IJIES-2008 VOLUME 1 ISSUE 1 - inass

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Δq Τ1,VinVinΔq Τ2,VinVinΔq Τ1,VoutVoutC 3Ron Ron RcntC 2(a) ËØØ Ì ½Δq Τ2,VoutVoutRon C 3C 2Ron3.2 2 ¢ ModeFigure 4 shows the instantaneous equivalent circuitsin the case of a 2 ¢ mode. In Fig.4 (a), the differentialvalues of the electric charges, ¡Õ Ì ½ÎÒ and¡Õ Ì ½ÎÓÙØ , are given by¡Õ Ì ½ÎÒ ¡Õ ¾ Ì ½Ò ¡Õ Ì ½ÎÓÙØ ¡Õ ¿ Ì ½ (16)In Fig.4 (b), the differential values of the electric charges,¡Õ Ì ¾ÎÒ and ¡Õ Ì ¾ÎÓÙØ , are given by¡Õ Ì ¾ÎÒ ¡ÕÌ ¾ ¾Ò ¡Õ Ì ¾ÎÓÙØ ¡ÕÌ ¾ ¾ ·¡Õ¿ Ì ¾ (17)Φ2,1 , Φ1,2 , Φ1,3Φ2,2 , Φ2,4Φ1,1 , Φ2,3(b) ËØØ Ì ¾TT1T2(c) Timing of pulsesFigure 4. Instantaneous equivalent circuitswhen 2 ¢ mode of operation.Ê ÄÊ Ä · Ê Ë¿¾ (13)where Ê Ë¿¾ depends on the resistance Ê ÒØ shownin Eq.(10). As Eq.(13) shows, Î ÓÙØ can be regulatedby controlling Ê ÒØ which corresponds to the on-resistanceof Ë ½¿ (see in Fig.2.). In other word, the regulation isachieved by controlling the gate voltage of Ë ½¿ .As Eq.(13) shows, the increase of the Ê Ë¿¾ causesthe decrease of the efficiency ¿¾ . In other word, themaximum power efficiency is obtained when Ê ÒØ Ê ÓÒ . From Eq.(10), the minimum on-resistance ÑÒ´Ê Ë¿¾ µcan be expressed byÑÒ´Ê Ë¿¾ µttt´ ·¿µ´½ µ ¡ Ê ÓÒ (14)In Eq.(14), the optimum value of the parameter isobtained when ÑÒ´Ê Ë¿¾ µ¼ Ò ¼ ½ (15)From Eqs.(14) and (15), the optimal duty factor forthe 1.5 ¢ mode is ³ ¼ 3 .From Eqs.(2), (5), (16), and (17), the relation betweenthe input current and the output current is derived asÁ Ò ¾Á ÓÙØ (18)In Figs.4 (a) and (b), the energy consumed by resistorsin one period, Ï Ì ½ and Ï Ì ¾ , can be expressedbyÏ Ì ½ ¾Ê ÓÒÌ ½ ´¡Õ¾ Ì ½ µ¾ · ÊÒØÌ ½ ´¡Õ¾ Ì ½ µ¾Ò Ï Ì ¾ ¾Ê ÓÒÌ ¾ ´¡Õ¾ Ì ¾ µ¾ (19)respectively. From Eqs.(1), (2), (5), (16), and (17),Eq.(19) can be rewritten asÏ ¾Ê ÓÒÌ ½ Ì ´¡Õ Î ÓÙØµ ¾ · ÊÒØÌ ´¡Õ Î ÓÙØµ ¾¾Ê ÓÒ´½ µÌ ´¡Õ Î ÓÙØµ ¾ (20)Ò Ï Ì ¾ By substituting Eq.(20) into Eq.(9), the SC resistancefor the 2 ¢ mode, Ê Ë¾ , can be expressed byÊ Ë¾ ¾¡ Ê ÓÒ · ½´½ µ ¡ Ê ÒØ (21)Therefore, by using Eqs.(18) and (21), the equivalentcircuit is given by the following determinant: ÎÒÁ Ò ½¼ ½ Ê¾Ë¾ ÎÓÙØ (22)¼ ¾ ¼ ½ Á ÓÙØFrom Eq.(22), the averaged output voltage Î ÓÙØ isexpressed by¿ In other word, the power efficiency becomes the maximumvalue when ³ ¼.Î ÓÙØ Ê ÄÊ Ä · Ê Ë¾¡ ´¾Î Ò µ (23)International Journal of Intelligent Engineering and Systems 1 (<strong>2008</strong>) 1-8 4
Furthermore, the power efficiency ¾ can be given byAs Eqs.(21) and (23) show, Î ÓÙØ can be regulated bycontrolling Ê ÒØ (see in Fig.3.). From Eqs.(21) and(24), the maximum efficiency is obtained under thecondition thatbecause the minimum on-resistance ÑÒÊ Ë¾ isobtained when Ê ÒØ Ê ÓÒ . From Eqs.(25), the optimalduty factor is ³ ¼.Δq Τ1,VoutIn Fig.5 (b), the differential values of the electric charges,Vout¡Õ Ì ¾ÎÒ and ¡Õ Ì ¾ÎÓÙØ , are given byC 3¡Õ Ì ¾ÎÒ ¼Δq Τ1,VinÒ ¡ÕRon Ron RcntÌ ¾ÎÓÙØ ¡ÕÌ ¾ ¾ ·¡Õ¿ Ì ¾ (27)VinCFrom Eqs.(2), (5), (26), and (27), the relation between2the input current and the output current is derived as(a) ËØØ Ì ½Δq Á Ò Á ÓÙØ (28)Τ2,VoutVoutIn Figs.5 (a) and (b), Ï Ì ½ and Ï Ì ¾ can be expressedbyRon C 3Δq Ï ¾Ê ÓÒΤ2,VinÌ ½ C 2 RcntÌ ½ ´¡Õ¾ Ì ½ µ¾ · ÊÒØÌ ½ ´¡Õ¾ Ì ½ µ¾VinÒ Ï ¾Ê ÓÒÌ ¾ Ì ¾ ´¡Õ¾ Ì ¾ µ¾ (29)(b) ËØØ Ì ¾respectively. As Eqs.(19) and (29) show, the consumedenergy Ï Ì ½ and Ï Ì ¾ for the case of the 2 ¢TΦ2,1 , Φ1,2T2t mode is equal to that for the case of the 1 ¢ mode.Φ2,4T1t Therefore, the SC resistance for the 1 ¢ mode, ÊΦ1,1 , Φ2,2 , Φ2,3Ë½ ,tΦ1,3can be expressed byt¾(c) Timing of pulsesÊ Ë½ ¡ Ê ÓÒ · ½´½ µ ¡ Ê ÒØ (30)Figure 5. Instantaneous equivalent circuitsTherefore, by using Eqs.(28) and (30), the equivalentwhen 1 ¢ mode of operation.circuit can be given by the following determinant: ÎÒÁ Ò ¾½ ¼ ½ ÊÊ Ä Á Ë½ ÎÓÙØÓÙØ (31) ¾ ¼ ½ ¼ ½ Á¾ ¾ÓÙØÊ Ä Á ÓÙØ · ÊË¾ Á ÓÙØAs Eq.(31) shows, the output voltage of the proposedÊ Ä (24) circuit becomes Î Ò when Ê Ë½ Ê Ä .Ê Ä · Ê Ë¾From Eq.(31), the averaged output voltage Î ÓÙØ isexpressed byÊ ÄÎ ÓÙØ ¡ Î Ò (32)Ê Ä · Ê Ë½As Eqs.(30) and (32) show, the step-down conversion¾Ê Ë¾ ¡ Ê ÓÒ · ½´½ µ ¡ Ê ÓÒ (25)can be achieved by controlling Ê ÒØ (see in Fig.5.).Therefore, different from [16], the proposed convertercan regulate the output voltage in not only the step-upcase but also the step-down case.From Eq.(31), the power efficiency ½ can be givenby¾Ê Ä Á ÓÙØ ½ ¾ ¾Ê Ä Á ÓÙØ · ÊË½ Á ÓÙØIn Fig.5 (a), the dif-Ê Äand (33)Ê Ä · Ê Ë½From Eqs.(30) and (33), the maximum efficiency is¡Õ Ì ½ÎÒ ¡ÕÌ ¾ ½Ò ¡Õ Ì ½ÎÓÙØ ¡Õ Ì ¿ ½ (26)3.3 1 ¢ ModeFigure 5 shows the instantaneous equivalent circuitsin the case of a 1 ¢ mode.ferential values of the electric charges, ¡Õ Ì ½ÎÒ¡Õ Ì ½ÎÓÙØ , are given byobtained when ³ ¼, because Eq.(30) is equal toEq.(21).International Journal of Intelligent Engineering and Systems 1 (<strong>2008</strong>) 1-8 5
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IJIES-2008 VOLUME 1 ISSUE 1 - inass

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