Filter & hold: a mixed continuous-/discrete-time technique for time-constant scaling

Summary The work reported in this paper introduces a periodic switching technique applied to continuous‐time filters, whose outcome is an equivalent filter with scaled time‐constants. The principle behind the method is based on a procedure that extends the integration time by periodically interrupting the normal integration of the filter. The net result is an up scaling of the time constant, inversely proportional to the switching duty‐cycle. This is particularly suitable for reducing the area occupied by passive devices in integrated circuits, as well as to accurately calibrate the filter dynamics. Previous works have been following this concept in an entirely continuous‐time perspective, either focusing on specific circuits or using approximations to provide an extended analysis. This paper includes input/output sampling to derive a closed‐form representation for the scaling technique herein coined as ‘Filter & Hold’ (F&H). A detailed mathematical analysis is described, demonstrating that the F&H concept represents an exact filtering solution. Simulation results and experimental measurements are provided to further validate the theoretical analysis for an F&H vector‐filter prototype. Copyright © 2014 John Wiley & Sons, Ltd. This paper introduces a periodic switching technique applied to continuous‐time filters, whose outcome is an equivalent filter with scaled time‐constants inversely proportional to the switching duty‐cycle. This paper includes input/output sampling to derive a closed‐form representation for the scaling technique herein coined as ‘Filter & Hold’ (F&H). Simulation results and experimental measurements are provided to further validate the theoretical analysis for an F&H vector‐filter prototype.