Magnetics. Important relationships. Magnetic quantities Analogies to electrical quantities

Transcription

1 Mor M. Peretz, Switch-Mode Power Supplies [3-1] Faraday s and Amper s laws Permeability Inductor Reluctance model Air gap Current crowding Inductor design Skin effect, proximity effect Losses Transformer Ideal transformer Real transformer Transformer design Magnetics Mor M. Peretz, Switch-Mode Power Supplies [3-2] Important relationships Faraday B v( t ) ( t),φ( t) Electrical Core i( t) Ampere H( t), F( t) Mor M. Peretz, Switch-Mode Power Supplies [3-3] Magnetic quantities Analogies to electrical quantities MMF Magnetic field H FM l H l Voltage Electric field E l V E l B,φ J, I B φ J I 1

2 Mor M. Peretz, Switch-Mode Power Supplies [3-4] Important relationships B H Faraday s law dφ db V n nae ; dt dt Amper s law Hdl n I ni H l e B µ H Mor M. Peretz, Switch-Mode Power Supplies [3-5] Units Φ - magnetic flux Weber [ Wb ] Wb B - flux density Tesla [ T] 2 m Gauss [ G ] 1T 10,000 G H - magnetic field [ A/m ] V - voltage [ V ] µ - magnetic permeability [ H/m ] Mor M. Peretz, Switch-Mode Power Supplies [3-6] Permeability B µ 0 B µ H µ r H Free space permeability (Vacuum) µ 0 4π 10 7 Typical magnetic material permeability 3 5 µ r Typical B sat Ferrite: T Iron powder: T 2

3 Mor M. Peretz, Switch-Mode Power Supplies [3-7] What is inductance? dφ di V n V L dt dt Mor M. Peretz, Switch-Mode Power Supplies [3-8] Reluctance model H B µ F Hl e B ϕ A l 1 e R µ H A φ3 φ1+ φ2 ɸ 1 ɸ 2 ɸ 3 F ϕr ɸ R Mor M. Peretz, Switch-Mode Power Supplies [3-9] Inductance with gap l e Rm µ A r e l g Rg µ 0Ae φ( m g) ni R + R 2 dφ n di v n dt R m + R g dt L 3

4 Mor M. Peretz, Switch-Mode Power Supplies [3-10] Current crowding l e Rm µ A r e l g Rg µ 0Ae ni R g Rg>> Rm + ( Rm Rg) ni Mor M. Peretz, Switch-Mode Power Supplies [3-11] Inductor design Air gap l If e <µ r lg l µ e re lg l g << l e lg+ le le Mor M. Peretz, Switch-Mode Power Supplies [3-12] dφ di V n V L dt dt Bmax db I pk di nae dt L 0 0 dt dt dt LI pk naeb max Inductor design Saturation - Ae LIpk n Bmax Ae 4

5 Mor M. Peretz, Switch-Mode Power Supplies [3-13] Inductor design Aw nwa Aw k Irms Wa J nirms Aw Jk Mor M. Peretz, Switch-Mode Power Supplies [3-14] LIpkIrms Ap Ae Aw B Jk Inductor design Ap max Mor M. Peretz, Switch-Mode Power Supplies [3-15] Calculate Ap Choose core Calculate n Calculate lg or adjust gap Inductor design summary 5

6 Mor M. Peretz, Switch-Mode Power Supplies [3-16] Inductor selection Off-shelf product Mor M. Peretz, Switch-Mode Power Supplies [3-17] Inductor selection Off-shelf product Mor M. Peretz, Switch-Mode Power Supplies [3-18] Skin effect DC High Frequency δ R AC > 1 RDC δ skin depth 72 δ ( mm) f f in Hz 6

7 Mor M. Peretz, Switch-Mode Power Supplies [3-19] Skin Effect Solutions Litz wire Foil/tape Mor M. Peretz, Switch-Mode Power Supplies [3-20] Proximity effect I I Current crowding due to magnetic fields Mor M. Peretz, Switch-Mode Power Supplies [3-21] Losses function of B P ~ K B i f j i, j material dependent B H 7

8 Mor M. Peretz, Switch-Mode Power Supplies [3-22] Losses function of temperature Mor M. Peretz, Switch-Mode Power Supplies [3-23] Losses material selection Mor M. Peretz, Switch-Mode Power Supplies [3-24] Ideal transformer φ R n I n I m R m n I n I φ dφ1 dφ2 V1 n1 V2 n2 dt dt 8

9 Mor M. Peretz, Switch-Mode Power Supplies [3-25] Transformer characteristics Current flow at the same time at primary and secondary Each winding represents inductance Average voltage 0 AC only on any winding Mor M. Peretz, Switch-Mode Power Supplies [3-26] Magnetizing inductance φ R n I n I V m dφ n dt n 1 d n2 V1 i1+ i2 R { m dt n1 Lm Mor M. Peretz, Switch-Mode Power Supplies [3-27] uncoupled magnetic flux Leakage inductance L lkg, M (mutual coupling) and k (coupling coefficient) M k L L 1 2 Llkg 1 Lm (1 k) L L n lkg 2 lkg1 2 9

10 Mor M. Peretz, Switch-Mode Power Supplies [3-28] Magnetizing and leakage inductances V1 V2 I2 Im I1 Mor M. Peretz, Switch-Mode Power Supplies [3-29] n W A w Irms Wa J n I A w 2n1I 1 Aw Jk Transformer design Aw + n Wa k 1 a n I Jk 1 1rms 2 2rms rms Mor M. Peretz, Switch-Mode Power Supplies [3-30] Transformer design Saturation - Ae 1 B Vdt nae B B + max max VmT on n 2B A max e 10

11 Mor M. Peretz, Switch-Mode Power Supplies [3-31] A A A p w e A A p p { V Ton} Transformer design Ap { V1 T on} 2 I1 rms { 2B } Jk 2 I 1 1rms B Jk { V Don} 2 I 1 1rms f B Jk s max Mor M. Peretz, Switch-Mode Power Supplies [3-32] Calculate Ap Choose core Calculate n1 Calculate n2 Transformer design summary Mor M. Peretz, Switch-Mode Power Supplies [3-33] Magnetic design Example Boost converter: P100W, Vin10V, Vo50V, IL0.1I Lav Calculate L Calculate Ap 11

12 Mor M. Peretz, Switch-Mode Power Supplies [3-34] Mor M. Peretz, Switch-Mode Power Supplies [3-35] Mor M. Peretz, Switch-Mode Power Supplies [3-36] 12

13 Mor M. Peretz, Switch-Mode Power Supplies [3-37] Mor M. Peretz, Switch-Mode Power Supplies [3-38] Mor M. Peretz, Switch-Mode Power Supplies [3-39] 13