sharing-loss-budget-three-row-scan - Electronic Circuits XVI: Switched-Capacitor Charge and Conversion Step by Step

A sharing loss budget is checked from final voltage and stored energy. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Charge sharing also has an energy-loss budget

The second capacitor begins uncharged. The first capacitor voltage is the only changed input.

E_{\text{loss}}\leq24\ \text{J}

Three source voltages show when the loss budget breaks

The same sharing check computes final voltage, final energy, and loss for every row.

\begin{array}{c|c|c|c}V_a&V_f&E_{\text{loss}}&m\\3\ \text{V}&2\ \text{V}&6\ \text{J}&18\ \text{J}\\6\ \text{V}&4\ \text{V}&24\ \text{J}&0\ \text{J}\\9\ \text{V}&6\ \text{V}&54\ \text{J}&\mathord{-}30\ \text{J}\\\end{array}

The high-voltage row fails because the loss exceeds the budget

The final sharing row loses more energy than the allowed budget.

m=\mathord{-}30\ \text{J}\quad \text{fail}