IJIES-2008 VOLUME 1 ISSUE 1 - inass

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 ÓÙص ¾ · ÊÒØÌ ´¡Õ Î ÓÙص ¾¾Ê ÓÒ´½ µÌ ´¡Õ Î ÓÙص 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 ʾ˾ 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 (2008) 1-8 4