4.5 A 2-phase resonant switched-capacitor converter delivering 4.3W at 0.6W/mm<sup>2</sup> with 85% efficiency (2014)

In this work, we present a 2-phase ReSC converter that operates with supply voltages from 3.6 to 6V, providing compatibility for a range of applications including Li-Ion battery supplies. Figure 4.5.2 shows the power train of the 2-phase ReSC converter. The architecture is similar to the 2:1 SC converters in [2-3], but uses inductance, L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</sub> , to resonate with the on-chip flying capacitor, C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</sub> . On-chip bypass capacitance, C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">bp</sub> , is used to filter the output voltage and complete the resonant loop in the energy transfer process. The timing of key signals in converter operation is shown in Fig. 4.5.3. In normal operation at the fundamental resonant frequency, ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> =(L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</sub> C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</sub> ) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1/2</sup> , resonant impedance Z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</sub> is configured in parallel with Vin-Vout in φ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> ; in φ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , Z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</sub> is configured in parallel with Vout. If there is a voltage difference between Vin-Vout and Vout-GND, voltage V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</sub> appears as a square wave at the resonant frequency. In φ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , a positive half wave current flows into Z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</sub> , drawing energy from Vin; in φ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , a negative half wave current flows out of Z <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</sub> , supplying energy to the load. Similar to the SC topology, this process can be modeled as an effective resistance, REFF, the details of which are discussed in [6]. Operation at the fundamental mode provides the lowest achievable R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">EFF</sub> , which is approximately R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ESR</sub> ·π <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /8 for the 2:1 configuration, near the minimum achievable R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">EFF</sub> for a comparable SC converter.