Prony Series Deconvolution of Viscoelastic Die Attach Relaxation in Accelerometers
Real-time digital inverse Prony filtering decouples time-dependent polymer stress relaxation from true acceleration signals in high-precision micro-sensors.
State Variable Filter
Operational Definition
Analog circuitry for signal processing defines this implementation through the simultaneous extraction of high-pass, band-pass, and low-pass outputs from a single input signal. A state variable filter achieves these responses by cascading multiple integrators and summing amplifiers within a closed feedback loop. The configuration permits independent control over natural frequency and damping parameters.
Designers tune these specific performance attributes by adjusting the resistor values that govern the integration time constants. Deviation from ideal performance arises from the finite gain and bandwidth limitations of the operational amplifiers used in the circuit.
Circuit Topology
Three primary stages characterize the physical arrangement of the components. Two integrator stages provide the reactive elements necessary for phase shifting and signal accumulation. One additional summing stage combines the integrator outputs to produce the desired transmission characteristics.
Stability remains a requirement for the feedback loop to maintain precision across the intended passband. Parasitic capacitance at the summing node introduces phase errors that degrade performance at high frequencies.
Performance Characteristic
Precise adjustment of the Q factor defines the operational utility of this topology. High Q values allow for narrow band-pass selection at the cost of increased sensitivity to component drift. Temperature shifts in passive resistors alter the pole positions and shift the resonant frequency away from the target value.
Calibration procedures require the selection of precision components with low thermal coefficients to minimize such variations during prolonged operation. Verification of the transfer function typically occurs through frequency response analysis using a calibrated sweep generator.
Calibration Metric
Measured performance depends upon the alignment of internal gains to ensure output symmetry. Gain errors within the summing stages create ripples in the frequency response that deviate from theoretical Butterworth or Chebyshev approximations. Maintaining the ratio of the feedback resistors ensures the damping factor stays within specified limits during temperature cycling.
Absolute accuracy for the resonant frequency depends upon the tolerance of the integration capacitors. Stable output amplitude rests upon the precise calibration of the input signal level against the dynamic range of the internal amplifiers.