1. SWITCH-MODE POWER SUPPLIES AND SYSTEMS Silesian University of Technology Faculty of Automatic Control, Electronics and Computer Sciences Ryszard Siurek Ph.D., El. Eng. Lecture No 9

2. Power losses in magnetic componenets Power losses related to winding restances - „copper power losses”  T I min I max t I  T t I Additional power losses resulting from higher frequency 1. Skin effect I...... H IwIw I+I w I-2I w IwIw

3. D PN Rzeczywisty rozkład prądu Równoważny rozkład prądu I max 1/e(I max ) J D PN - penetration depth (skin thickness) Penetration depth decreases with frequency increase It may be calculated for copper wire in the temperature of 100 o C from equation: where f – frequency in Hz At the frequency equal to 100kHz - D PN =0,24mm, at f =1MHz - D PN =0,075mm 1,5 2,0 3,0 5,0 10,0 2101005 Additional rise of effective AC resistance appears for square waveforms (distorted) due to wide spectrum of high frequency har- monics

4. 2. Proximity effect I I H H’ Proximity effect is responsible for exponential growth of current density in the area close to the surface of every winding layer according to number of layers! As a result the useful area of conductor is further reduced........ + + + + + + +............. + + + + + + + + + + + + + +.................................... 1A 1+2-2+3

5. Dowell’s diagram 10 -1 110 1 10 2 10 3 FRFR R AC =F R R DC h – unified layer thickness for round wire diameter d - h=0,866d D PN – penetration depth F l - copper layer factor z l – number of turns in a layer d – wire diameter w - layer width P - number of layers P 10 5 4 2 1 0,5 Copper power losses: P CU = I RMS R AC 2

6. General rules for winding design 1. 1. Using low diameter wires (minimum d/D PN ) – in case of high currents several wires in paralell 2. 2. Using copper foil (or several foils in paralell) of thickness not exceeding 2D PN 3. 3. Using special „litz” wire, a braid of very small diameter isolated wires (interwoven wires) – skin effect is minimized due to electric field cancelation 4. 4. Reducing (if possible) the number of layers of the winding 5. 5. Arranging windings in sections (to reduce proximity effects by decreasing of effective number of layers) Two different methods of windings arrangement P1 P2 S1S2 S3 H(Z*I) P1P2S3S2S1 H(Z*I) Electric field distribution in windings

7. Magnetic core losses (eddy currents, hysteresis losses)  B [mT] P core [mW/cm3] 100200300 10 100 100kHz 60kHz 20kHz 10kHz 5kHz T=100 o C Temperature [ o C] Power loss P core [mW/cm3] 100 200 f=500kHz  B=0,2T  B=0,1T f=100kHz  B=0,2T 10020604080

8. Temerature rise of transformer and inductor Temperature rise estimation is essential in consideration of: - Curie temperature (possibility of total loss of magnetic properties) - permissible temperature of isolation materials (safety requirements) - permissible temperature rise inside the equipment Usually simplified equations are used (empirical)): S C - total surface area of the magnetic component [cm 2 ] Magnetic leakage due to air-gap introduced to the magnetic path copper foil band air-gap should be made in the center pole of the core only copper band decreases leakage field streght (EMC disturbances) but causes additional power losses copper band must not create the short-circuit turn!