# Force Measurement With Capacitive and Eddy-Current Sensors

General Sensor Application Note LA05-0026

###### Summary:

Force is often measured as a deflection of an object of known stiffness. Noncontact methods are ideal for measuring the force-related deflection as they do not load the object with additional mass or affect it’s stiffness.

These noncontact sensors are very precise and are best used in applications requiring very small and very precise measurements to justify the cost of precision sensors.

###### Force Related Linear Displacement

The force related deflection of the object is a linear displacement measurement – the measurement of the position change of an object. Capacitive sensors and eddy-current sensors provide high resolution measurements required for precise measurements of force.

###### Limited Displacements for Accurate Force Measurements

Force measurements using deflection are generally designed for minimal deflection. Larger deflections could change the force as in spring rate measurements. The smaller the deflections, the more accurate the force measurement. Capacitive and eddy-current displacement sensors can provide sub micron, and even sub nanometer resolutions. A force measurement system with such small deflections can make very precise measurements of force.

For more details on displacement measurements see our Displacement and Position Measurement Application Note.

###### Force Calibrations

A deflection based force measurement system must be calibrated. A series of forces must be applied to the deflected object and the deflection measured. A mathematical function describing the relationship between force and deflection can be derived to quickly convert the deflection numbers into units of force. If the system is linear, the calculation is simple. If the relationship is curvilinear, a regression analysis will be required to determine the conversion function.

###### Error Sources

With tiny deflections and small forces, error sources become a more significant factor. Thermal changes in the system are often the biggest source of error. Thermal effects on force measurements must be known so they can be compensated, eliminated, or determined to be within tolerance of the force measurement.

For a discussion of error sources in deflection (displacement) measurements, see our Displacement and Position Measurement Application Note.