Calculating Group Delay in Delta Sigma Converters
Delta-sigma converter group delay equals the phase derivative across decimation filter stages, calculated as K times M minus one divided by twice the modulator clock for sinc filters.
Phase Dispersion
Waveform Distortion
Frequency-dependent phase velocity within a transmission medium or filter causes different spectral components of a signal to travel at different speeds. In high-speed data acquisition, phase dispersion deforms complex pulse waveforms and spreads them out in time. This distortion can lead to errors in pulse-amplitude and timing measurements.
Metrological Consequence
Signal degradation occurs because the phase relationship among the constituent frequencies is not preserved as the signal propagates. In fiber-optic and high-frequency coaxial cables, this effect must be carefully measured to prevent data errors. Compensation filters are often installed to neutralize the dispersion across the operating band.
Calibration Procedure
Metrological calibration of cables and instrumentation systems involves measuring the phase shift across a broad frequency sweep. This phase dispersion is calculated by comparing the measured phase against a straight-line phase reference. The deviation is then logged to certify that the cable or instrument meets the required signal transmission specifications.
Physical Origin
Physical characteristics of the dielectric material and the geometry of the transmission line represent the primary causes of this phenomenon. Temperature changes can also alter the dielectric constant of the insulating material, which shifts the dispersion characteristics of the system. Calibration laboratories perform these measurements in temperature-controlled rooms to ensure that the results are repeatable and to establish the thermal coefficient of the dispersion.