1. 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

2. ADXL150

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

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

5. 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

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

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

8. Position – velocity - acceleration Oscillatory motion Position Velocity Acceleration

9. Second order system with forced oscillations x

10. Block function F

11. Block function from Senturia x/f v/f

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

13. Sensitivity vs. bandwidth

14. Q-factor definition

15. 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)

16. Experiment Q,f

17. Q from power function FWHM HM f0f0

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

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

20. Capacitor as a two port element

21. Capacitor cofiguration

22. Differential read out

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

24. System configuration

25. Specifications

26. Construction