Calculating Equivalent Noise Bandwidth and Flicker Corner Integration in AFEs
Calculating AFE noise requires integrating white floor spectral density across equivalent bandwidth while summing flicker contributions over the measurement duration.
Aliasing Noise Folding
Spectral Redistribution
Continuous-time random noise processes sampled by discrete-time converters undergo irreversible mapping into the baseband Nyquist interval. This mathematical redistribution, termed aliasing noise folding, superimposes broadband noise components from integer multiples of the sampling frequency directly onto the target signal spectrum. Total noise density in the sampled passband rises in proportion to the ratio of the pre-sampler input bandwidth to the half-sample Nyquist boundary.
Uncorrelated thermal noise spreads uniformly across the baseband, diminishing the achievable signal to noise ratio.
Decimation Mechanism
Modern oversampling converters use digital filtering alongside decimation to attenuate out-of-band energy before decimation lowers the sample rate. When high-order delta-sigma modulators operate at high clock frequencies, high-frequency quantization noise shifts far beyond the interest band. If decimation occurs without steep analog or digital filtering, aliasing noise folding returns high-frequency noise into the instrumentation register.
The resulting noise floor elevation cannot be subtracted mathematically by downstream calibration algorithms because phase information is lost during digitization.
Frontend Attenuation
Anti-aliasing filters placed ahead of the sampling switch set the boundary conditions for noise folding. A passive first-order resistor-capacitor network suppresses wideband thermal noise from input buffers, yet incomplete roll-off allows several high-frequency noise decades to fold. Higher-order active filters provide sharper cut-off characteristics, but their internal operational amplifiers introduce broad spectral noise that folds during sampling.
Designers balance source impedance against settling time at the converter input nodes.
Procurement Criterion
Qualification of data acquisition instruments requires evaluating the signal-to-noise floor across specified source impedances and temperature corners. Factory test sheets state baseband noise spectral density alongside converter clock jitter, isolating internal thermal noise from external interference. Laboratory evaluation exposes the analog frontend to wideband out-of-band white noise sources to verify that filtering meets specified stopband rejection metrics before production release.
If an incoming instrument exhibits an elevated noise floor despite quiet input conditions, deficient frontend roll-off exposing the digitizer to aliasing noise folding remains a primary cause. Acceptance protocols verify that measured root-mean-square noise matches simulated values within an agreed metrological margin of two decibels across the full thermal envelope.