flying-capacitor-stacks-voltage - Electronic Circuits XV & XVI: Transformers and Switched-Capacitor Conversion Step by Step

A flying-capacitor-stacks-voltage scan holds the source rail fixed and varies the charged flying-capacitor voltage across three rows, checking that the stacked output V_out = V_s + V_fly adds the two row by row. The arithmetic is exact only for the stated source voltages, flying-capacitor voltages, output voltages, and rows in the ideal capacitor, switch, and phase-topology model. Real switched-capacitor converters add switch resistance, ESR, parasitic capacitance, charge injection, timing skew, load current, probe/calibration limits, finite precision, and measurement uncertainty.

A second phase can place a charged flying capacitor above a source. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A stacked phase names the source and flying capacitor

The output row is accepted only after the phase points to one source rail and one charged flying capacitor.

V_s=6\ \text{V}\quad V_{\text{fly}}=6\ \text{V}

The stacked output rises one-for-one with flying voltage

The source stays fixed; each row rebuilds the phase with a different flying-capacitor voltage.

\begin{array}{c|c|c}V_s&V_{\text{fly}}&V_{\text{out}}\\6\ \text{V}&4\ \text{V}&10\ \text{V}\\6\ \text{V}&6\ \text{V}&12\ \text{V}\\6\ \text{V}&8\ \text{V}&14\ \text{V}\\\end{array}

Stacking adds the source and flying voltage

The output label is accepted only from the declared phase topology.

6\ \text{V}+6\ \text{V}=12\ \text{V}