two-phase-step-down-cites-both-phases - Electronic Circuits XVI: Switched-Capacitor Charge and Conversion Step by Step

A ratio claim must preserve source and flying-cap identities across phases. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Two phases must share the same rail and flying capacitor

The cycle check rejects same-valued phases that do not cite the same source identities.

\phi_{\text{one}}:\ 4\ \text{V}\quad \phi_{\text{two}}:\ 4\ \text{V}

Changing the rail keeps the identity gate explicit

Each row rebuilds both phases and the cycle identity from the same rail and flying-cap sources.

\begin{array}{c|c|c}V_s&V_{\text{out}}&\text{cycle}\\6\ \text{V}&3\ \text{V}&\text{linked}\\8\ \text{V}&4\ \text{V}&\text{linked}\\10\ \text{V}&5\ \text{V}&\text{linked}\\\end{array}

Two phase rows must cite the same cycle identities

Same-valued phases are not enough; source rail and flying-cap identity are checked.

8\ \text{V}\rightarrow4\ \text{V}