Mathematical Representation
A mathematical model describes the relationship between the input force applied to a body and the resulting displacement or acceleration. The mechanical transfer function provides a complex-valued representation of how a sensor responds across a spectrum of frequencies. It captures both the magnitude of the movement and the phase lag relative to the excitation.
Frequency Domain
Evaluation occurs by sweeping a sinusoidal load through the operational bandwidth of the instrument. At low frequencies, the mechanical transfer function is usually flat and follows the static sensitivity of the device. As the frequency approaches a resonance, the phase shifts by ninety degrees and the magnitude increases.
Calibration technicians use this data to calculate the natural frequency and the damping ratio. They apply a curve-fitting algorithm to the measured points to derive the coefficients of the underlying differential equation.
Signal Processing
Compensating for the physical lag of the sensor requires the inverse of this model.
Error Source
Non-linearities in the suspension or the presence of parasitic capacitance can distort the shape of the plot. Temperature changes further shift the poles and zeros of the mechanical transfer function by altering the material stiffness. Reference measurements in a climate-controlled chamber establish the baseline for these variations.
