Chapter 16: Magnetic Materials and a Few Devices

Transcription

1 ELECTROMAGNETIC COMPATIBILITY HANDBOOK 1 Chpter 16: Mgneti Mterils n Few Devies 16.1 For the mgneti iruit given in Figure 1 ontining liner mterils (free spe surrouns the ore), etermine the flu, mgneti flu ensit, n mgneti fiel everwhere in the ore n smll gp. Assume the ross-setionl re is equl to A everwhere n the reltive permebilities of the ore mterils re muh greter thn one. Then, etermine the inutne of the N-turn oil. Use superposition n urrent n voltge ivision, n o not simplif the epressions. l l µ r µ r l 4 l 1 g N I Figure For the mgneti iruit given in Figure ontining liner mterils (free spe surrouns the ore), etermine the flu, mgneti flu ensit, n mgneti fiel everwhere in the ore n smll gp. Assume the ross-setionl re is equl to A everwhere n the reltive permebilities of the ore mterils re muh greter thn one. Use superposition n urrent n voltge ivision, n o not simplif the epressions. l l µ r N l µ 1 I 1 r 1 N l 4 I g Figure 16. A urrent probe ple roun ir twin-le line res 1 ma. When the urrent probe is ple roun onl one wire it res 0. ma. If n iel ommonmoe hoke is ple on this line, etermine the new urrent level in eh onutor. Note whether the mgnitue of the urrent inreses or ereses in eh onutor. Copright 00 b Kenneth L. Kiser, Version 08/17/04

2 ELECTROMAGNETIC COMPATIBILITY HANDBOOK 16.4 For two-onutor bles suh s twin-le, refull eplin wh the entire ble n be wrppe roun toroi if ommon-moe hoke is esire rther thn phsill seprting the two onutors n then iniviull wining them roun the toroi Wh woul Lit wire be use for the wining of oil with ferrite ore? 16.6 A short piee of speker wire tht is onnete to n mplifier is essible (the remining portion of the wire is hien in the wll). Vrious tpes of ommonmoe hokes re use t this lotion. The hve little effet on the interferene. Does this impl tht the interferene is entering the sstem from nother route? Eplin. To (help) ensure tht it is not entering vi the speker wire, wht n be one? 16.7SC Moeling wire insie ferrite be s prllel RLC iruit, etermine the geometr ftor K n the vlue for the R, L, n C for three ifferent bes b using tul mesure impene hrteristis. Plot the mgnitue of the impene of the RLC iruit for eh be from 1 to 1,000 MH n ompre to the mesure vlues. [Fir-Rite] 16.8 For the populr 4 ferrite mteril, formul seen for the sturtion urrent of ferrite be is I st = 10R where R is the outer rius of the be in m. Determine the vliit n limittions of this formul. [Kimmel, 94] 16.9SC Compre nltill n numerill the ielie inutne eqution for wire inserte in be versus the inutne eqution for one-turn toroilwoun oil Eplin how ferrite be n be use s ommon-moe hoke How oul ferrite filter roun shiele ble tull inrese the suseptibilit of iruit to ESD? 16.1 For two-hole ferrite be, where is the be most likel to sturte first? Stte ll ssumptions. 16.1S It is stte tht bout 10 B of insertion loss is possible from 1 MH to 1 GH for ertin ferrite bes. Determine whether this is resonble. Clerl stte ll ssumptions If the ommon-moe signls on line re not sinusoil, will the ommon-moe hoke still funtion properl? Eplin If ll three wires of n eletril power line (the hot, neutrl, n groun wires) re woun on one ommon-moe hoke, will it still funtion s hoke to ommon-moe signls? Will it ffet the esirble signls on the power line? [Nve] 16.16S Eplin how one pper towel rbor roll n severl bunhes of steel wool oul (in theor) be use s rue RFI reuer for television set. Assume the interferene is onute. Steel wool onsists of long fine fibers of low-ost, low-strength low-rbon steel. Steel wool n be purhse in ifferent gres (ifferent fiber imeters n fineness) n is use in wie vriet of pplitions rnging from polishing woos to souring pns. Mesure the inutne of one onutor of tpil power or with n without this steelwool filter. Wht frequen(s) is the inutne meter using to etermine the inutne? How oes this ffet the inutne mesurement? Copright 00 b Kenneth L. Kiser, Version 08/17/04

3 ELECTROMAGNETIC COMPATIBILITY HANDBOOK For ifferentil-moe urrents, for rel los, n for rel hrteristi line impenes, it is stte in this hpter tht when the lo impene is smll ompre to the hrteristi impene, then the urrent is lrge t the lo. Using the trnsmission line equtions show tht this sttement is true Wh re ferrite-loe ntenns tpill onl use for reeiving n not trnsmitting? Sometimes n ir gp is introue into the ore of oil wrppe roun toroi. Does the ir-gp erese or inrese the mimum urrent tht n be hnle b the toroi before sturtion? Does the ir gp erese or inrese the lekge flu n the inutne of wining on the toroi? 16.0 Grphill show tht the ifferentil permebilit n be less thn or greter thn the reltive permebilit Wht is the sturtion flu ensit for opper? 16. Derive the epression given in this hpter for the totl power issipte per le ue to hsteresis losses: P, totl 8 = ν Hm fv W/le This ssumes tht the B-H urve n be esribe b the Rleigh-loop epression: ( µ i ν m ) ν ( m ) B = + H H ± H H Notie tht B is given s funtion of H not H s funtion of B. Nevertheless, the hsteresis energ loss per unit volume per le is the re enlose b the hsteresis urve. 16. An pproimtion for the emgnetition ftor for generl ellipsoi is N 1 b = b + + b where, b, n re the lengths of the three es of the ellipsoi. The mgneti fiel is prllel to the is. Determine whether this is resonble epression b proviing three unique heks of this result with epressions provie in the hpter. [Wtson] 16.4 Design, if possible, mh ir-gp toroil inutor with totl length of less thn 5 m if the urrent is 1. A n the signl mplitue is 0 ma. Use the Hnn urves given in this hpter Design, if possible, mh ir-gp toroil inutor with gp length of greter thn 100 mils if the urrent is 1. A n the signl mplitue is 0 ma. Use the Hnn urves given in this hpter Determine the net torque bout the is for irulr loop rring urrent of I when in mgneti fiel of Copright 00 b Kenneth L. Kiser, Version 08/17/04

4 4 ELECTROMAGNETIC COMPATIBILITY HANDBOOK H = H ˆ where H is onstnt. The loop hs rius of, is entere bout the origin, n is lote in the plne. Is this torque equl to m µ oh? Wh or wh not? 16.7 Determine the net torque bout the is for irulr loop rring urrent of I when in mgneti fiel of H = H ˆ + H ˆ + H ˆ ρ ρ φ φ where H ρ, H φ, n H re not funtion of position. The loop hs rius of, is entere bout the origin, n is lote in the plne. Is this torque equl to m µ oh? Wh or wh not? 16.8 For the given four-sie loop # in Tble (provie b our instrutor) in mgneti fiel H # given in Tble 1 (provie b our instrutor), etermine the fore ( vetor) on eh sie of the loop. Then, etermine the net fore on the loop. The urrent in the loop, I, is either lokwise or ounterlokwise (provie b our instrutor). Then, etermine the torque bout the origin for sie X (provie b our instrutor). Tble 1 # H # # H # ˆ ˆ ˆ ( ) 1 ( ) ( ) ( ) ( ) ˆ + ˆ + ˆ ˆ + 1 ˆ + 4ˆ 5 ˆ ( ) ˆ + ( 1) ˆ ˆ ˆ ˆ ˆ 1 ˆ + ˆ ( ) Tble # loop # # loop # = + 5 = + = 0 = 4 b = b = 10 = 4 1 = 4 Copright 00 b Kenneth L. Kiser, Version 08/17/04

5 ELECTROMAGNETIC COMPATIBILITY HANDBOOK 5 = = + 8 b 1 = b = 4 5 = 4 = 0 5 = 0 6 = = 4 b 1 = + 5 b = 5 4 = 0 = Determine the mgnetiing volume n surfe urrents for ro of totl length n rius tht hs been mgnetie to M = M + o ( ρ ) ˆ The is of the linril ro is long the is n the ro is entere bout the origin. Note tht the mgnetition, whih is long the length of the ro, vries in the ρ iretion Using the hsteresis moel B = ( + ) B B H H s r B H + B H r s for permnent mgnet in the seon qurnt, erive the epressions provie in this hpter for B m n H m orresponing to the lotion of the mimum energ prout When is the following integrl epression true? B 0 HB = 0 B HB 16. A soli sphere of rius R is uniforml mgnetie to M ˆ o r. Free spe surrouns this mgnet. Determine the volume mgneti hrge ensit within the sphere n the surfe mgneti hrge ensit t r = R. Determine the net hrge insie the sphere n long the surfe of the sphere. Is this result surprising? Then, using the nlogous epressions for the eletri fiel from rel hrges, etermine the mgneti fiel both insie n outsie the mgnetie Copright 00 b Kenneth L. Kiser, Version 08/17/04

6 6 ELECTROMAGNETIC COMPATIBILITY HANDBOOK sphere. From this informtion, etermine whether the self energ of this mgnet is given b the epression πµ om R E = o Copright 00 b Kenneth L. Kiser, Version 08/17/04