SWITCH -MODE POWER SUPPLIES AND SYSTEMS

1. SWITCH-MODE POWER SUPPLIES AND SYSTEMS Lecture No 8 Silesian University of Technology Faculty of Automatic Control, Electronics and Computer Sciences Ryszard Siurek Ph.D., El. Eng.

2. Components used in output filters Electrolytic capacitors Real capacitor equivalent circuit UC C iC(t) C Lc rc T iC(t) t ULC UrC UCC ULC for the capacitor 100mF/35V with DIc = 1,25A C = 100 mF DUc = 0,1V rc = 200 mW DUrc = 0,25V Lc = 100 nH DULC = 0,0125V UrC UCC ESR - Equivalent Series Resistance UC Series resistance of the electrolytic trcapacitor has most significant influence on the output voltage – special capacitors with low rs are to be used in switching applications

3. RMS current value influence on the output capacitor Flyback converter Single-ended forward converter Considering critical current flow and g = 0,5 I0 = 5A ID ID Imax I0 I0 t T t T Imax = 4I0 = 20A DID< 20%I0 = 1A IC IC DULC DUC DUC DUCC+DULC assuming: rC = 20mW DUC > 400 mV DUC < 20 - 25 mV Icrms= 8,16 A Icrms= 0,81 A

4. General rules of electrolytic capacitor selection for switch-mode applications Kt capacity nominal rated voltage [mF] [V] 25 50 80 2200 1780 2120 2480 4700 2770 3240 6800 3670 4350 2 1 Maximum permissible RMS current value [mA] for electrolytic capacitors in the temperature of 85oC or 105oC and frequency of 120Hz (such current value causes the capacitor temperature rise < 8 deg) 20 40 60 80 100 [oC] Kf 160-450V 1,4 63-100V Icrmsmax=KtKfIrms 1,2 1 120 1k 10k [Hz]

5. select special capacitors with low ESR to keep output voltage ripple small • use proper capacitor (or several capacitors connected in paralell) with permissible RMS current much higher than the maximum RMS current value in real circuit • Select capacitors with biggest admissible dimensions as they perform better heat transfer to the environment (due to power losses on ESR) • make external series resitances of electrical leads and connections as low as possible and symmetrical (traces on PCB, wires, metal buses etc.) • place electrolytic capacitors apart from components generating heat (power resistors, heat sinks etc.) D1 rt rt UOUT=U0 ZS

6. Output filter inductor Magnetic material choise depends on: - operating frequency - for high AC currents (magnetic field) and frequencies over 1 kHz ferrite materials are generally used due to low power losses, for low frequencies ferrosilicon cores should be used due to high saturation flux density Bs (windings with smaller number of turns – lower „copper” losses), modern technological solutions – nanocrystallic or amorphic cores may be used up to the frequencies of 100 kHz as they combine adavantages of ferrite and iron cores (high Bs and extremely low core power losses) - IDC/IAC relation - core dimensions, air gap width, so called „window area” - mechanical properties – mounting method, resistance to temperature, shocks, vibrations itp. Inductor design procedure Specifying required inductance of the output choke basing on the AC output current component L IL Io UIN U0 Ro C

7. 2. Winding wire diameter usually assumed current density 2,5 < J < 5 [A/mm2] 3. Core volume and air-gap selection B without air-gap with air-gap Bs DB B0 Sw DH H H0(I0) H1(I1) -Bs

8. Using Hahn diagrams AL.=250 AL.=800 ETD34 AL.=6600 (1) AL.=400 EE30 AL.=1000 AL.=10000 0,1 1,0 10 100 1000 NI [Azw] Initial core selection (diameters) assume air-gap lenght (AL) find the maximum value of ampere-turns IxZ [Azw] check if the required inductance may be achieved - (1) if not, try with bigger air-gap (lower AL) and go back to d) if yes, check if there is enough space for winding in the core window area if not, select bigger core and start from a) if yes - output choke is ready eventualy try with the smaller core if it is to much free room in the window area

9. Core selection basing on „AP” (Area Product) – characteristic value for the core of certain dimentions AP [cm4] Sw 100 10mH l 1mH 100mH 10 Se 10mH For the presented example ETD34 – AP=1.185 cm4 , l = 34 mm 1,0 1mH 0,2 I0 [A] 1 2 5 10 20 50 100 Calculating the number of turns przyjmujemy DI = I0+0,1I0 orazDB = BS

10. Air-gap lenght calculation permability of the air (=1) magnetic field constant (4p10-7) Empirical method Make the winding with the number of turns zL> zLmin, use wire of maximum possible diameter and then under the nominal load try to decrease the air gap step by step measuring the inductor current waveform (output ripple) Set the air-gap, which gives lowest ripple but without any sign of saturation IL (UrC) IL (UrC) IL (UrC) optimal air-gap