sharing-capacitance-voltage-final-scan - Electronic Circuits XVI: Switched-Capacitor Charge and Conversion Step by Step

The final sharing voltage moves when source capacitance or source voltage changes. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Final voltage divides conserved charge by total capacitance

The final voltage is downstream of both source capacitors; changing either source capacitance or source voltage changes the quotient.

V_f={Q_{\text{total}}\over C_{\text{total}}}=24\ \text{C}/6\ \text{F}

Capacitance and voltage changes enter the same quotient

The table separates changing source capacitance from changing source voltage so the final-voltage quotient is visible both ways.

\begin{array}{c|c|c|c|c}\text{scan}&C_a&V_a&Q_{\text{total}}&V_f\\C_a\ \text{changes}&2\ \text{F}&6\ \text{V}&12\ \text{C}&3\ \text{V}\\C_a\ \text{changes}&4\ \text{F}&6\ \text{V}&24\ \text{C}&4\ \text{V}\\C_a\ \text{changes}&6\ \text{F}&6\ \text{V}&36\ \text{C}&\tfrac{9}{2}\ \text{V}\\V_a\ \text{changes}&4\ \text{F}&3\ \text{V}&12\ \text{C}&2\ \text{V}\\V_a\ \text{changes}&4\ \text{F}&6\ \text{V}&24\ \text{C}&4\ \text{V}\\V_a\ \text{changes}&4\ \text{F}&9\ \text{V}&36\ \text{C}&6\ \text{V}\\\end{array}

The final sharing row is a quotient of checked totals

This row is not a lossless-energy claim; it is only the charge-conservation voltage row.

24\ \text{C}/6\ \text{F}=4\ \text{V}