flipped-capacitor-makes-negative-rail - Electronic Circuits XV & XVI: Transformers and Switched-Capacitor Conversion Step by Step

A flipped-capacitor-makes-negative-rail scan holds the ground reference fixed and varies the charged flying-capacitor voltage across three rows, checking that the inverted output V_out = -V_fly reverses sign row by row. The arithmetic is exact only for the stated flying-capacitor voltages, output voltages, modes, 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 reversed flying capacitor creates a signed output reference. 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 flipped phase measures output from the ground reference

The source row is the ground reference; the output sign comes from the declared inverted topology.

V_s=0\ \text{V}\quad V_{\text{fly}}=5\ \text{V}

A larger flying voltage makes a larger negative rail

Each row keeps the ground reference and changes only the charged flying-capacitor voltage.

\begin{array}{c|c|c}V_{\text{fly}}&V_{\text{out}}&\text{mode}\\3\ \text{V}&\mathord{-}3\ \text{V}&\text{invert}\\5\ \text{V}&\mathord{-}5\ \text{V}&\text{invert}\\7\ \text{V}&\mathord{-}7\ \text{V}&\text{invert}\\\end{array}

Flipping the flying capacitor reverses sign

The negative rail is a reference ledger, not a device-safety claim.

V_{\text{out}}=\mathbin{-}5\ \text{V}=\mathord{-}5\ \text{V}