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.
Sinc Filter Latency
Propagation Delay
Temporal delay between the arrival of an analog input sample and the availability of the corresponding digital output is a fundamental characteristic of digital filter blocks. In oversampling systems, the sinc filter latency defines this processing time for sinc-shaped decimation stages. This delay is proportional to the filter order and the oversampling ratio.
System Feedback
Measurement performance is affected by this delay because it limits the speed at which a control loop can react to sudden changes in the sensor signal. High-latency filters can cause instability in feedback networks if the system is not properly compensated. Designers must calculate this delay precisely to maintain phase margin in active control loops.
Metrological Calibration
Calibration of this parameter involves measuring the step response of the digital acquisition system under test. The interval from the input step to the midpoint of the digital transition is measured to determine the sinc filter latency. This value is checked against the datasheet specification to verify correct firmware configuration.
Design Selection
Filter architectures often allow a choice between different trade-offs, where higher-order sinc filters provide superior noise rejection at the cost of increased propagation delay. For example, a third-order sinc filter has a latency of three conversion periods, while a fast-settling sinc filter might reduce this to a single period. Calibration engineers document these latency settings in the instrument certificate to ensure that the timing budget of the larger system can be verified during commissioning.