s nas se d thr-ouvh a fifteen c:J. or thirty turn coi 1 woun'i onposi te the the center of the rin v 1.'.';~. s Ell c gen. romyl ?Tr J Et so rnountvi the: t it coul •. be turned. :n block of wood , On this b ~.ock v:as mounte·~. 2 coi 1 of fLne v.·tre v. h t ch f ,,c e d tn(,, r in ~ s1:rfc,ce. As a rbsult, the m2gnl:tic flux le&kin f from th~ ring wo ~ld generate a voltage in this coil. At the airg&p itself, of co urse, the coi 1 sho,. -·e ~i no vol tEtge, ,:; !.=: the vol t,~,ge generated in E: b.ch sidE: : of the coil opposed thr.t in the other side. A diagra m of this device will bs included in the FJ:•nen r) iX. vFs 1 The voltar;e ge m.: ri:.te 'i 2cros~ tht: coil l ed out to ,,. ce.librated v;::cuum tube voltmEter. Informr tion on this p.J so will bt: in the a tipf; n di x. consists of a t ".'O :::t stc: ~e an:y:lifier driving ,-, detector stE ge • v:i th a one rntllinmpere meter for thl: ~➔ ctuc=tl m~ ;-1 s uremf:mt s . 0 ".'~1e mArni.tuc1 e of voltP- P:e : r.:e[:..~,ur e d wa.·s from 2'oout three to ten or tir.1en ty thousnnr1.ths of r, volt. An arr:me ter "'Fl s usPd in series ~1 th t~e excitor coil s o th~t the condi. tions frorr, one rim~ to c1".'lothET could bE: duDlicc,tf:.,d. ':!.'he a:ir 0 ep;- tried in the s ~,rr; Dlt, s re.n from an inc:'l to rm inch c,nd a qunr t er . on the ~:e s,-,rr·ph, s □ c F s1 1r E:: d , across the excitor coil. 1u c.rtt:r 0 of Not only wn s the flux but a lso tne vol t agE:.' drop N2 turally, the : :; e~ t conditions for o rx:r P tion ar u those ;.ihich measured by the coil 1,: i th P. E., ~'0 0-• '.: a m;::ximurr f'l 11x ,. ~ rdnimum voltage dro p in t ~:e 9. excj_tor. Thfr 1_fore tnis v.'2s the condi.tion 1rhich v'Ft S s.our-ht. It took cons.i'J.erable til17e to &0 et thf': e ri_ uipment opere.ting properly, ;Jut '-"htcn thJ. s V.',, s 5orw, the following 1 result'S were obtB.1rwd. The :rr.ost uniform distritmtion • of flu 1_ occurred, ,; s might airgE,.D. bic, ,. xptc,Ctt:d, with the lh.CgE:'.st 1\ lso the sm,;llest voltE1.re ,;rap occurreo. undt-',r this condition. Still, howev1:,: r, considerable flux was knov,;n to be passing a.cross the air gap i tse.lf. flux w ,:t ~! -vmrthless i':.s this as fas as the opt,ration of the instrument was concerned, either the complete removal of the flux ph ssing across there or minimizing of it wHs nec e ss,ry. There v.:,,s but one 1:vay to do this, nb_mely, place a coil at that location so connected th~ t it ~ould be onoosed to the fh1x tr;:i.nr- to cross, thereby, if the coil is of the rir,ht sj_ze, or , vent_Ln;,· that flux fro1-:--, crossinF. Thi~ cRused all flux to pass across tho ring. ~hen t h is chanve w&s introducea, the rinf was APain closed for the purnosc s of symJH; try. f ,inr:E, thf' incJ.uctnnce of the coil is dE, ::iend.ent on the flux flowing through the coll, the inductance of the c1muination w2s gr 8 atly reduced by tht: double coil assemJly comparvi to thE.-, single for the ssme flux. f schematic a1Hgram of both the single and double coil combinations c;:~n be seen in fig-urE~s 8 and ., res nEoctively. Flux ciistri,Jution curve;:; for three 10. 2re for the s Rrre total annere turns 0:xc ;_ tation. inductenc~~ ·ill b8 fcund st h ted the ,,ctuc.l ins trrnr_cnt s themse br, s C·•l/. r /{..H LucrR/C-',I. •1-. · \- ., :, \ '.1RCI-I is vfrv sirnil~n· to the ir,nrovr:::d Pat!VC!PLE OF OPERArlON A, C PulLEN Figure INSTRUl'1Uv: 19..J i'3 DRAWN CA LIF /N:Ji .1 Cl< e. DC construction =1th the addition of exciter coils. Tlw doubl( coil instrument 1Y;.2 the first in~tuemtn built on the rt.: vi sed pc=1 ttf?rn, with the result thPt some difficulties were encountt-?red in v'orkinv out satisfactory asser:r:oly rcc thorJs. CAlTECrl ClECTRKAL P. drnvdnp; of the Ei SSemoly for ftvc1tvea,,.,.,·f'rscARCH PRINCIPLC OF OPERA770N REJ/!SE0 AC /N5TRIJMCNT DRAWN /930 KE,H.f PuuEN the s~u1r:le coil r:,o -fol i_s shovm in f :i f;u.re 10. The on1y difference vd th thf'-: r .ocll-, ls ouilt is th\. f;- ct that the Sf'Cond coil is acided and tht, :ring closed. .LL-'--1 the rinf'.S d' '--- cut into two segments, most of th~m ionc,ry coils. L fev.' ;cxe cut unri_ r the station&ry coils so ~ s to hold t:ne ':.hole s~em'oly toge thsr. OnAw1Nc ?iEUl'e l!J. W£STON -~ For. 1938 II. CommGr ci a l as semoly me tho .~s v· ould The cuts in th,., ring ~: e r e p l i:i C t. d 'ck f: Ome wh n t d iffe r e nt. h E1lf v.:ay between the fixed coils, as theor e tic a lly the flux through the iron is zero at th a t point any~ay , s o the field distr i bution r in,;::· wi ll not oe ch2n ged . A cl s fu ning• ·1\ ~ould hold the s ~ctions to pe tht,r. Ths nuni"oc r of turn,c.: of wire on thr. moving c:,sse rno ly shol1ld be ,is nec=,.r to equrl to thos,c on th~~ str1tionary as po ss ib l e , as th F:t is tht::, cowli t ion f or minimum vol t c-Jre ,:i.rop dw=· to in duct rmce . 0f' cour se , the r esis t;:mce of th<~ r:i ov:in c:· r1sse.rnbly v• ill increr:se gr e;:, tly on doing t hat. The bi _: -: c e ~ t dr nwba c k to lu -.vinp, coi 1 ampere turns t iw S<', JTie is thE~ effect of' s tr e.y fie ~~d.s . ~,r;y ,·,r esent guE: ss 0n the best rel &ti o::1.ship , t c:-.kin g Jnt o o.cc oun t these e ffect s , is th<'- t t }-1e ratto sh oul d be &bout five s tc=,. tion a r y to one moving turn. Probnbly c ;r e ful inv s ti g;:,tion shoul r:i per mi t set tin g u r1 0 1 rel,:;.tionr: which .s hould ern1ble one to c hoose the b st all PT oun rJ r E: tio. :-Jei thf:: r e ,: uipr :ent nor ti rre h r" ve b~,en 2-v;::,i l able to cc:crr y out this investigr, tion , howew;r. In none of the e ,- rly mode l:=:- V' c-'. S r, br.'- CE: put in the cE,nter Ect t he pivots. I!owe ve r, it was founrl. advi~ b ole to do this, so th t,.t thE-: instrur1.ent " 111 re t e in its iJa l Pnc e in all positions. I t "'ri f-. not found nE:ce;:s , ry to sti ffen u p t he cr ossfr ames to nrevent oth~ r thRn t IDis tine move me nt erain~t /2. the S?rings . The mass being carried by th~ crossframes is easily within their ~l as tic limit. They probably could carr y much rnorF load ·,. 1 thout ex~eeding it. ' 11 he me thod developed for assemoly of the se experimenta l models is as follo ws : the rinrs of tran Ef orrner iron we r P first dr i lle0. for as sern.uly. Then the y vrere cut i.nto tht· sections as desc r ibed previously for the assembly. The support structure ,,.r r:,s made, it lookinv, much like thn t sho~~m in the improved design. on thi::, iron. The coils vrere 1"oun•i u p , e.n d r-laced The set of ho l •:U.np: rings , which we re cut unr1er the stat.ionary coil, were bolteri on the main iron in such a way the.t ectch section of the main body had these holdine rings on one end . The co ils were placed out of the v,'EJY , and the t wo sections prE:ssed tO f, (:: the r. After a little adjustment, the SlJpport a::semblies vrere pl nced in their proper holes. Then the coil E ~ere braced a t the center of the rin~, and the cro ss essemblies, cRrryinr: :)O in ter, s pr irni; s , 2.nr!_ re l Pt erl e :U1 pmen t, '·'·' ere cemente r:1. on 2no allov;ed to dry. cr~1en t ht! 2 sse!"bly wps 2djusted to cJearm1ce, c onnected up, balanc ed , D.nc' the sDr in p; s conne cted. Corr.rnr:; r cial r roduction ,. ould re-7uire a number of changes over thi s method, including ; ssembly of the mov l ne structure before :•Utting the 'Rhole thing to ge t her . Ho difficul ti ef 11Vould be encountered if c;:c,re is taken to permi t t he c oi ls to be ~et u 0 in proper or rter 2.ni then r4rop r• cler:n,i.nF:, rlev:ice i.n pl, ce "'hich 1Pill perrni t 0 doino this on l2ree sc~lP h~ve been develope1. OoeratinP Characteristics In this section the VHriou::, extf:rnelly noticeuble charRcteristics will be discusse~, and comprre i ~ith those of corrrr,crcic=1 l types of instru.D:ent:. one Co.n Bv ctoinet so '1 C> get an id.ea e.bout what the in~trur::ent c=:t its The DC model which w~ts built is inertic:t job. H dPcidedly high 'ThL,t is accotmtc.ble 1phen one notices the weight of the couls is eycessive ~ue to the celluloi~ coil forrr: used i.n t?1E-0 _i_n :- trtir~E:nt. these r4efGcts, it sho~s 11 'hec1testone brir:l.ge 8nd ~ F, T~1t: r::c:1.ss cf· the belcncing sen~itivity of sev~n perio0 of c:.bout E,. s e cond c,nJ a 13ccor1~-:'Ln.r:: to results ol ta1nc~ on · other in:::trl.lI'.lcnts. The r::E,gnc t U'.'.:ed. in the, instrument i:· c( ~pr ci,:lly made {4. 36 perce nt cobalt steel ma gns t \Vith o half inch f:,_ irgap. The division of the sc nl 0 for thi;-0 instrument is almost perfe ctly uniform. However, proper arr a ngerrce nt will gre a tly alter this same distri bution to any form one de sirP s. D2mping is also nE,eded in this instrume nt, as it i s far from cri tic <'c lly d amped . Thi, t i~ easily c=1 cquire d for the DC mode l, however, by use of li ght d1:1mping frnrnes of metal for the coils. The instrument has of tor que production for H given inertia. r1, maximum In a s much as on l y supersensitive :L ines of in~trume nt :.~ can becJt this cons t ruction on sensitivity, and they are in general instrumPnts hPvinp a much longer perio~, this instrument comnare s very f ;:-;,voro.bly with thE: c ommer cia.l ty pes of DC meters. t n ordinar y D0 Ar s e nn.l t •. n milli- ampe r e rr:illiarnme:ter hc, s a_bout fj_ve ohr!:s r ~, sistance:, as compared to the seven milli ~mpe t e s an1 two ohms of this one. The AC milliammeter looks extremely inter es ting whe n compar ed to comrnerc ic.l AC in::::trument~; . 'I'he originc::_l ~od e l showe d a full scale sens i tivity of fort y se ven milliamperes with a volta ge drop of only ab out 2 . 3 volts. Ordinary instruments with this range dro p anound thirteen volts. The period in this case WhS a~out a half s ncond, wh ich compare~ rather fa:vor ab ly v1i th that of th,, instrument bei ng calibr a ted against. Tt had B period of bet'"een 15. a quarter and a half secon,i. Th~,t, of course, means th ;- ;, t the s ·~ings on the new design werE rather strong. model teste d had no damping. The Thi5 ould be best supp lied by use of an Rlurdnum vane in th(~ space between the coils. Pro per ly ma de, it would 0 1f er sufficient damping a nd would not noticeably increRs e the neriod of the in s trument. As the scale distributes j_tseli' now on the in::,.trument, the r e i~ a t Pndency Ht high readin p s tow2rrt inc r e ~s ing sensitivity with incre as ing deflction. As is ob~ious, if one wishes, he could unaer these conditions build· a. r.1eter whose tor 1 ue j_ncreasetj r-i s the · spring return tor r1ue increPrEd, resulting in a meter which would r ead 8 certain current 2nyv!he r P on the s cale . For DE'. s t of rr.oveme nt torq ue c::.nn saing torque as resu lts, a l) lot 11 function of deflection in r~1dians shoulr:1 hnve the t•.·'o curvf-.: S 2 ;', ne r:.rly at ri~ht angle s as uossible, a s thi~ condition i ~ the condition for b es t reliability a nd accur c: cy. Eu-pprEi.:sion of the hifh end of the sc;:,le s o th2, t the cvr-ve s will be more neBrly normc1l is ther -: fore advisable. 1 Reduction of s e nsitivity a.t hir.h currents and. incr c:a.se of sensitivity B.t low currents wo uld even out the scale distri:.mtion considerably. P.n irr:Drow1ment of ch;:;,racteristics ,-,ould result q uite n a turally f'ro r:: s1.1ch a chan,e-e, as the voltmeters and amr:leters follow a sqm;re s cci. le. Proper p l Etc e ment of coils will also he lp this. In the DC instrumen t, the e quivalent circ uit is the sance c:,::· th,\ t of the. D0 Ar senval instrurri.ent, nnrr:E.· ly a resistance in series with an inductanc e and with a parallel circuit of inductance fsprinp] and ca pa citance[inertia l in series with that co~b i~ation . On AC, the circuit consists of t wo induct ance and resistance combinations in serie s with mutual cou pling be t we en the induc tan°As , and two eddit i onal parallel circuits of~ r~sistor and inductance in series with the r es t of the r eactanc e~ . Futu2.l inductance wi 11 exist be t we en the !Jure inductive components, and betwe en the magnetizing inductive componepts. The dyna.mometer ffit;ter has this circuit wi thout the magnetizinr, components. Therefore the characteristics of the two in s truments a.re v,~r y simil; ,r. Theory • The basi c e quat i on by wh ich th~' o-oe r c: tion of this 1 instrument C<"'n be no s t e a sily studied i s dF = i dlxl. Fro!Yl t i:1 is, as derive d in ths ap pendix, we fjn d that r. "cY ::: l{ l• .u ·:::i;rr"· • He r P k and Tare cons tants depending upon the parts me a surements. Bis a variabl e in e, so can be expanded i n a Four ier se ri es if thi s form ~ouli r~ovs convE:ni en t. It v.,ciuld. consist of r fm1ction of sine I 7. terms. This vrnu1d give a rather convenient mec=ms of handling computations of sensitivity. The de rivation given makes.severc=:.l assump tions, namely, tha.t the flux leaves the mClgnet normal to the surfe.ce of the r:iagnet, and that the conductors are near enough to the stirf&ce of th o magnet . thbt the flux is still normal, or nearly so, at tha. t distance. The~;e assum ption~, E,re justif'ieed, as the pe rmeability of the iron in the magnet is so great com pu.red to the air surrounding it th,:;t the flux is in effe ct leaving an almost perfect magnetic conductor. Careful construction will assure the coils being · close enough to the flux conductor that the flux is still for all prRctical pur :)ose s normal to the conductor. Precise d0termin::.1tions of the allowable spacinp, b <:: tween t::ie iron and the wire of the coils has not yet be.en made. The results of the preliminary ex per imen t &re the rr,Fi.jor source of i:--ifor rnn tion on this source. /._ deve loprilen t was undertc..ken to determine the effect of the reduction of t he size of ti:1e instrument ot half the present model size on the sen s itivity of the instrument. c1. Thes0 calculn tion~~ ind icated. tha t ror const r.1 nt exciting mr1f, ,md b constant period o.nd resistance in the rnove r:;ent, t he s en sitivity of the • s trument i_ s i· , t r:1 in . _nc r e~s =bS l/r 3 • , .,_L _·n1· s_ of cour·se means 18, that reduction in size of the instrument will definitely incr e ase its sensitivity. In an actual milliammeter, one would achieve an increase of S8nsitivity of about three to one overall, if the instrument is of the AC type, or four to one in the DC t:'ne, for to half size. E. r e duction That is, r 0ctuction to a tenth presefit size, if it were pr acticP-1, would yic ld ct one :milliampere AC milliam~eter. The reduction in size to half that of present models actually lowers the inductance of the meter to about half that of t'.-1.e la.r1!er size. amount of iron loss The rela.tive iD be the same percentage, as the volume of the iron drops to an e i;:hth of the larger size. As one notices from the equations of the instrument, thic: sensitivity denends upon the flux le akinf; from the rinv,. Terefore the distribution of the scale c~n be e<',sily cha.np:ed by merely chanf:;ing the amount of this lee.kap;e flux. As the flux 1,vill leak most rapidly where the flux ,-Jensi ty is the greatest, all that · is necessary to incrense the flux at any point is the re 0uction of the e.rea of the r inr, at th;:i_t point. Precise dr1. ta has not been collected on this, however, sensitivity at the 1011',' end of the scele CR.n be mFide to take on the value desired, within limits, by cuttinp 2~ay part of the area of the rinr et the point in question. Tn as much as the iron laminations are easily duplic ~ble, and the flux density in the iron does not-aoprec±ably effect the accuracy, it is a simple m2tter to get c:lccurate m~thods of cha ni;:ing the sensi ti vi ty of thl~ instrU1:1ent. The iron is be Et chenped in such a ~anner thit the outside surfc1.ce remains close fi tti.nv to the coil. This can be done by takine iron out of the center of the lamination, or by trimmin g part of the iron along the_ edge . on some of the laminations but leaving enough so thc t the flux wi 11 bE~ h r, ld approximately a. s de sj_re d. by it s pr ~ s e nce. Thus a very versatile in s trumen t result s , as scale, modific a tion is extremely ea sy to carry out and very e 2. 2y to reproduce accur a tely. The the ory of the AC ammeter of thi s construction has one im por te.nt consider c=ttion ":hich i s not r,r ese nt in t ht: other forrris of the instn1mE:.m t. E:inc e thl, sprinp,s of r->.n instrument v,rill not c e.r ry he2.vy curr e nts it is necess ar y to use mec.ns to 0. liminAte he2.vy curr e nts from the rrovin r coils of the a~re ter. The best me thod of doing this is by a shunt conne c~ ion . ~n order for an instrument to be independe nt of f req uency Ni th 1 t hi s connection, it i s necessary for thb time con ~tant (1/R) of the moving assembly to equal that of the stationary, assuming no reduction of tor que due to increase of losses. In or·1.er to ovc rcomF a r eduction in tor <(Uf! , th• 0 ti me 20 constant of the ~ovin~ Assembly should be a little less, just enough to c orr ect the error, t~an t h2 t of the stP_tionAry. This caw::e s an increa~e j_n mo ving coil curr en t v.'i thout an E,-: nreciE,_b l e change in stationary. Other them this, the re is no'theoretic a l differ~nce from the other instrument:::; . It is possible to work out field distributions for the r:io u ble map:ncot construction oy methods g ive n in Dr. fmythe 0 s E'trctic and Dynamic Electricity . As time hAs not yet b.::e n fou_n d in whi::h to c,,rry out thi s oper a tion, it hr,s not yE':t oeen ettech<1. A s imul s integr 2 l, once set up, is all thAt has to be done in thB ev&luRtion of thi s problem. E'ource ~: of Frror TheI'e nr e c e rt rin sources of c, rror whi ch a.re pres en t in ell instrurrents. ~hese errors ~ ill be ~is cuss e~ here first under f.Erne r e. l errors, Rnd thLn e rrors 1·1 hich effect primR.rily one g iven type of in strume nt. General errors There ;-.re several t empE:1'; ture er rors v;hich come un \ e r thi ~ classification. The first is the e rror due to tempe rBt1J.r e effec ts on the s,·rinv:-:. ThH error intro- '3_1J ced by the sr,rinr,s, a cc or di n g to La 1 ·: 2- Electrical 21. 1egree Centi er 2de. This mebns that f or a half pe cent i.nstrument, the error over c'l rcm:e of ::10°C. "Fi ll be less than the a.ccur2cy statec1.. It ccm be comp<c:nsr-ited for, if rlesire1, by having a suitable resistor with a temperature coerfj_cient v1hich crrnnges the rusistance at such a. rate s , rings. bs to counter,:,ct the e ~Tor i.ntroduced by the J. nothe r sour cf''. is the e xpansion of thf:-' cross fra r, s carrying thP coils. (linHr) for b_ 2ss is 'i'he ex r1c;n::,ion coefficient o.oooo;-:/°C or tht::, totc1 possible t':':tc.n the c.: ccur Ecy set. The rncfnt tic flux errors :::re due to t T O rnc:tin source'°, fr.ctor under si.ffcrent ;:,; no v11t ~, of r:.rsnetic excit,tion. L cE:lculation of the effEct of' this· chan F;e ls founr5 in ~O kilolines per squEr e inch, the lo~~ in th~ iron is 0.16 '.' ·atts per po1-~nd.. fteinrnetz formulE. if e.pplied v.· ill g ive~ value of loss 2t flux de nsity b~ ing use ~ ~hich 1,r,; ill bfo hi gh , c1s it does no: tc~ks into <: ccount c'"J.dy ·1 [The exponent i:: t ake n c:1s 1 • b, T:m,r(;f ore v·e will u se tilis eq_u, Lion to determine the me xirr:um v r lue of thi ~' loss e.pproxim.c,tely. The evrlu2tion i ~- gi vc n in the a0]')endix. The in:-=trument 1:ill shor; E-:rrors dm· to s.tray fielc.s unless some shiE:, l d. ing i~. added. On DC, the error nith 1 no shielding on the AC model turner:l out to be ;_.,. couple of percent. Iioweuer, pl2cing of :.-, thing T:Ln1: of low permeability iron surrour1'1ing a. thin ring of high pcrmeabili ty iron to shiel i th1:: ~ovinr, 2ssP:mbly ~"ill cut • thiE error do~ n to a point th~t it is neblighble. shielding ._.,ill st"1rve a secon'3 purpose, E lso. This It ":ill drav,, t!'le flux out of th€-; outsi1e of the flux: conducting ring , and can be f;.rranr,ed to CRllSt": c:.diii tion2l flux to leak where it is rt~sirable. The result is an incre&se in sensitivity and another me .s ns of modifying the scale distribution. Vol trr:e ter err ors Voltmeters Ere bothered by another temper ;1_ ture efff,Ct, namely change in re:' istance in vdndings duP to chc:nge of terr;pE-rature. is 8in·'e thl· tempe r2.ture coefficient of copper' o.omss ohms pe.r ohm per degrE:e Centigr a de, for a. temper ;:, ture ra.nv,e of ±10<>, the, change in re~ist a, ,r;e is. :: .8 percE-nt. T:!:lf-: r ,, for e a s 2impin 1~ resistor hc=:ving ten or r.c.ore times the re~.ista'.1ce of the copper " ill s F~ rve to hol d thi'.: to c=:: s~r;ll value. Proper ;;d justr.'!e nt of the va.lue of this resistor will counteract tht error due to temper ct ture effE:;cts on the springs, Rs the copper error is greater than the spring error, and in the opposite direction. Resistors will r Hduce the e ! f ~ct of the copper error, ma.king possi ble a desi gn which ,·dll be iwier,en'Jent of temper;.:itur ;, . This is' general prr:1.cticf.: in instrurr:ent work a.t the present time. The sensitivity of the voltmeter should also be looked into. Using only a swamping resistor to hold the error due to temperature down, the maximum voltage drop allov,.c:ble in the meter move ment prope r is ten volts for a 100 volt meter. fince a t e n milliampere meter of this design drops about ten volts at full scale deflection, one can e.sily build a 100 ohm per volt .meter [V = r'/i in this range:. = 0.1/0.01 = 10] Comparison with commerci::il P.C voltmeters of thi!: rEmge i;; interesting. Dynmrco_m eter type me ters show about 25 ohm ~~ p1c'r volt. Repulsion iron ·about fifteen to thirty-five, depending on ecuracy of the in:,trument. 1r 1attmt: t e r errors n'e no·11• consider the errors in the wattmE., tE,r type 1 of construction. 1!.'i th a seven arrrt re cw'c e nt coil, 0 consisting of five turns of nu1ioer eir:ht 1•·ire per coil, the current coil consurr.ption of power is about 0.15 volt amperes. The potential coils takEc only 0.006 m1peres at 150 volts. Zc of the moving, or pot8ntial, coils '24. is ai-;out fj_fty ohms. Therefore the potential error rJ.ue to temperr1ture is a oout 0.006 pt,rcent. For tht:; phase angle error, the equ 2, tions Riving this nre derived in the appendix. These equations g:i ve the rel2tion b,·tween the pahse angle err.or, maxirrum err or r \-, sul ting in th0 me t E~ r, and the power f r ctor at which this error occurs. 'rhere is also ;:L;. t a shov•ing th,.-::, the phase a.ne:lr: err or in the . current coils • ill comp( nsate for the tir::t: con!; tant 8rror. By taking propE:T veluc ~ from th8 gra:-ih o..:. maximuF.: error datc:r, one c;:m design a <'n ttme t er for ony pr:. rticular po,:e r factor range ,:;i th nny stated rr:Lximum error. DC model err ors . 3 esirles sr.>rinv and ,..vire tr:·rr: pe";·, ture l0 rror:::, th only error which has to be taken into c.)_ccount on tne DC rr.odel is the matter of magnet stability. ~his is a subj0ct on which quite a bit of r8searc~ will have to be done, stuiying thH different possible magnHt m~terials~ and put ting them through very rigorous t,: s ts for stability under h~rd useage. Further Development There c1re many directions in v1hicr1 furthE:r devE:olopment must be undertakt:n. This section will t ake up the diff e rent form s of tlY instrument and discu:; s the work yet to be done on them. 26, DC instruments Vodels of the double mae;net Dr type:> of the instrurnent will h:. .ve to be built an d tested. The desic;n v:hich ','.'ill ~ive the best mngn6t permanency has to be fow1d. Finding these proportions for thr: mfaximurn sensi ti vi t:.? and stabili t " is a job wh icD mill trd•re a gr 1.. at def,l of inv(:; stigc:,tion. V:hen thi_s de sien is found, the mHgnet will have to ue given ve ry extensive test s to find if its st,•. bili t;;., is goo · enough for accurate stRndards, port2cble standards, sv:itchbOFJTd meters, etc. It will be necessary to collect all possible data on thi ~ 2 s by doine so only can it be found out whether the structure vrill hnve a -3.vantage~ sufficient to warrant mc1king a lin1°: of co~:.rn.E: rci2l instruments. P•.C in5trmr:ents. The major things to be done ½ith thiJ form are the investigation of fre ctuency error?, ~ to look into thE, results of scale modificntion, Rnd to investig a te the srr:&llcr in ~trumen t si zc. Ll.co th€. AC f;rnme t er has to be ex perimented with. As might be expected, the investi eRt ion of scHle modification must be done in way of check 1)r2lc tic-"'. lly of the idec-l S presented in the theory section of thi~. subject. Tests shoul'1. be carried out to che ck the E1ethods, 26. see if bending of the pointei· of a.n in s trume nt 1;1· i l l introduc e size able error, an d to find out the e rror s incurr ed in r,r e sent JJ_C in s trurnents from be n ding the pointe r and r e setting to zero. On the str a i ght mo de l, without Rny scale jugg linr , the error is sm&ll, due t o uniformity of the sc a l e . As soon . As one chan ge s the scale distribution fr om un i form, ho :eve1.', t hen errors i:.· t 11 r ,: , ~u.l t ,~' h '"" n thi s chan pe is ma de. As t h i s i s a n i rn 0orta nt questi on, it will nave to be c on si J~ r ed c arefully . An invE: sti gation oi' fr e riue ncy error s wa:.=· s t E,r t ed by the a uthor , but h EJi to be g iven u p v1he n the in s trument being used for the _tests ,,,as burne d out by s horting a cross lH1 vol ts. The results indic r. ted wer <:J t ha t the fre 1uency error 2.t 5 00 cy clr!S 1,"a s of t iH'J o.r der of one to t wo pe rc e nt, a.t 1000 cy cles, about thr e e to four perce nt, a n d a t 20 , 000 cycle s about forty p~rc e nt. The e xactnes s of these pe rc e ntages c an not b e gu arante e'i , a s a n accur a te calibration had not be en pl &.ced on t ".1.e in .c trumen t, est i rn;.:,_t es be ing m2de on t hE: b Ps is of defle ct i on an d t he };:nown f , :ct that 0 the instrume nt ha . a s quar e s c fl l e , r a. t hi=r than u.11.iform. These investi gations will ha ve to be cont i nue d and made c ompl e tely quantitative, r e t h~ r t hRn s emi - qu e ntitative . T~e chrtr&cte ~·istj_c s of a mini a ture l i ne of this type of instrume nt will h c ve to be s tudi ed . Ce.lcul&tion s , as z 1. str:ted, indicate a greet a.dv,:.ntG.ge in the smaller size. Pr a cticG.l experiment ,·:ill hr;tVe to br, u ::::ed to either c onfirm o:r refute thi ~ . I sus PE· ct con f ir me. tion •.·.ri 11 result. fio,.':ever, small mode ls s1)i tFJ.ble for or inary use in radio and other purpo rc~ s CF.n e;.:,.si ly be b uJ.lt if t h j_::. doe:: check, so · it is v~~ry much wcrth while to carr y on a careful check of this possibility. The possibilitiEs of construction of an J1_C P-mmeter have to be reckoneri ,~.'i th, also. No exr•e rime ntal models of this typt· of instrum0nt wer (:, built, for reasons to be disclosed. As h a s been stated, th~ instrument has to be one of the shU]Jted dynamometer type of construction. Calculations of c1. five ampere ar:m1eter were c2.rrhid out. It vvas found th1-:1t such an instrument could b,, built which would consume 0.?5 volt amperes and v10uld have the sa.me time constnnt in thE movina dnd s tF.,. tionc1r:· ass(: mblies. One hun dred milliamperes would have to pass through the moving asserr.bly. Diff icul ties wer e encounte.: red in de sign of this type of instrument in keepin~ the voltage drop in the movinf assembly low enough to get a low power consumption and at the same t.ime keep tht: pE:riod of the moving_ ass embly low. Pince the desi~ning wa s difficult, it was decided not to build such <':. n instrument for the time being. I.,9w po 11.'er factor accura..cy of the vrattmeter type of instr ument should be checke1. As no r ~ally sat isfactory method o f' checkinp, this w~s kno".' n to be avRilr,ble when te~ts were me.de, only quali.tative a greeme nt he'' been found h ,r e. 0 A phrtse shiftinE transformer or its equivalent should be used for thi s check, E1E• one c2.n by th&t ·means get the equivalent of zero power factor ;:t uite e2.sily o.nd Rccuratel;s/. There are probably new types cif in~~truments '''hict1 can be built u s inr, the same design a s this ins~rument. Tht='Y rr.ust be '''orked out, and more che ckinp, done on the pr l:se nt designs to see how thc~y c c1n be further improved. in rugge 1ness, sensitivity, and operatinr chPr2cteristics. Concluston Her e is c1.n instrument v'hich EhO"•' S a rJ.ef ini t e j_rr.prove- ment over the sensi ti vi ties of the in~~trument~ ave.ilcole in the mRrket todPy. T. t and sensitivity. th,:· devc;! lopmE:rn t of th•:: construction 1_: hen h2, ;: rur,gedness , hi e h torque, has been carri ed to ,J point th[,t production i s prc,.ctic c. l, the results r(:•por ted here mny even r~,rth<-r -~· urpnss the Dresent des igns. Even ,:, t thE pr c~ ~ent time , howe ve r, tht~ results represent::: defin:ite ;-:. dvanci: : rrRnt in the art of measurement 01' AC voltagr. , s and current~, especially when these voltages and currents are small. Often meFtsurements are difficult ovring to the f2.ct th;, t pre : ent instr1.ments 0 under some cond itions ,..·ill radicr.lly a l b..:r the concli tion; 0 in a circuit when they e.re ins e rte d. shows much lowe r ins ~· ,.-tion error oy Thi.r instrume nt '''2Y of the f ;- ;ct the:• t it cut:: ,ower ~onsurr.ption to 2,bout r. fifth th; t of exi~ting instrum1mts. This instrumtmt thc rv for e opens ne v, fields for the mer sur . ment of those JJ', vol tc~ge s. ,\Wl cur re nt~, v.rhich h E. ve been rather difficult to hanr'J.le ,_;;i th c~xi sting in f tTumen t;:. P. One finds in tni c:. instrument, the ref 01 e, 1 mec1surinp: devide "'hi.ch h,-! S ver sati li t y ;-:i n "l flexiOili ty, '::)eing eccur;:ite on both N:'. awl :::-ir, Rnd ·· hich c:ho1'':C: :1ro!::ise of !Y,re 8 t p, r3.vance s qmrnti tie -~. in the :· rt 0f ::r.c~, sur i np- of c l e ctr i c 2 1 30. INDEI. 1'0 APPENDIX Meas urement of flux Drawing of sample hol1er Circuit of VBCU1.l!:. tube vol trr.e ter Sample gra ph of distribution Equations of oper a tion 07 Relation of size to sensitivity 68 Design equations Coil rela tions for arnmet,.cr 41 Determination of errors PermeE;.bili ty · error Core loss error Wattmeter phase angl e error 46 3 I. Vea suremE',nt of Flux. The first rnattE~r to be ta:ken up is the mc <, surement of the flux distribution of the rings un! i.er diff-:erent gap condition : .~. Ji drawing of tht. &.sse mbly use:J for the picking up the voltage is shown on page 36. The coil on the ring itse }f consiste rl of thirty turns, and carrie d s half ampere AC in the tests. the block in the center fine vdre. The coil on was of five hundred turns of The flux leaking from the ring pas s ed through the coil, thereby setting up e.n ,:ltern2.ting vo).tage, which was measured by the vacuum tuoe voltmeter. This form of voltmeter was selected as it would draw a negligible amount of current from the circuit. The instrument was vJOrkinr, at about twenty five ElE:·gohms per volt. f, drain of po1:1ere would hnve rendered the reading i ·n accurate. A dia.pram of thi~ voltmeter is shovm on page tS4. As wiJl be noted, the voltage output is regulated by means of a neon tube regulator which holds the voltage on the tubes constant to within a percent for Fl voltage change in the po ,:er line of c=i.lmost tvventy five percent. 1 Since it also loviers thee power supply coupling h ,pedance, coupling between the tubes due to this sonce is gr~atly r e duc8d. the inherent stability. This increases It i~ of interest to note tha t 32. the hum volt&.ge input to the 6J7 from the power su pply is less th;;.n a thousandth of , j volt. The meter was used over the r&nge of thre e to forty thousandths or ;:-, volt. ThE. smallest recorded voltage is about one and a half thousandths, ~ith a distributed coil sample on a ring with a half inch air gap. from the voltage. E = n d¢/dt. uni ts. The flux c c:,n be calcuil.ated The formulR used of course is E = 5OOx l?O:(0err, in e lectromaenetic Therefore 0eff = E 8 _u•xlO 8 /1?O:t: Thi :.:- of course assumes th,i t hyst(:; retic errors 2..re negligible. A sample set of data is included on page 6 5. The graph numbers corre S-T,ond to thE:: Sf!ffi ]:) le numbers given with this do.ta. Speciman numb (or one is a ring samT•le with an airf:<'~P rtn inch and a quarter long. has an airga of a qur1.rter of an incn. Numb e r tv:c 1JUilJL)er thr f;e shows the curves fo r a s am~le with t wo coils bucking each oth~r on opposite legs of the rinc. Fach coil has fifteen turns, inste a d of the th1rty present in the sinile coil test s~mples. Eince the inductive re a.ctance is of extreme import ance in thi s c,,se, the impedance, the resistance, and th8 cfilcula te d reactance are also included in th8 ~et. I I I n I I I LJ FOR MEASUk'ING LEAKAGE FLUX FROM l?INC LJE VICE ---- C ,....._ ~ t..\) ,Spf.: c i mr:.n I No. Im E di ¢ .S_nec i mc:,.n I.,,., F rb No. II <:'. :·':} Ci m,:n III 0 '~ Irr .i':.i (J 0 o. ··-:? o .01 2$ 6 . 8 1 0 . 57(D. 0 ? 52 1 ;3 _4 1 ) . 540 . oi)40 11?. 7 2 0 . 54, .0?.43 1 2 . 9 2 ) • 4.~:c.y.. ;)· . (J:'24 11. 8 0 l on r . . 011 3 3 () . 1.1.4 ( . 0~07 11. 0 5 ) . 401 4 0 . i\ ?( . 0200 10 . 6 5 • ,,1 G. 3 • () 1 - ~ ,t) :::- ·, 1() . 2 0 .160 • Ol OLl 5 . C 4 J . ;s?G . (' l 8c5 1 .7 0 .160 . 0105 :s . 6 0 . 4 7( . 021 5 11 .. 4 5 J. ?~ ·? !? . IJ 18:'.:J 10 . () 0 .180 . 011:2, 6 . 0 6 0 . so, . ()~!2 :> l P .l 6 , . 46? • O;:·14 11 . .-· 0 . :-! 40 . OL~. 5 7 , P, 7 o . ;:s41 . 0176 '.:\ • t~ 7 b . 56 /, . 0? 51 1 6 . 3 0 . f! 8~ . 0151 8 . 0 a 0 .11Jr . 0 115 6.0 8 I'\ . 457 . 021.S 11. ;5 ~ . :o: oo • Ol f'O 6 . 4 9 0 . 46( . O~?. l ?~ 11 . 3 10 <:'.• Ll 0 . 52( . Of'?i4 l ·-·. - 10 P. 44 ~3 . 0207 11 . 0 0 .1'.,;8 . 0094 5 . 0 11 0 . 461 . O? l G 11 . 5 11 D. LJ 18 . 0? 00 10 . t) 10 .11:.) . 0086 4 . 6 12 0 . 48( . 02f-0 11. 7 ') P d6··, ·; . 0~21 4 11 . ;3 I0 . 115 . 0088 '1 . '7 l ,~ L-S 0 . 58 ( . 0255 l."3. 5 14 0 . 63( . 0~·)71 l _·_; . -<~ 14 l b l.!= I¢ L¢ C) h. 5:::1::, . 02 -~ 5 l ? .5 0 . 180 . 0116 6 . 0 • l \ ~ . ....._ f' I D. b'.S6 . mJ7? 14 . 4 IO . lvO .0105 5 . 6 ) . 0 . 0~)73 1 5 .0 ( · 4 (..) ·- o . ::'. OO . 0 1 '?0 G. 4 84 . r 1 6 5 .1 R . nto R . 061) . 07b7 L . 070 L . 082 . 0086 '7 . 090t z .10/.i . 0772 ~:.507 .. lj ~~0 1 4 9849 i... LJ> '- L 36, I ')' -i -~ ~ ---< 1 140° 220· -~ 130° 230° 120• 240° 110° 250° 260° 100° 100° 260° 900 270° ;;; 280° 80° 80° 280° 290° \ 70° / ; 70° 290° . .,.I, 0 z ·!.. ► • C z 'E Ji Ut.J :] .=. cf .. w 300° 60° , / / 6b· 300° w ::, w "' 310° ,· 50° 50° 310° 320° 40° 40° 320° j (. Appro~irnate Governin1 Equa.tions Instrurne n t from ~t ectro m a.'1 net i c theory: dF =[d/xH ¼le. define:- y- = tne4n radius of nn1 f - f u.rnin<j force - le,,'jth of one. tu.rn H = ( (3e, - (3 e~) $;- 1 !:; d (3 ~ W he r € A = c r-o s ~ e ct io n ct Y e a. <p=::Ahj ular vv;Jfh of r ,n 1 of co ii. A d.F = n Tcll 6 (3(frl . ·_ T : : z r F = 2 n I I , 6 (3 /,., = --re e -_2nI60A -t({J -= kIJ (3 Th i5 d er-iv at i o h Q.SSU rn ,s b Q 5e d <J n bi (i ty f o l I o v..:, n 'j p+ io h5'. 6f-> is _L to ma.1net or r,rj that fh e surf a. ce. j5 This r-e q u. ,' res surface nEar to th a. t the r,ermeQ- much 'jreater th an u.nd:y, or the rin9 is for practical purposes a fl(.(.x for. The conductor ca.rry,·n be nea,r the .sur fa.ce 1 condu.c- current mLLst of the flu.x condu.ctor: Ho.ve == (Pt), - /30~} \Jhere a.::;- :r, == ( ~e, - ;:jeJ $:, := Jf ;~~ w;Jth of r-in'jj d-:::: th,ckness. dT= nidl·2r•cSf3 · $~ l o /3 = a fipro x tnz.m.f. _ Yl. r - 2r /'\ 2l a. d f n,. - a.'E'cl to = n I I •2 r • 2. ,,-i. 1 <p == n t=my- 2 k for p~riod of i-net~r co n sia.nt. . _ nin o. d ri I11, "'d .. e - --rce r = mr 1<'..<('r' 1 for r€s i sto.nc~ c.onsta.rit : D-C -.J.L f\.,- A . , . C, A: J f . -fl--i. . . m= C n I l1.. a. d. <. : . e ::::: f t"if> k r- 3 - nI'1.C? ( 1<. cp where !f a.) ad1 -= K r~ I l EA. t ~ r"i. n,I,)t,CJf, ~c:u,c:1.<f a.re const a. nts. d J ,, t1 "'cl I : : : 11 If a., d1 t'; q.,d t =- 1/21 0 = 8k, Then:: fo.,..e to the the .sensif,vi~ i~ inverse!), proport,·ot"lal cub~ of the. ra.d·,c.es a.re r-e t a , n e-d. ,· f th4il .Sa.me r-, rorarfi~ns 39. ) The ooe rRti nr equations used for t h8 desirn of o ui ld 2 modsl, of course, ;::nj_ then cv;-,lua t c tlw cons t a nt s for t he tyn of con f truction fr 0rr mensur brn~ nts on ~his operatin p; equ ations for this 5-n' trurne nt. operat ion d e-oen·'. s on t h, [' in ce the in tcr;c;ction of t h E: c-,: ci ti n g coil mF.1.gnFti c field , v:hi h is pr oportion a l t o tht· ar:;pf' re 0 turn s , a n ri t he cur:ccnt flov,in f thr·ouch the: movin v o. ~s emuly , thf-. equa t ~ on t P..r e !? t h· f o.rr.1 of r, m· o rl u r: t o f t '•''O t e rms , ea. ch con ~ i.s ti ng of the ;:~mp· r e tlrrn 0ro-:1u c t for it s s pe c tfi c a ss i=>Y":b l y . Tn o t her "·or ,)" 1 T 1 :•J 2 :- 2 = C. i\T This of cour se c1.2s 2tu:Y: no c hr:. n ["e in th <" c .- -. Hr 2c t e ri st ic s r:letermLned by t h€ c ons t:-:i.ntc . It turnu3 out th,·t tJ-:e rr;o'1els b uilt hFrrl 2n c•.rrriere turn pr-00.uct o:; · be t ween l ~1 rJ ;-ind ,:l oo . .i.he f 1.1 ll s c& 1e curre nt S'l U F~:'Fi ti mrc5 the pro riu ct of th(: movi nr, a.nd s tF.t i onar y tur·ns for one sC::t of co i l s , The se tu r of e ve ry c oi l bei n g bucke~ by ano ther coi l ho l d s the i m~er!Rn~e ~ uc h belo~ t hn t PXD8ctei for the s2me t o t Dl numoer of ar.: p,_r ~; t1.rr n s . On n.mmc- t 8, s, c=inothi,· r of' ec;u: t iO!l ~orr.1c, s into play . Thi~ re l a t i on i s the on0 e li mi. n : -• t es thE: f r e r; ut.on c y e.r ror in the i n sti· me nt. oth r::r forms of th Tha t h i ch On t he in, trumen t , it i s b et tf- r not to h;-~ve 4o. I this rel2.tion e.dhered to, as .it ·,r ill result in ,·:. rr.c.ximurn volta ge r:l.rop from Uw £',; ct thr t the vector vol t ,:.f~e drops will add directly, in::-:te ,,d of v0 ctorLi lly. To k eE:' P this es small as possible, in series in!':trun1ents thf~ povier f2ctors of the movin ~ a n ~ station~ry elements shoulrl difft:r t .s widely as possjble . I t is of intere ~t to note that the instrm10,nt lE-nds itself e c1. sil:. to thi~ ve ctor sep;,r ;:,. tion, c.s the 1i:ire on thf,, moving coil has to b e small in ord(,r th;-t the p,.rior} of tht in >,ti'um<,mt be small, Hn d the rr:inirr:um los s in t:tw s t ;..;tiornwy coils occurs v;i tri th(' l;or r;es t possi.b le ,.,:ire in order to hol 'i the resistnnr,e no~''n. r deriv!'i tion ""hi.ch givcc thr· ootir.:um value of k, thee :r atio b P tv.ree n ': 1 given on thr· nE·xt P<"-F"C. i'e Sf:-,•E, th t the v2lue of thi.;'. constant deuHn son the resistance of one c oi l set, an d th<:: p ,' o •U: ts of t >o constrmts rle:fi ncd di v:L ted b;,, the products of the c1ir1' E:n r s. qundra.t:i e ifi 1r 2 • H For ttit , n ,.lue o:i k to be 1 hap,£•ne thkt thir ,:.lco a.u:urcr: t:,1 t t:ivor cositive roots to the ..: ' '\J' tl.on un- 111r tb.1 "' 0 on'.:tion. 4 I. Best Cod Relations for Ammeter N, l\1 1 I, 12 = C j Given:- N"l. N-i. R: -= ~ j To find:- Valu.e L =C, N? ; UJ L2 -== [ 1 N: W of N, ::= k N2 1 k for- l to be minimum. 12, -: : : I< 1. 122 k N; I,I2 -=c • -:z -::: • .z_ Jk'- g;k2.+t A,. 1 -iz-- az. -= o = ok 1c1+1 k I< ~1.l.. v - V (, - ~2.) -==- (1<~•)2· :. ( k1.+1) 1,..1-R:- (kt-1)(k1.R1.-i._,_ Al.) ==-0 K4 R: +kl.R; - k4 Rt-kl.AL +kl. R21. -t A1..=0 • k ___ + A • • .,/A...-2R! 42. I De t errdna tj_ on .9f_X rr or: A~: s 1. mE.' pD th are P in iron ont t,,.-c n t iE th t h , t in c: ir. tL A.. 3X 9)(20 approx 2x2"2800 -t-4.5 0.006 4.5S4 - o. ,2 %~ be no tic ~'' c:ble . o. 16 w . •. Wz. < o. ooo 615 f.6 /~O,OOQ):::. 26e \ 1000 AB in r:i c tentiF.l Let c cil nh:::•sf, r..n.c l c . P-= true povve r -=.. pow-er ind ;co. +ed Pin by ,,," te r. P-Pm-::=:t1P P= Ei cos e ci cos ( e-~e) . •. ~ P = £ j ( cos B - C 05 tJGo~lie-sinB sin .Lle) ~ ,~ P> M Glximu.m Ll P occur.s at o e -==- 0 . Pm:=:: . •. - sin 0(1 - cos ~8) - c.os 8 sin LlB==O e -:= - -r I a.n sinA6 I -co~C>8 =-Co~~ z = f o. n (90° + A2.G) .•. e = 90° -t ~ e 2. ft= (1-c.osAe-tan(9o"+~) sinA6 )c.os 0 = (2$;,..,~~ +2. cost.~) cos a 0 =-2sin~j e, .. P. == E j cos -OP == -2sin..D8 ---2P, Cose. For u.nify power fa. cto r meter, d8"'•x is . b ~cveh y 0. 005 = S ;n ~ 8 = o . 002s- • ~ 9,-,,111_y - A • • 2 V • - .. ~Brnax-== 16 / I 2 Sin e:.prncx. _ :;,in ~rno l o.s- 44. For a 20% power factor- wattmeter, cos e,=0.20. t!;.P P, =o. 005= sinM 0 .1 1 sin~0 =.ooo5 '¥-=2' 60=4' For a. 5"7o power fa.do r 6P_ P, - 0,oo5" = wattn,efer, c.os e, - O.o5" 2sin~ o.os sin '1J7 =. 00012 M - 25/1 2 ~e::;; so// To bu.ifd such a. meter, out as follows; To be within errorj the constants come set ton 68-::::=0.0002 .'.Zr =50ooZL for poh~ht,al a.ssern bly. TakezL 2:. +w .•. Zr :::: 1 sao<,u z 15tv..rhS = 0,02 W n"l. • 3'3 = .02 225" .•. n = 6 7 fu.rns 67 I~ 5"n = 2 ~ 0 X20 l{o. Spr-,n~ con5ta.nt = 2 5 6.7n ==Zoo; n-=3oturns Zl := Q~08Lv Ve,:.: surin.P." Instruments, vollu:'Jc I) th; t cureent coil pha~.e anP,lE, error ch.1E:, to cor e loss i ;:: H!•-,-,roxi:r.:ately con:=:tcmt. There fore it is Dossible , since this er r or tends to increase e as potential assembly error ten~s to re0uc e current coll error . . I f /)J<fl :i.::. t;-1kf~n so that Al/' == -4'P, say c"1.t Bn.Pl t= sixty cycles, thi>n thf-! metr•r v· ill h~•V f' no phase error. A'fcr,n be helr!_ !:'.UC'.h iwlo1',' the o.e -o,rcent cE<lcul< ted, as the same ref ,rence st u t e s that :~tE:: inmc-tz constant is n c c,rer :J thrm 1. 6 ta ve n ht,r c . It hr_ To;- ens th a t both of the se errors ~re proportional tc the fre quency, so th t if they L I'! ! correctf::'1 ,' ;_ t one f reque ncy, '":ill keep to a very lov: v,-. luE:' , t.hty •s ill be correctcd at all frP qut:,ncir:2. 2ince 1Joth errors ,• r '. l e ss th,n r:. helf perc-ent for ;::, unity pov:(~r f;-:ctor ','.' attrr:t; t er, they othF-,r, ther e by givin g correct r c,-cLlnr,P ;:,t ;c,ny ~o, -er f' 1 ctor.