Accelerometer approaches Measure F Compression Bending Stress/force based Piezoelectric Piezoresistive Measure x Capacitive (Optical) (Magnetic) AC DC FP Thermal Parallell plate Comb Measure v Inductive

ADXL150

Parameter extraction Partitioning and choice of variables (z,v) Find values for the parameters (m,k,γ) Couple Analyze z

Quasi static sensitivity of a displacement based accelerometer Utbøyning z Mechanical part of the sensitivity

Doubly clamped beam with point load at midpoint Spring constant: z-central beam displacement W beam width (poly thickness) H beam thickness (lithography) Stiffness of folded spring: 2.8 N/m Stiffness of two springs: 5.6 N/m Spring softening due to applied voltage gives: 5.2 N/m

Mass and mechanical sensitivity Estimate: Analog devices: Mechanical sensitivity: sm=sm=

Dynamics Partitioning and choice of variables (z,v) Find values for the parameters (m,k,γ) Couple Analyze z

Position – velocity - acceleration Oscillatory motion Position Velocity Acceleration

Second order system with forced oscillations x

Block function F

Block function from Senturia x/f v/f

Resonance frequency For zero damping, the response diverges when hence, we introduce the resonance frequency:

Sensitivity vs. bandwidth

Q-factor definition

Q-factor appears as Stored energy divided by energy dissipated during one cycle at resonance Number of oscillations before the amplitude is reduced by a factor 1/e Eigenfrequency divided by the Full Width at Half Maximum for the transfer function squared (power)

Experiment Q,f

Q from power function FWHM HM f0f0

Contributions to damping = 7 µN/(m/s) = 5

Consequence of damping Brownian motion of the accelerometer results in: Force noise: Equivalent acceleration Measured noise:

Capacitor as a two port element

Capacitor cofiguration

Differential read out

Capacitance Capacitance from parallel plate approximation: Capacitance including fringing fields about 100 fF

System configuration

Specifications

Construction