equivalent-resistance-inverse-factor-scan - Electronic Circuits XV & XVI: Transformers and Switched-Capacitor Conversion Step by Step

A switched capacitor can look like an equivalent resistance because the same voltage difference drives an average packet current. More capacitance or more clock rate lowers that ideal resistance; real equivalent resistance also depends on switch on-resistance, dead time, parasitics, voltage swing, ripple, and measurement uncertainty.

More packet current lowers the equivalent resistance for the same voltage swing. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Equivalent resistance uses the same packet voltage and current

The inverse trend comes from current increasing while the voltage difference stays the same.

R_{\text{eq}}={\Delta V\over I_{\text{avg}}}

More capacitance or more clock rate lowers equivalent resistance

The two scan groups show the inverse relation through the cited packet current, not by a standalone resistance label.

\begin{array}{c|c|c|c|c}\text{scan}&C&f&I_{\text{avg}}&R_{\text{eq}}\\C\ \text{changes}&1\ \text{F}&\tfrac{1}{2}\ \text{Hz}&2\ \text{A}&2\ \text{ohm}\\C\ \text{changes}&2\ \text{F}&\tfrac{1}{2}\ \text{Hz}&4\ \text{A}&1\ \text{ohm}\\C\ \text{changes}&4\ \text{F}&\tfrac{1}{2}\ \text{Hz}&8\ \text{A}&\tfrac{1}{2}\ \text{ohm}\\f\ \text{changes}&2\ \text{F}&\tfrac{1}{4}\ \text{Hz}&2\ \text{A}&2\ \text{ohm}\\f\ \text{changes}&2\ \text{F}&\tfrac{1}{2}\ \text{Hz}&4\ \text{A}&1\ \text{ohm}\\f\ \text{changes}&2\ \text{F}&1\ \text{Hz}&8\ \text{A}&\tfrac{1}{2}\ \text{ohm}\\\end{array}

The final resistance row divides the cited packet voltage by current

The displayed resistance uses the same voltage difference as the cited packet row.

4\ \text{V}/4\ \text{A}=1\ \text{ohm}