Full-Bridge Hybrid Switched Capacitor Case Study

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II. DERIVATION OF THE CONVERTER STRUCTURE
The new generated topology is called Full-Bridge Hybrid Switched Capacitor (FBHSC) Inverter. A Half-Bridge version was previously presented [30]. The new topology was generated initially by differential connection [31]–[33] between two HSC dc-dc converter [16] (cf. Fig. 2a), which was generated as a bidirectional version of the HSC boost dc-dc converter [34], [35]. The unidirectional dc-dc version can be seen as an integration between a conventional boost dc-dc converter and a voltage multiplier circuit [36].
Some known characteristics of a dc-dc converter are necessary to ensure the generation of a dc-ac converter through differential connection. The HSC dc-dc converter, used as building cell, has all these characteristics, which are:
1) Topology must have
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Both unipolar and bipolar PWM [41] can be employed. FBHSC modulation scheme is the same as the conventional FB inverter, only with addition of the modulation signal to additional switches.
The proposed topology has only four conduction states, which are presented in Fig. 3.
MOSFET on-resistance Ron is necessary to limit the instantaneous current when two capacitors are connected in parallel (e.g. in Fig. 3c). Seeing that, MOSFET is the preferred switch to realize the proposed converter, due to its resistive behavior when conducting.
With the intention to simplify the analysis, it was assumed the current, independent of the direction, always will be conducted by the MOSFET channel, instead of the body diode. The MOSFET on-resistance is the only parasitic resistance considered in this analysis. However, all resistances in the loop (e.g. equivalent series resistance (ESR) of the capacitors and trace resistance) will assist the capacitor switching.
In order to obtain a steady-state model, it is necessary to extract the equations of each conduction state. First switching state (cf. Fig. 3a) equations are presented in

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