equivalent-resistance-floor-three-row-scan - Electronic Circuits XVI: Switched-Capacitor Charge and Conversion Step by Step

An equivalent-resistance floor is checked through the cited packet current. 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 resistance floor limits how fast the packet clock can run

The voltage swing is fixed. Faster clocks increase current and reduce equivalent resistance.

R_{\text{eq}}={\Delta V\over I_{\text{avg}}}\quad R_{\min}=1\ \text{ohm}

Three clock rates show the inverse boundary

The one-hertz row fails because current doubles and equivalent resistance drops below the floor.

\begin{array}{c|c|c|c}f&I_{\text{avg}}&R_{\text{eq}}&m\\\tfrac{1}{4}\ \text{Hz}&2\ \text{A}&2\ \text{ohm}&1\ \text{ohm}\\\tfrac{1}{2}\ \text{Hz}&4\ \text{A}&1\ \text{ohm}&0\ \text{ohm}\\1\ \text{Hz}&8\ \text{A}&\tfrac{1}{2}\ \text{ohm}&\mathord{-}\tfrac{1}{2}\ \text{ohm}\\\end{array}

The fastest clock fails the equivalent-resistance floor

The final row drops below the resistance floor, so the margin is negative.

m=\mathord{-}\tfrac{1}{2}\ \text{ohm}\quad \text{fail}