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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 8

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Components used in output filters Electrolytic capacitors Real capacitor equivalent circuit LcLcLcLc rcrcrcrc C i C (t) U LC U rC U CC UCUC U LC U rC U CC UCUC T C for the capacitor 100 F/35V with I c = 1,25A C = 100 F U c = 0,1V r c = 200 m U rc = 0,25V L c = 100 nH U LC = 0,0125V Series resistance of the electrolytic trcapacitor has most significant influence on the output voltage – special capacitors with low r s are to be used in switching applications ESR - Equivalent Series Resistance

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RMS current value influence on the output capacitor T T IDIDIDID I0I0I0I0 I0I0I0I0 Flyback converter Single-ended forward converter IDIDIDID Considering critical current flow and = 0,5 I 0 = 5A I max I max = 4I 0 = 20A I D < 20%I 0 = 1A ICICICIC UCUCUCUC U CC + U LC U LC ICICICIC UCUCUCUC assuming: r C = 20m U C > 400 mV U C < 20 - 25 mV I crms = 8,16 AI crms = 0,81 A

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General rules of electrolytic capacitor selection for switch-mode applications capacity nominal rated voltage [ F] [V] 25 50 80 2200 1780 2120 2480 4700 2770 3240 6800 3670 4350 Maximum permissible RMS current value [mA] for electrolytic capacitors in the temperature of 85 o C or 105 o C and frequency of 120Hz (such current value causes the capacitor temperature rise < 8 deg) [ o C] KtKt 1 2 20406080100 [Hz] KfKf 1201k10k 1 1,2 1,4 160-450V 63-100V I crmsmax =K t K f I rms

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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.) rtrt rtrt U OUT =U 0 ZZSZZS DD1DD1

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Output filter inductor 1. 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 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 frequencies ferrosilicon cores should be used due to high saturation flux density Bs (windings with smaller number of turns – lower „copper” losses), modern Bs (windings with smaller number of turns – lower „copper” losses), modern technological solutions – nanocrystallic or amorphic cores may be used up to the 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 frequencies of 100 kHz as they combine adavantages of ferrite and iron cores (high Bs and extremely low core power losses) (high Bs and extremely low core power losses) - I DC /I AC relation - core dimensions, air gap width, so called „window area” - mechanical properties – mounting method, resistance to temperature, shocks, vibrations itp. shocks, vibrations itp. Inductor design procedure 1. 1.Specifying required inductance of the output choke basing on the AC output current component L C Ro IoIo ILIL U0U0 U IN

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2. Winding wire diameter usually assumed current density 2,5 < J < 5 [A/mm 2 ] 3. Core volume and air-gap selection B H BsBsBsBs -B s B0B0B0B0 HHHH BBBB H 0 (I 0 ) H 1 (I 1 ) without air-gapwith air-gap SwSw

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Using Hahn diagrams 0,11,0101001000 NI [Azw] AL.=10000 AL.=1000 AL.=400 EE30 AL.=6600 AL.=800 AL.=250 ETD34 a) a) Initial core selection (diameters) b) b) assume air-gap lenght (AL) c) c) find the maximum value of ampere-turns IxZ [Azw] d) d) check if the required inductance may be achieved - (1) e) e) if not, try with bigger air-gap (lower AL) and go back to d) f) f) if yes, check if there is enough space for winding in the core window area g) g) if not, select bigger core and start from a) h) h) if yes - output choke is ready i) i) eventualy try with the smaller core if it is to much free room in the window area (1)

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SeSe SwSw Core selection basing on „AP” (Area Product) – characteristic value for the core of certain dimentions 0,2 1,0 10 100 125102050100 I 0 [A] AP [cm 4 ] 10mH 1mH 100 H 10 H 1H1H1H1H For the presented example ETD34 – AP=1.185 cm 4, l = 34 mm l Calculating the number of turns przyjmujemy I = I 0 +0,1I 0 oraz B = B S

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Air-gap lenght calculation permability of the air (=1) magnetic field constant (4 10 -7 ) Empirical method 1. 1. Make the winding with the number of turns z L > z Lmin, 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) 2. 2. Set the air-gap, which gives lowest ripple but without any sign of saturation I L (U rC ) optimal air-gap

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Self-Inductance When the switch is closed, the current does not immediately reach its maximum value Faraday’s law can be used to describe the effect.

Self-Inductance When the switch is closed, the current does not immediately reach its maximum value Faraday’s law can be used to describe the effect.

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