A Helmholtz coil for high frequency high field intensity applications. S. Ciurlo, A. Mariscotti, A. Viacava

Transcription

1 A Helmholtz coil fo high fequency high field intensity applications S. Ciulo, A. Maiscotti, A. Viacava Dipatimento Ingegneia Elettica (Univesità di Genova, Via all Opea Pia A, 65 Genova, , , unige.it) Abstact In this wok a geneal intoduction to Helmholtz coil is pesented and then attention is on a pactical implementation of a wideband (50 khz) coil fo high magnetic flux density applications (seveal mt may be obtained). Field unifomity is within ±.5% and ±0.5% inside cubic volumes of 5% and 0% of the coil side espectively, so suitable also fo high accuacy applications such as senso calibation. I. Intoduction Geneating fields of known and unifom stength is impotant in laboatoy wok. Such fields ae necessay fo accuate and epeatable immunity testing and also fo equipment calibation. Pehaps the simplest type of field geneato seen is a plana coil. The magnetic field in the cente of a cicula coil is given by the fomula H NI/ whee N is the numbe of tuns, the adius and I the cuent passed though the coil. The simple coil has its uses and its dawbacks. Simple coils ae used in some EMC tests []-[] to geneate magnetic fields, eithe as small field coils placed next to the equipment unde test (EUT), o in a lage immesion configuation. The benefits ae simplicity of constuction, small size and ease of installation; the dawback is non-unifomity of field: the field inceases significantly at points nea the wies and outside of the coil, the magnitude and diection of the field ae sensitive to positioning and oientation. Thee ae seveal ways of poducing a unifom magnetic field []: ) a solenoid, ) a tooid, ) a spheical coil with vaiable winding, ) a Helmholtz coil aangement of stacked simple coils. The solenoid is a coil wound in a cylindical fashion; fo a long and naow solenoid the field in the cente egion is HNI/L, whee L is the length. A tooid is a solenoid wound aound in a donut so it closes on itself; the magnetic field is moe unifom and it is still given by HNI/L, whee hee L is the cicumfeence of the tooid at the mean adius of the coil. Thee ae two mechanical difficulties: size, because the tooid must be much lage than equipment inseted into its inteio, and accessibility, because the tooid is a closed suface that must be opened fo insetion. The spheical coils is a sphee wound so that the sheet cuent density is popotional to the sine of the angle elative to the coil axis, a unifom field esults thoughout the entie volume of the sphee. A sinusoidally distibuted sheet cuent can be appoximated eithe by multiple windings diven though esistos of diffeent values, o by vaying the winding density ove the suface of the sphee. The standad geomety fo a Helmholtz pai is two paallel coils spaced one adius apat and diven in phase [6]. Vaiation of the spacing ove a faily wide ange has some effect on the field amplitude and unifomity; the Helmholtz coil can be constucted with eithe cicula o squae coils and this choice has a slight influence on field unifomity. The field it geneates is the sum of the fields geneated by the two spaced coils; the supisingly lage volume of field unifomity esults because thee is a good deal of cancellation fo the off axis field components geneated by the coil. The advantage of Helmholtz coils is that they have a simple geomety (with espect to configuation ) and they allow lage equipment to be fit within the two coils, that is impossible fo all othe solutions. The ectangula geomety is convenient, especially fo constuction and installation. Single squae coils have been used fo calibation of extemely low fequency magnetic field metes fo applications that equie uncetainties of a few pecent [5][7]. Multiple ectangula loops with a common axis have found applications in a numbe of fields, including biological exposue systems fo in vivo and in vito studies [][5]. It is also notewothy that a squae Helmholtz coil poduces a geate volume of nealy unifom magnetic field than a cicula Helmholtz coil of compaable dimensions. Finally, it is to be undelined that immunity standads [][] equie single (o few) tun coils not only fo high fequency but also fo supply fequency testing. If this equiement is vey impotant to limit stay capacitance and esonance effect at high fequency, it eally asks fo a high cuent capability amplifie. The pesented design and implementation is a viable solution to keep the equied cuent amplitude low while ensuing a lage bandwidth (above 50 khz).

2 II. Field equations Only some expessions ae epoted to ease the analysis of the Helmholtz coil and the optimization of geometic paametes. Fo a single squae coil of side a and b, N tuns and input cuent I, one can obtain the field B z on coils axis by Biot-Savat law application and integation [8] B z whee µ 0 NI π n n C C D D ( a + x) ( ) Dn Cn n+ [ n + ( ) Cn] n ( n + D a + x C C a x b + y ( a x) n D D + ( b + y) + ( b y) b + y n ) ( a x) ( a + x) + ( b + y) + ( b y) () With attention to the coodinate system with its oigin on the cente of the fist coil and oientation of z along coil axis (see Fig. below), one can add the second coil with the coodinated tanslation by d (coil spacing) and bing the second deivative to x of the total field (with ab in ou case) to zeo, to obtain the solution fo maximum flatness d.07a. Numeical simulations then indicate that the optimal spacing fo minimum field vaiation along the x axis is slightly lage, aound d.a. Bonaugh [6] epots a useful fomula (fo cicula coils) to locate the majo souces of field eo. δb. B ( δ / + δ / ) 0.6δs / s + δi / I + N / N 0 δ The most impotant tems ae δi/i and δn/n, that ae the elative eos on the input cuent and numbe of tuns: the fist may be made vey small in the ode of the accuacy of the shunt used fo the measuement (about 0.% o bette ove the entie fequency ange, since stay capacitance and inductance tems ae not elevant fo a esistance value in the ode of a faction of Ω); the second tem may be excluded since the numbe of tuns is exact (8 in ou application). The coil fame is made of plywood with einfocement wood patches and bas; the machining toleance is below mm fo edges, pofiles and holes and we may estimate an equivalent size elative eo of mm / 50 mm (half the aveage side length of each coil). Spacing is contolled twice befoe each test on all sides of the paallelepiped and in this case the eo is elated to the eading eo on a mm scale, oughly about 0.5 mm / mm. The calculated theoetical wost case eo is less than % and the expanded k uncetainty is appoximately 0.%. III. Coil design Helmholtz coils ae squae with m nominal side length. To account fo the effective winding thickness, eight layes of mm thickness, the intenal side length was set to about 0.98 m, so that the aveage side length is appoximately m. Each coil is composed of N t 6 tuns and N l 8 layes. Winding geomety was designed to minimize stay capacitance. The analysis of inte-tun stay capacitance C t and inte-laye stay capacitance C l tems suggest that the most impotant tem of the total coil capacitance C c is C l : because of Mille effect C l fo each tun pai is inceased appoximately by the atio of the effective voltage diffeence between two tuns on adjacent layes V ll and the voltage diffeence between two adjacent tuns in the same laye V t. () w α d Figue. Helmholtz coil geomety with coodinate system and patten of the single laye

3 Figue. Constuction of the Zig zag winding and final implementation with the positioning system The winding stuctue is as shown in Fig. : the tun is wounded with a zig-zag path; the skew angle α may be computed fom the pitch d and the winding width w. The total tun length L t is d/cosα, and fo usual values of α (about 0-5 ) this epesents an incease with espect to the staight length d of the fame of about 6-0%. In ou case 8 tuns with an aveage peimete of.6 m took about 580 m of wie fo each coil. The tun esistance R t (and so the total coil esistance R c ) is a linea function of tun length and coss section atio; it was found fo both coils R c 8.0 ± 0. Ω. Coil inductance and capacitance measued at input teminals ae L.8±0.8 mh and L.±0.8 mh, C 70 ± 0 pf and C 76 ± 0 pf espectively fo the two coils. The stay capacitance was detemined based on the measuement of the coil self-esonance, found at 6.8±0. khz fo both coils. Coil inductance is not an issue fo lage field tests at a single fequency at each time, since inductive eactance may be almost canceled out by the seies capacitive eactance of the tuning capacito bank, eaching magnetic field levels well above mt at audiofequency. Tansient field tests o fast sweeping field tests may be accomplished by means of a cuent souce amplifie o a high voltage souce followed by a lage seies esisto (much lage than the coils inductive eactance), because of field unifomity with espect to fequency (see next Section). IV. Expeimental chaacteization In addition to the detemination of the basic electical paametes of the two coils, a seies of measuements have been done in ode to: fist, define the coil input impedance Z c ; second, check unifomity of bulk cuent I b (the sum of the cuents in the individual wies, as defined in [9]) with espect to input cuent I i ; thid, evaluate magnetic field level and unifomity, with the definition of egions of space of given field unifomity, whee expeimental values ae compaed with those deived fom magnetic field equations (efeed to as theoetical values ). The coil impedance Z c has been measued with a voltampeometic method and the esults ae those epoted at the end of Section III to illustate coil design. Unifomity of bulk cuent was qualitatively checked by moving a Rogowski coil along coil peimete and no appeciable diffeence was detected (within appoximately %). A Rogowski coil with impoved common mode and extenal electic field ejection [0] has been used also and it confimed the fist measuement esults up to the esonance fequency. Magnetic field unifomity was tested fo diffeent coils sepaations d, opeating fequencies (attention is focused on 55 khz, a vey high value close to coil esonance, and a smalle value, 0 khz, epesenting low fequency behavio) and positions with espect to coil cente. Othe tests at lowe fequency values have shown that, excluding the small uncetainty elated to the seach of the esonance fequency fo each capacito bank configuation, the flatness of the fequency esponse is within about 0.%. Some sample test esults ae shown in Fig. to illustate the activity. Two coil spacing values (found in the liteatue as suggested optimal values) have been investigated: 80 cm (indicated by the CENELEC standads [][]) and 60 cm (found as indicated in Section II); the field values ae nomalized pe A of bulk cuent.

4 (a) (b) Figue. Measued values of B z [µt] / I b [A] fo coil spacing of (a) 80 cm, (b) 60 cm: z0 cm (uppe left), z cm (uppe ight), z cm (lowe left) and y0 cm (lowe ight)

5 Fo d80 cm spacing (Fig. a) it can be obseved that in the cental potion of space the B field is vey unifom and attention is concentated on a cubic space of cm side (5.5 cm in the half plane plots), whee any magnetic field senso may be placed fo calibation. The aveage field H av.09 µt/a and the dispesion is %. If the consideed potion of space is now a sphee (that fits much bette the shape of the majoity of magnetic field sensos [][]) with diamete of cm, the aveage field incease slightly to.0 µt/a, but the dispesion educes to 0.5%. Field unifomity is even bette fo d60 cm (Fig. b) ove the consideed cubic space ( cm side): H av.78 µt/a and the dispesion is 0.5%; fo the sphee with diamete of cm, H av.6 µt/a and the dispesion is still 0.5%. This clealy ensues a bette unifomity with espect to lage spacing, and a 5% highe field (if the aveage field values ae consideed). It is woth to undeline that the maximum spead of values, i.e. H max H min vs. the aveage field is only.%. The Type B uncetainty fom declaed uncetainties of used equipment and assumed eos in positioning and geomety of the test setup is aound %, but a diect evaluation of Type A uncetainty with k fom epeated measuements (9 fo each point in space) indicates a value always bette than 0.5%. This leaves only positioning and geomety eos of less than % (computed at the end of Section II); to give a bette estimate epoducibility needs to be tested with seveal complete tests taken with diffeent envionmental conditions (especially tempeatue and humidity, taking into account that the coils suppots and the positioning system is made of wood). Conclusions The main elements fo the constuction of a wideband Helmholtz coil pai and elated test esults have been pesented and discussed. The taget applications ae the magnetic field immunity testing of equipment of consideable size, the application of faily constant and unifom magnetic field to laboatoy specimen (such as duing biological expeiments) and finally the calibation of magnetic field sensos with a satisfactoy field unifomity and epeatability within a faction of % fo a wide ange of senso size. The Helmholtz coil is attactive with espect to solenoids and simila achitectues because it is an open achitectue that doesn t impose constaints on the geomety of the device unde test, so that one equipment fits seveal applications, with a vey satisfactoy accuacy. Refeences [] MIL STD 6E, Requiements fo the contol of Electomagnetic Intefeence Chaacteistics of Subsystems and Equipment, [] EN , Electomagnetic compatibility (EMC) Pat : Testing and measuement techniques. Section 8: Powe fequency magnetic field immunity test Basic EMC publication, [] EN , Electomagnetic compatibility (EMC) Pat : Testing and measuement techniques. Section 9: Pulse magnetic field immunity test Basic EMC publication, [] I. Staus, Magnetic field calibation: unwinding the Helmholtz coil, Confomity, May 00, pp. 0- ( [5] M. Misakian, Equations fo the Magnetic Field Poduced by One o Moe Rectangula Loops of Wie in the Same Plane, J. Res. Natl. Inst. Stand. Technol., vol. 05 n., July/Aug. 000, pp [6] E.L. Bonaugh, Helmholtz coils fo calibation of pobes and sensos: limits of magnetic field accuacy and unifomity, IEEE EMC Symposium, 995, pp [7] IEEE Std. 9, IEEE standad methods fo measuing electomagnetic field stength of sinusoidal continuous waves, 0 Hz to 0 GHz, 99. [8] IEEE Std. 6, IEEE standad pocedues fo measuement of powe fequency electic and magnetic fields fom AC powe lines, 99. [9] C. Caobbi, S. Lazzeini and L. Millanta, High fequency opeation of the coils fo standad magnetic field geneation using the bulk-cuent technique, IEEE Tansactions on Instumentation and Measuements, vol. 5 n., Aug. 005, pp. 7-. [0] A. Maiscotti, A Rogowski coil fo high voltage applications, Intenational Instumentation and Measuement Technology Conf. I MTC, Victoia, Vancouve Island, Canada -5 May 008. [] IEEE Std. 0, IEEE Standad Pocedues fo the Measuement of Electic and Magnetic Fields fom Video Display Teminals (VDTs) fom 5 Hz to 00 khz, 99 [] A. Maiscotti, A Lage Bandwidth and Dynamic Range Magnetic Field Pobe, IMTC 007, Wasaw, Poland, May -, 007.