Multi Coil Quadrature Demodulation Signal Chains for Proximity Measurement
Multi coil quadrature demodulation isolates amplitude and phase in inductive proximity chains, resolving sub-micron targets while rejecting thermal noise.
Effective Resolution
Statistical Precision Metric
Measurement capability under noisy conditions is expressed as the number of stable bits available from a digital output after accounting for random fluctuations. Effective resolution describes the performance of a sensing system in a specific bandwidth. It differs from nominal resolution because it excludes the bits that are lost to thermal noise or quantization errors.
Practitioners use the root mean square noise of the signal to calculate this value.
Noise Floor
Calculating this value involves taking the base 2 logarithm of the full scale range divided by the standard deviation of the noise. If a system has a high signal to noise ratio, the effective resolution approaches the bit depth of the hardware. Averaging multiple samples can increase the result by reducing the impact of random noise.
This improvement comes at the cost of slower response times.
Bandwidth Constraint
High speed sampling usually results in lower effective resolution because the wider frequency range captures more total noise power. A specification for a sensor is only valid when the filter settings and the data rate are stated. At a one hertz bandwidth, a precision instrument might offer twenty bits of stable data.
Increasing the output rate to one kilohertz could drop that figure to sixteen bits while adding significant jitter to the timing of the conversion.
Signal Integrity
Drift and non linearities are not included in this particular metric, which focuses strictly on random variability. While effective resolution indicates the smallest change a system can reliably detect, it does not guarantee absolute accuracy. Proper grounding and shielding are required to reach the theoretical limits defined in a data sheet.