Lab Manual: Limits of Detection

Overview

Resolution limit

Second order system

Second order circuit with alternating current source and parallel resistor, capacitor, and inductor.

$ Z_{eq}=\frac{\hat{V}_o(s)}{\hat{I}_{in}(s)}=\frac{Z_R Z_L Z_C}{Z_R+Z_L+Z_C}=\frac{RL/C}{R+Ls+1/Cs} $ $ \frac{\hat{V}_o(s)}{\hat{I}_{in}(s)}=\frac{RLs}{LCs^2+RCs+1} $

Mechanical circuit analogy

Ideal mechanical and electronic lumped elements.

Underdamped system: atomic force microscope

Overdamped system: laser tweezers

Optical trap procedure

AFM procedure