Q show or drive, as appropraite that this equations(1)&(2)&(3) are correct Q_2 i

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Q show or drive, as appropraite that this equations(1)&(2)&(3) are correct

Q_2 is turned on and Q_1 is turned off in this state. C_1 and L_r resonate together with Vs while C_16 and L_r resonate together with C_2. They all start resonating at to from the current equal to zero in sinusoidal manner. Since the current increases gradually at t_0, Q_2 is turned on under zero-current switching condition. They stop resonating when the current reaches zero again at t_1 by the reverse biased D_1 and D_16. Let L = L and C_1 = C_16 = C. Assume that C_2 and D_26 are large enough to keep the voltage to be constant, and the circuit is lossless, the equations of this state can be derived by classical circuit equation

Explanation / Answer

The triple-mode switched-capacitor resonant circuit is like a two double-mode switched-capacitor resonant converters combined together. Similar to double-mode circuit, when is turned on while is turned off, and are connected in series resonance through . is charged from source . Both and are very large capacitors for keeping the voltage to be constant. is like another voltage source with its voltage equals to . discharges to through while and are connected in series resonance. When is turned on while is turned off, and are connected in series resonance with and their polarities are in same direction and add up. Since has a dc component 1057-7122/$20.00 © 2005 IEEE 944 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 52, NO. 5, MAY 2005 Fig. 3. n-mode of switched-capacitor resonant converter. Fig. 4. Proposed switching-capacitor cell. equal to . They charge so that the voltage across equals to . and are connected in series resonance as well with in the same direction of polarity. has a dc component equal to . and release energy to the load together. is not necessary equal to , but is usually made them equal in order to ensure zero-current switching can be controlled easily. The voltage conversion ratio of the converter is 3. Actually, can be considered to be another output with voltage conversion ratio equal to 2 so that this circuit can be a multiple output circuit. III. MATHEMATICAL ANALYSIS The computer simulation waveforms of the triple-mode circuit using the parameters of V, and F, and F, H, W) are shown in Fig. 5(a) and (b). For analyzing the circuit, it would be divided into four states in each switching period. Fig. 6(a)–(d) shows the equivalent circuits of the triple mode switched-capacitor resonant coverter for the four states. A. State I [ to ] is turned on and is turned off in this state. and resonate together with while and resonate together with . They all start resonating at from the current equal to zero in sinusoidal manner. Since the current increases gradually at is turned on under zero-current switching condition. They stop resonating when the current reaches zero again at by the reverse biased and . Let and . Assume that and are large enough to keep the voltage to be constant, and the circuit is lossless, the equations of this state can be derived by classical circuit equation (1) (2) Fig. 5. Simulation waveforms of triple-mode switched-capacitor resonant converter. V and V stand for the drain–source and gain voltages of the Mosfet. V is the interim voltage develo

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