What Is the MEMS Capacitive Accelerometer Pull-In & Resonance Calculator?
MEMS capacitive accelerometers measure acceleration by detecting sub-nanometer capacitive shifts in suspended silicon combs.
How Does the MEMS Capacitive Accelerometer Pull-In & Resonance Calculator Work?
External acceleration deflects proof mass against silicon springs; electrostatic sense voltages attract plates until pull-in snap-down threshold.
MEMS Capacitive Accelerometer Pull-In & Resonance Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
V_{ ext{pi}} = sqrt{ rac{8 k d_0^3}{27 epsilon_0 A}}, quad f_0 = rac{1}{2pi} sqrt{ rac{k}{m}}
Electrostatic pull-in limit and undamped mechanical natural frequency in MEMS sensors.
How to Use the MEMS Capacitive Accelerometer Pull-In & Resonance Calculator
- Input proof mass in micrograms, spring stiffness in N/m, rest gap in microns, and electrode overlap area in µm².
Step-by-Step Example Calculation
Automotive Airbag MEMS Accelerometer
Input Values:
proofMassUg:2.5
suspensionStiffnessNPerM:12
gapSeparationMicrons:1.8
electrodeAreaUm2:60000
Worked Steps: Pull-in voltage V_pi = 6.27 V, Mechanical resonance f0 = 11.0 kHz, Rest capacitance C0 = 0.295 pF, Sensitivity = 2.41 fF/g.
Understanding Your Result
Displays pull-in voltage V_pi, mechanical resonance frequency in Hz, rest capacitance, and sensitivity in fF/g.
Factors That Affect the Result
- Operating bias voltages must remain well below pull-in voltage to prevent catastrophic electrode stiction.
When Should You Use This Calculator?
- Automotive crash detection, smartphone inertial measurement units (IMUs), and industrial vibration monitoring.
Assumptions & Limitations
- Assumes 1D parallel-plate electrostatic approximation without fringe-field correction.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard MEMS microdevice electrostatic mechanics.