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

Charge sharing can meet or break an energy-loss budget because the final shared voltage and lost energy rise with the starting voltage. The 3, 6, and 9 V source rows lose 6, 24, and 54 J against a 24 J budget exactly for the ideal charge-sharing model; real sharing adds switch resistance, ESR, charge injection, parasitic capacitance, leakage, ripple, heating, and voltage/energy measurement uncertainty.

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}