snapshot-charge-limit-three-row-scan - Electronic Circuits XV & XVI: Transformers and Switched-Capacitor Conversion Step by Step

Snapshot charge is capacitance times voltage, so each voltage row can be checked against the same charge ceiling. The 2, 3, and 4 V rows give 4, 6, and 8 C against a 6 C limit exactly for the ideal capacitor snapshot model; real switched-capacitor circuits add switch resistance, charge injection, parasitic capacitance, leakage, clock jitter, ripple, and voltage/charge measurement uncertainty.

A charge ceiling is checked by recomputing Q = CV for three voltages. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The charge limit starts with one checked snapshot

The ceiling and capacitance are fixed; each row changes only voltage.

Q=CV\quad Q_{\max}=6\ \text{C}

Three voltage rows reveal the boundary

The middle row lands exactly on the charge ceiling; the third row crosses it.

\begin{array}{c|c|c}V&Q&m=Q_{\max}-Q\\2\ \text{V}&4\ \text{C}&2\ \text{C}\\3\ \text{V}&6\ \text{C}&0\ \text{C}\\4\ \text{V}&8\ \text{C}&\mathord{-}2\ \text{C}\\\end{array}

The last row fails because the computed charge is above the ceiling

The final row has a negative margin, so the gate fails.

m=\mathord{-}2\ \text{C}\quad \text{fail}