THE FUNDAMENTALS OF CURRENT SENSE TRANSFORMER DESIGN. Patrick A. Cattermole, Senior Applications Engineer MMG 10 Vansco Road, Toronto Ontario Canada

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1 , Snior Alications nginr MMG 10 Vansco Road, Toronto Ontario Canada Abstract Th following ar will first rviw th basic rincils of oration of a Currnt Sns Transformr and thn follow a simlifid dsign rocdur. Th dsign rocdur will tak into account th ffcts of tmratur and frquncy and how thy rlat to th choic of a magntic cor. Introduction Currnt sns transformrs (CTs) ar usd in a varity of alications ranging from owr managmnt to rcis currnt masurmnt in th automotiv tlcommunications, comutr, industrial, consumr and mdical industris. A currnt sns transformr is ssntially a standard transformr whos rimary is lacd in sris with a conductor carrying AC currnt. Th scondary is usually trminatd in a rsistanc and th voltag on th scondary is mor or lss roortional to th currnt in th rimary. Som CTs ar dsignd to roduc a voltag outut which accuratly tracks th AC comonnt of th currnt in th rimary; a linar dsign. Othrs may b dsignd to mrly roduc a chang in outut for a significant chang in inut currnt so that a logic dvic or fault circuit may b triggrd. This ty would not b linar. Basic Princils of Oration Th quivalnt circuit of a tyical currnt transformr is shown in figur 1. Zsac Rt out I Figur 1 This standard dsign uss an accurat and scific rsistiv trmination on th scondary. By transformr action, th loading ffct of this rsistanc is transfrrd to th rimary and aars as a shunt rsistanc across th rimary. Th aralll combination of this shunt rsistanc and th imdanc of th rimary winding form th imdanc through which th currnt flows.

2 Tyically, th transformr is dsignd so that th imdanc of th rimary winding is much grathr than th shunt rsistanc rflctd into th rimary sid and thus th rimary imdanc is mostly rsistiv. This shunt rsistanc acts as a currnt viwing rsistor for AC currnt and it is this AC voltag dro that gts transfrrd to th scondary. It is this AC shunt rsistanc that th circuit ss and it is rlativly asy to k its valu vry low so as to hav minimal ffct on th circuit. Bcaus of th isolation fatur of th currnt sns transformr, it can b lacd at any dsird location in a circuit, including abov ground, to monitor currnt thr. Dsign Procdur Tyical starting oints, or inuts, to th dsign rocss ar th following: Primary turns (N ) Snsitivity (S) Dsird sris AC imdanc (Z sac ) Maximum currnt rating (I max ) Minimum frquncy rsons (f min ) Dsird dsign rsults or oututs would includ: Scondary turns (N s ) Scondary trmination rsistanc (R t ) Minimum inductanc factor (A min ) Th suggstd dsign sts using th inuts listd abov ar as follows: 1. Th dsird sris AC imdanc (Zsac) introducd into th circuit by th currnt transformr can b xrssd in volts r amr instad of ohms. Using this figur as th volts r amr on th rimary sid of th transformr and using th dsird snsitivity (S) in volts r amr at th scondary, th turns ratio (n) is calculatd. n = S Z sac 2. Calculat scondary turns (N s ) using th rimary turns (N ) and th turns ratio. N = n s N 3. Calculat th scondary trmination rsistanc (R t ) using th turns ratio and th sris AC imdanc at th rimary. R = Z t sac n 2

3 4. Th minimum rimary inductanc rquird ( ) is a function of how accurat and linar th volts r amr vrsus currnt transfr function of th transformr nds to b. A good rul of thumb for an accurat and linar transformr is to dsign for minimum rimary inductanc whos inductiv ractanc is 100 tims th rimary Z sac at th minimum low frquncy (f min ) dsign oint. min = X (2π f min ) 5. Calculat th rquird inductanc factor to obtain th rquird rimary inductanc ( ) with th scifid numbr of rimary turns (N ). min A = N 2 Dsign xaml Following is an xaml of a dsign using th abov aroach: INPUT OUTPUT Primary turns (N ) = 1 Scondary turns (N s ) = 100 Snsitivity (S) = 0.5 V/A Scondary trmination rsistanc (R t ) = 50 O Sris AC imdanc (Z sac ) = O Minimum inductanc factor (A min ) = 3981 nh/n 2 Maximum currnt rating (I max ) = 5 A Minimum frquncy rsons (f min ) = 20 khz Choosing a Cor Quit oftn, a soft frrit toroidal cor is usd for a currnt sns transformr. A cor of surrisingly small cross sction will b sufficint for currnt transformrs handling multil amrs at tyical switch mod owr frquncis. A toroidal cor is wll suitd for a transformr with a singl turn rimary sinc it is dsird to k th rimary to scondary couling as good as ossibl. Th toroidal cor works wll hr bcaus th scondary turns ar comltly surrounding th singl rimary conductor assing through th hol. Othr shas ar also usd, articularly at lowr frquncis, whr th rquird cross sction is largr and highr numbrs of both rimary and scondary turns ar usd. As sn in th quivalnt circuit in Figur 1, th rimary is in shunt across th rimary sid sris AC imdanc (Z sac ). If th rimary is only on turn, th inductanc factor of th cor nds to b rlativly larg to rovid sufficint inductiv ractanc at th low frquncy nd of th assband. A toroidal sha is also fficint for this rason bcaus th magntic ath lngth of a small toroid can b mad small rlativ to th cross sctional ara which will yild a high inductanc factor r unit volum.

4 A high rmability matrial is also dsirabl in achiving a high inductanc factor. Howvr, on also has to tak into account th rquird orating tmratur rang of th transformr. Th rmability of high rmability grad matrials can dro significantly with rasing tmratur. Th rquird cross sctional ara of th cor is aroachd in ssntially th sam way as with any transformr. It is a function of th cor matrial, th sris AC imdanc (Z sac ) on th rimary sid, th maximum AC rms currnt th rimary will s, and th numbr of rimary turns. It will first b ncssary to calculat th maximum voltag ( max) that will aar across th rimary. max = I max Z sac For a sinusoidal AC currnt with no DC comonnt, th formula rlating rimary voltag ( ), turns (N ), frquncy (f), and cross sctional ara (A) is: = 4.44 f N Bak A Solving for A, w hav: A = 4.44 f N B ak As with any transformr, dtrmining a suitabl Bak is a function of cor matrial and th maximum orating tmratur of th transformr, as wll as cor losss. It is suggstd to k th maximum ak flux dnsity at no mor than 50% of th saturation flux dnsity of th matrial at a articular tmratur. Dsigning for A DC Comonnt As with any transformr, if th currnt in th circuit into which th currnt sns transformr will b insrtd has a DC comonnt, it must b takn into account in th transformr dsign. Th DC comonnt of th currnt in th rimary will roduc a DC comonnt of flux dnsity in th cor matrial. An quation for calculating th aroximat valu of th DC comonnt of flux dnsity is as follows: Whr: B ak = µ H ak H = 4π N I l ak

5 Th units ar B in gauss, I in amrs, l (th magntic ath lngth of th cor ) in mm, and H in orstds. This is only an aroximation bcaus th rmability of th cor matrial will ras as DC currnt incrass. Th µ in th B formula abov is th ffctiv rmability of th magntic circuit of th transformr. Of cours, if an ungad toroid cor is usd, th ffctiv rmability is th rmability of th matrial. On th lus sid, usually th rimary of a currnt sns transformr has a small numbr of turns. Sinc H is roortional to turns, this is dsirabl. A gad frrit cor or owdrd mtal cor may b rquird for situations with high DC comonnts. Frquncy Rsons As has alrady bn discussd, th low frquncy rolloff of th transformr is a function of th rimary inductanc. A high inductanc factor cor is dsird bcaus of th low numbr of rimary turns. As th inductiv ractanc of th rimary rass with rasing frquncy, it will ffctivly shunt an xcssiv amount of currnt away from th sris AC currnt sns imdanc as frquncy rass. As for th high frquncy rolloff of a currnt sns transformr, thr ar both ositivs and ngativs to this ty of dsign. On th ositiv sid, couling btwn rimary and scondary is usually good, so lakag inductanc is rlativly low. On th n gativ sid, th turns ratio of ths transformrs tnds to b high which causs a rlativly larg shunt caacitanc to aar across th rimary. It is th distributd caacitanc of th scondary winding rflctd into th rimary. Th rflctd caacitanc varis with th squar of th turns ratio. C = C n Th largr th valu of C, th lowr th high frquncy rolloff of th transformr. It bgins to shunt currnt away from th Z sac lmnt as frquncy gos u and ractanc gos down. s 2 Transint or Puls Rsons Th currnt sns transformr will rsond adquatly to uls or transint ty currnts. akag inductanc and shunt caacitanc tnd to dtriorat transint rsons. Th lakag inductanc of a toroidal unit using a high rmability cor is rlativly small. Th shunt caacitanc at th rimary is not larg xct for vry high turns ratios. With a uniolar rctangular uls of currnt alid through th rimary, a uniolar rctangular voltag uls is dvlod across Z sac and a calculation of th rsulting flux dnsity chang (?B) in th cor matrial can b calculatd on th basis of voltag.

6 B = T 10 N A 4 Whr B is in gauss, is in volts, T is in µs, and A is in mm 2. nrgy is stord in th magntic fild of th transformr whn th uls is alid. If thr is an off tim btwn ulss, that magntic fild collass and th nrgy is rturnd to th circuit. Howvr, in th cas of most currnt sns transformrs, th vry low shunt rsistanc maks th discharg ath highly ovr-damd and thr is no significant voltag sik during nrgy discharg. Conclusions With th vr xanding lctronics univrs, thr will continu to b a ush for th rcis masuring of lctric currnt for safty and control issus as wll as a nd for bttr dvic fficincy through owr managmnt solutions. Currnt sns transformrs ar ssntial comonnts in ths solutions. Th dsign nginr nds to rmain awar that thr ar many diffrnt tys of CTs availabl using srval diffrnt tys of cor matrials from frrit to iron owdr to amorhous alloy. A siml dsign roduc lik th on dmonstratd in this ar can aid in th dsign rocss and incras th sd at which nw solutions ar brought to th marktlac.