IJIES-2008 VOLUME 1 ISSUE 1 - inass

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 ÓÙص ¾ · ÊÒØÌ ´¡Õ Î ÓÙص ¾Ê ÓÒÒ Ï Ì ¾ ´½ µÌ ´¡Õ Î ÓÙص 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 (2008) 1-8 3