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

Switched-capacitor circuits move charge packets, and each packet starts with the basic relation Q = CV. The rows use exact ideal capacitance and voltage values to expose the two-factor product; real capacitors have tolerance, leakage, voltage dependence, parasitic resistance, switch charge injection, and measurement uncertainty.

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}