ESE 529
Introduction to MEMS and NEMS
Lecture 6
Troy Olsson
Assistant Professor
Department of Electrical and Systems Engineering
rolsson@seas.upenn.edu
2
Lecture Overview
• Last Time
• We learned the differential equations describing the dynamic response of MEMS devices
• We learned the equivalence between the dynamic responses of mechanical and electrical
harmonic oscillators
• We learning how to model mechanical devices using equivalent circuit elements
• We learned to solve for the sinusoidal steady state (or frequency) response of
electromechanical devices
• Today
• Examine the frequency response
• Define and discuss quality factor
• Sources of damping in MEMS
• Impact of Q factor on the performance of different devices
• Laplace transforms for solving the transient response of MEMS devices
3
Last time we solved for the sinusoidal
steady-state velocity
Velocity =
Current ? ? =
?
?? + ?? + ?? =
1
?
?? + ??? + ?
?
?∠? = ?∠?
? = 0
Let’s reference
phase to the input