IJIES-2008 VOLUME 1 ISSUE 1 - inass

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VoutVoutΔq Τ1,VoutS2,3 S2,4C 3C 3Φ1,iΦ2,jVinTS1,1S2,1S2,2S1,2C 1 C 2T1T2S1,3Figure 1. Proposed SC DC-DC converter.ttΔq Τ1,VinRon Ron RcntVinRonΔq Τ2,VinC 1 C 2(a) ËØØ Ì ½VoutRon C 3C 1 C 2Δq Τ2,VoutVinRonTo adjust the output voltage, on-resistance controlscheme [9,12,13,16] or pulse width modulation (PWM)scheme [10, 11] is usually employed in the SC DC-DC converter, because the ratio of the voltage conversionis predetermined by circuit structure. The powerefficiency of the SC power converters gets worse bythe regulation of the output voltage. In the case of avoltage doubler circuit [14-16], for example, the efficiencydecreases greatly when the low output voltageis required, because the output voltage must be regulatedstrongly. To solve this problem, we proposedthe circuit topology of a 1.5 ¢ mode SC DC-DC converterin [9], because it is necessary to create a 5 Vpower supply 1 from a 3.7 V supply of a lithium-ionbattery. However, by changing the control scheme ofclock pulses, fortunately, the converter proposed in [9]can work as a versatile step-up/step-down converterwhich can offer a 2 ¢/ 1.5 ¢/ 1¢ mode of operation.As mentioned above, to extend the battery life,the step-up/step-down converters are useful.In this paper, aimed at backlighting applications,battery management applications, etc., the converterproposed in [9] is modified to provide stepped-up /stepped-down voltages, and the handy theoretical formulasare given concerning the power efficiency andthe optimal duty factor. Compared with the conventionalversatile converters based on doubler circuits[16], the proposed converter can realize high efficiencyand flexibility of output voltages, because it offers a 2¢/ 1.5 ¢/ 1¢ mode of operation. To confirm the validityof the circuit design and the theoretical analyses,SPICE simulations are performed.½ The typical voltage for backlighting applications is 5 V.Φ1,1 , Φ1,2 , Φ1,3Φ2,1 , Φ2,2 , Φ2,3 , Φ2,4Ron(b) ËØØ Ì ¾TT1T2(c) Timing of pulsesFigure 2. Instantaneous equivalent circuitswhen 1.5 ¢ mode of operation.2. Circuit StructureFigure 1 shows a 1.5 ¢ mode DC-DC converter designedby using the SC technique [9]. The converterconsists of 7 power switches and 3 capacitors. InFig.1, the power switches Ë ½ and Ë ¾ ´´ ½¿µand ´ ½µµ are driven by 2-phase clock pulses¨½ and ¨¾ , respectively. The interval of ¨½ and¨¾ is set to as follows:Ì Ì ½·Ì ¾Ì ½ ÌÒ Ì ¾ ´½ µÌ (1)where Ì is a period of the clock pulse and denotesa duty factor. By controlling the power switches Ë ½and Ë ¾ , the converter performs a DC-DC conversion.The control scheme and the circuit properties for a2 ¢/ 1.5 ¢/ 1¢ conversion will be described in thefollowing section.3. Theoretical Analysis3.1 1.5 ¢ ModeFirst, the equivalent circuit when a 1.5 ¢ mode isanalyzed. In the theoretical analysis, we assume thatttInternational Journal of Intelligent Engineering and Systems 1 (<strong>2008</strong>) 1-8 2
1. parasitic elements are not effective and 2. the timeconstant is quite larger than a period of the clock pulse.Figure 2 shows the instantaneous equivalent circuitsin the case of the 1.5 ¢ mode. In the steady state, thedifferential values of the electric charges in ´ ½ ¾ ¿µ satisfyI inVin1 : MI outRSCVo VoutFigure 3. General form of equivalent circuit.¡Õ Ì ½ ·¡Õ Ì ¾ ¼ (2)where ¡ÕÌ ½ and ¡Õ Ì ¾denote the electric charges whenËØØ Ì ½ and ËØØ Ì ¾, respectively. In the caseof ËØØ Ì ½, the differential values of the electriccharges in the input and the output terminals, ¡Õ Ì ½ÎÒand ¡Õ Ì ½ÎÓÙØ , are given by¡Õ Ì ½ÎÒ ¡ÕÌ ½ ½ ¡Õ¾ Ì ½Ò ¡Õ Ì ½ÎÓÙØ ¡Õ Ì ¿ ½ (3)Here, a general equivalent circuit of SC power converters[3,4,9,12] can be given by the circuit shown inFig.3, where Ê Ë is called an SC resistance, Å is aratio of the ideal transformer, and Î Ò and Î ÓÙØ denotean averaged input voltage and an averaged output voltage,respectively. The consumed energy Ï Ì of Fig.3can be expressed byOn the other hand, in the case of ËØØ Ì ¾, thedifferential values of the electric charges in the inputand the output terminals, ¡Õ Ì ¾ÎÒ and ¡Õ Ì ¾ÎÓÙØ , aregiven by¡Õ Ì ¾ÎÒ ´¡ÕÌ ½ ¾ ·¡Õ¾ Ì ¾ µÒ ¡Õ Ì ¾ÎÓÙØ ¡ÕÌ ½ ¾ ·¡Õ¾ Ì ¾ ·¡Õ¿ Ì ¾ (4)Here, the average currents of the input and the outputare given byÁ Ò ´¡Õ Ì ½ÎÒ ·¡Õ Ì ¾ÎÒ µÌ ¡Õ ÎÒ ÌÒ Á ÓÙØ ´¡Õ Ì ½ÎÓÙØ ·¡Õ Ì ¾ÎÓÙØ µÌ ¡Õ ÎÓÙØ Ì (5)where ¡Õ ÎÒ and ¡Õ ÎÓÙØ are the electric charges inthe input and the output, respectively. From Eqs.(2) (5), the following equation is derived:¿Á Ò Á ÓÙØ (6)¾In Fig.2, the energy consumed by resistors in oneperiod, Ï Ì , can be expressed bywhereÏ Ì Ï Ì ½ · Ï Ì ¾ (7)Ï Ì ½ ¾Ê ÓÒÌ ½ ´¡Õ½ Ì ½ µ¾ · ÊÒØÌ ½ ´¡Õ½ Ì ½ µ¾Ò Ï ¾Ê ÓÒ¾ÊÌ ¾ Ì ¾ ´¡Õ½ Ì ¾ µ¾ ÓÒ ·Ì ¾ ´¡Õ¾ Ì ¾ µ¾ From Eqs.(1) (5), Eq.(7) can be rewritten asÏ Ê ÓÒÌ ½ ¾Ì ´¡Õ Î ÓÙØµ ¾ · ÊÒØÌ ´¡Õ Î ÓÙØµ ¾Ê ÓÒÒ Ï Ì ¾ ´½ µÌ ´¡Õ Î ÓÙØµ ¾ (8)Ï Ì Ï Ì ½ · Ï Ì ¾¡Õ Î ÓÙØ ´ µ ¾ ¡ Ê Ë ¡ Ì (9)ÌBy substituting Eq.(8) into Eq.(9), the SC resistancewhen the 1.5 ¢ mode, Ê Ë¿¾ ,isgivenbyÊ Ë¿¾ ¾´½ · µ´½ µ ¡ Ê ÓÒ· ½ ´½ µ ¡ Ê ÒØ (10)The equivalent circuit of Fig.3 can be expressed bythe determinant using a Kettenmatrix. Therefore, byusing Eqs.(6) and (10), the equivalent circuit of theproposed converter is given by the following determinant: ÎÒ¾¿Á Ò¼¼¿¾½¼Ê Ë¿¾½ÎÓÙØÁ ÓÙØ (11)As Eq.(11) shows, the output voltage of the proposedcircuit becomes ´¿¾µÎ Ò when Ê Ë¿¾ Ê Ä .From Eq.(11), the averaged output voltage Î ÓÙØ isexpressed byÊ ÄÎ ÓÙØ ¡ ´ ¿Ê Ä · Ê Î Òµ (12)Ë¿¾ ¾Furthermore, the power efficiency ¿¾ 2 can be givenby¾Ê Ä Á ÓÙØ ¿¾ ¾ ¾Ê Ä Á ÓÙØ · ÊË¿¾ Á ÓÙØ ¾ Of course, the consumed energy of the peripheral circuits suchas pulse generators, comparators, etc. is disregarded in thepower efficiency of Eq.(13).International Journal of Intelligent Engineering and Systems 1 (<strong>2008</strong>) 1-8 3
Page 1: International Journal ofIntelligent
Page 5 and 6: Furthermore, the power efficiency
Page 7 and 8: and SPICE simulations.Concerning th

IJIES-2008 VOLUME 1 ISSUE 1 - inass

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