capacitance-voltage-charge-two-factor-scan - Electronic Circuits XVI: Switched-Capacitor Charge and Conversion Step by Step

The charge product needs separate capacitance and voltage rows. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A charge row starts from both capacitance and voltage

This is a two-factor relation: a scan that changes only voltage does not show what capacitance does, and a scan that changes only capacitance does not show what voltage does.

Q=CV\quad C=2\ \text{F}\quad V=6\ \text{V}

Capacitance rows and voltage rows both move charge

The top three rows hold voltage fixed and change capacitance; the bottom three rows hold capacitance fixed and change voltage.

\begin{array}{c|c|c|c}\text{scan}&C&V&Q\\C\ \text{changes}&1\ \text{F}&4\ \text{V}&4\ \text{C}\\C\ \text{changes}&2\ \text{F}&4\ \text{V}&8\ \text{C}\\C\ \text{changes}&3\ \text{F}&4\ \text{V}&12\ \text{C}\\V\ \text{changes}&2\ \text{F}&3\ \text{V}&6\ \text{C}\\V\ \text{changes}&2\ \text{F}&6\ \text{V}&12\ \text{C}\\V\ \text{changes}&2\ \text{F}&9\ \text{V}&18\ \text{C}\\\end{array}

The final row pins the product, not a free charge label

Changing either input in the table changed the same product rule; the diagram is one checked row of that rule.

2\ \text{F}\cdot6\ \text{V}=12\ \text{C}