Difference between revisions of "Lab Manual: Limits of Detection"
From Course Wiki
Line 21: | Line 21: | ||
[[Image:Ideal Mechanical and Electronic Lumped Elements.png|thumb|right|Ideal mechanical and electronic lumped elements.]] | [[Image:Ideal Mechanical and Electronic Lumped Elements.png|thumb|right|Ideal mechanical and electronic lumped elements.]] | ||
− | <math>\frac{\hat{V}_o(s)}{\hat{F}_{in}(s)}=\frac{\dfrac{1}{ | + | <math>\frac{\hat{V}_o(s)}{\hat{F}_{in}(s)}=\frac{\dfrac{1}{m}s}{s^2+ \dfrac{b}{m} s+\dfrac{k}{m} }</math> |
===Underdamped system: atomic force microscope=== | ===Underdamped system: atomic force microscope=== |
Revision as of 04:17, 25 November 2012
Overview
Resolution limit
Second order system
- $ \dfrac{1}{Z_{eq}}=\dfrac{1}{Z_R}+\dfrac{1}{Z_L}+\dfrac{1}{Z_C} $
- $ Z_{eq}=\frac{Z_R Z_L Z_C}{Z_R Z_L + Z_R Z_C + Z_L Z_C} $
- $ Z_{eq}=\frac{\hat{V}_o(s)}{\hat{I}_{in}(s)}=\frac{RL/C}{RLs+\dfrac{R}{Cs}+\dfrac{L}{C}}=\frac{Ls}{LCs^2+\dfrac{L}{R}s+1} $
Mechanical circuit analogy
$ \frac{\hat{V}_o(s)}{\hat{F}_{in}(s)}=\frac{\dfrac{1}{m}s}{s^2+ \dfrac{b}{m} s+\dfrac{k}{m} } $