Magnetics Design. Faraday s law. Ampere s law

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1 Prf. S. n-yaakv, DC-DC Cnvrtrs [3- ] Mantics Dsin 3. Iprtant antic quatins 3. Mantic sss 3.3 Transfrr 3.3. Ida transfrr (vtas and currnts) 3.3. Equivant circuit f transfrr (cupin, antizatin currnt) Dsin f transfrr 3.4 Inductr dsin Prf. S. n-yaakv, DC-DC Cnvrtrs [3- ] DC Faraday s aw DC A Φ dφ d V n na ; dt dt Φ - antic fux Wbr [ Wb ] V - vta [ V ] Wb - fux dnsity Tsa [ T ] As : Gauss [ G ] T 0,000 G Prf. S. n-yaakv, DC-DC Cnvrtrs [3-3] Apr s aw I n - antic fid [ A/ ] d n I n I n I [ A/ ]

2 Prf. S. n-yaakv, DC-DC Cnvrtrs [3-4] Mantic sss DC W 3 c P DC Mantic sss ~ Gd nubr 00W/c 3 00KW/ 3 Prf. S. n-yaakv, DC-DC Cnvrtrs [3-5] Mantic Lsss Gd nubr 00W/c 3 00 kw/ 3 Prf. S. n-yaakv, DC-DC Cnvrtrs [3-6] Mantic sss DC W 3 c P DC Mantic sss ~ Gd nubr 00W/c 3 00KW/ 3

cnstant ss: 500W/c 3 Fiur f rit *f Each atria has ptiu pratin tpratur (iniu ss) n-yaakv, DC-DC

3 Prf. S. n-yaakv, DC-DC Cnvrtrs [3-7] Mantic Lsss Prf. S. n-yaakv, DC-DC Cnvrtrs [3-8] Mantic Lsss Curvs fr cnstant ss: 500W/c 3 Fiur f rit *f Each atria has ptiu pratin tpratur (iniu ss) Prf. S. n-yaakv, DC-DC Cnvrtrs [3-9] Transfrr currnts I I n n I I n n Fr ida transfrr n I ni I n I n At any ivn nt n I ni I,I ppsit dirctin. N antic nry strd du t usfu currnts I, I (thy canc ach thr)

4 Prf. S. n-yaakv, DC-DC Cnvrtrs [3-0] Transfrr vtas n n V V φ dφ V n dt Assuin d φ dφ dt dt V n V n dφ V n dt φ φ Prf. S. n-yaakv, DC-DC Cnvrtrs [3- ] Vtas Sinc ach windin as rprsnts an inductanc, thrfr fr any windin V n 0 Prissib vtas: AC ny n any windin A V S S t V S S S S t S S C V S S S S t Prf. S. n-yaakv, DC-DC Cnvrtrs [3- ] Equivant circuit (priinary) Ida Ida L k L k L L :n :n L Ida L k L L n Ida transfrr L :n

5 Prf. S. n-yaakv, DC-DC Cnvrtrs [3-3] Laka inductanc I V n n I V Laka Laka inductanc is th uncupd antic fux :n L k L L k ida Ratinship btwn L k, M and k (cupin cfficint). M k L L L ( k) Lk L k L k n Prf. S. n-yaakv, DC-DC Cnvrtrs [3-4] Laka L k :n L k L V L k L L' k ida V V n L V' L k n k Prf. S. n-yaakv, DC-DC Cnvrtrs [3-5] Mantizatin Currnt I Ida L k V in t V in I L V I R V t :n I t I t I t

6 Prf. S. n-yaakv, DC-DC Cnvrtrs [3-6] Transfrr I V n I sat ax n V Β sat- ax-. ax ( cud b sytrica r asytrica ). ax < sat 3. In st cas ( hih frquncy ) ax iit by antic sss. dφ d V n na dt dt Prf. S. n-yaakv, DC-DC Cnvrtrs [3-7] V V Sytrica pratin Vdt n A t n ax ax T s ax - ax n A ~ t n TS tn Vt n ax na { V,t } n ~ f s ax n A Prf. S. n-yaakv, DC-DC Cnvrtrs [3-8] Skin ffct DC ih Frquncy δ R AC > RDC δ skin dpth 7 δ ( ) f f in z

7 Prf. S. n-yaakv, DC-DC Cnvrtrs [3-9] Skin Effct Sutins Litz wir Tap Prf. S. n-yaakv, DC-DC Cnvrtrs [3-0] Prxiity ffct I I Currnt crwdin du t antic fids Prf. S. n-yaakv, DC-DC Cnvrtrs [3- ] Aw A w [ w n w n ] A A k wa A w k - fiin factr k< w I rs A J J - currnt dnsity A/ J 4.5 A/ A w - windin ara n I I n

8 Prf. S. n-yaakv, DC-DC Cnvrtrs [3- ] ni rs A w Jk { V,t n} n A ax Ap JkA n I w rs JkA w { V,t n} I A rs ax A A A p w { V,t } n I { }Jk ax { V,t n} I Ap Jk { V,Dn} I Ap f Jk s rs rs rs Prf. S. n-yaakv, DC-DC Cnvrtrs [3-3] Transfrr dsin stas. Cacuat A p A p { V,D } I f Jk s n rs In sytrica pratin ax - - ax In asytrica pratin ax -0. Lk fr cr 3. Cacuat n by: 4. Cacuat n { V,t } n ax n A Prf. S. n-yaakv, DC-DC Cnvrtrs [3-4] Inductr dsin I Nd t str nry ( in transfrr n I n I ) L r - air (vacuu) prabiity r - rativ prabiity

9 Prf. S. n-yaakv, DC-DC Cnvrtrs [3-5] Prabiity nry r f frrits r r r < r If is hih wi rach quicky sat Nd t swr Prf. S. n-yaakv, DC-DC Cnvrtrs [3-6] Gaps Discrt air ap r Φ Distributd air ap Sa Φ antic ins in frrantic atria and in air. << Prf. S. n-yaakv, DC-DC Cnvrtrs [3-7] Currnt Crwdin Currnt crwdin du t antic fids R AC hih arund ap

10 Prf. S. n-yaakv, DC-DC Cnvrtrs [3-8] Φ cnstant cnstant ni << Inductanc with Gap Prf. S. n-yaakv, DC-DC Cnvrtrs [3-9] a Dividin ut and dfinin Inductanc with Gap Prf. S. n-yaakv, DC-DC Cnvrtrs [3-30] r r r r r r r r r r r If < r Gap Cacuatin

11 Prf. S. n-yaakv, DC-DC Cnvrtrs [3-3] Inductanc di V L dt di dφ L n dt dt dφ V n dt L-? dφ d d n di n na na na dt dt dt dt di n A di L dt dt n A L Prf. S. n-yaakv, DC-DC Cnvrtrs [3-3] Tw windins n sa cr L n L n Inductr dsin ax Prf. S. n-yaakv, DC-DC Cnvrtrs [3-33] di dφ L n dt dt L Ipk 0 di dt na dt L I pk na ax Saturatin Liits 0 ax d dt dt LIpk n Aax LIpk A nax quick dsin and chck JkA n w Irs

12 Prf. S. n-yaakv, DC-DC Cnvrtrs [3-34] LIpkIrs Ap AA w axjk LIpkIrs LI LI Enry strd Ap Air appd cr Dsin. Cacuat A p. Chs a cr 3. Itrat 4. Cacuat ( r incras ap unti L is as rquird ) Prf. S. n-yaakv, DC-DC Cnvrtrs [3-35] Crs Transfrr cr Inductr cr air ap Prf. S. n-yaakv, DC-DC Cnvrtrs [3-36] Crs. E - cr. TOROID 3. ARENCO 4. POT

13 Prf. S. n-yaakv, DC-DC Cnvrtrs [3-37] Crcia crs Prf. S. n-yaakv, DC-DC Cnvrtrs [3-38] Distributd ap cr Th cncpt f A L y AL y ( sti turn 000turns ) L fr n turns: L n AL Distributd air ap Prf. S. n-yaakv, DC-DC Cnvrtrs [3-39] A L

n-yaakv, DC-DC Cnvrtrs [3-4] Lsss Misadin ntatins!

14 Prf. S. n-yaakv, DC-DC Cnvrtrs [3-40] Trid Data Prf. S. n-yaakv, DC-DC Cnvrtrs [3-4] Prabiity chan Ap/ 79.5 O L dcrass with DC currnt! Prf. S. n-yaakv, DC-DC Cnvrtrs [3-4] Lsss Misadin ntatins! NOT Gd nubr 00W/c 3 Ths curvs ar asurd by fdin ac sinas. If th currnt is cpsd f DC ripp, cr ss is du ny t ripp cpnnt! DC bias tnd t incras ss

15 Prf. S. n-yaakv, DC-DC Cnvrtrs [3-43] Tp. Riz t Spt - Critica paratr Prf. S. n-yaakv, DC-DC Cnvrtrs [3-44] anna Curv LI pk n A ax LI pk n A ax ni LI n A ax LI V ax ax LI V ax r Prf. S. n-yaakv, DC-DC Cnvrtrs [3-45] anna Curv

16 Prf. S. n-yaakv, DC-DC Cnvrtrs [3-46] Cr Siz Sctin Prf. S. n-yaakv, DC-DC Cnvrtrs [3-47] asic Dsin f Distributd Gap Cr. Cacuat LI. Lk up anufacturr data 3. Sct Cr L 4. Cacuat n 000 A L( 000) 5. Chck L in ni 6. Cacuat sss. Tp ris and and f( ) 7. Itrat

SAFE HANDS & IIT-ian's PACE EDT-15 (JEE) SOLUTIONS

SAFE HANDS & IIT-ian's PACE EDT-15 (JEE) SOLUTIONS It is not possibl to find flu through biggr loop dirctly So w will find cofficint of mutual inductanc btwn two loops and thn find th flu through biggr loop Also rmmbr M = M ( ) ( ) EDT- (JEE) SOLUTIONS