A state machine samples an asynchronous proximity sensor's output directly at the…

PHYSICS · Multi-part · Fermi University Physics · Electronics, Instrumentation & Communication · Digital electronics, embedded systems and data acquisition · Digital electronics, embedded systems and data acquisition

Electronics for Measurement, Ch Digital logic and its physical realisation

Problem

A state machine samples an asynchronous proximity sensor's output directly at the data input of its first flip-flop, clocked at

f_{\rm clk} = 20\,\mathrm{MHz}

(

T_{\rm clk} = 50\,\mathrm{ns}

). The system occasionally jumps to a nonsense state, about once every eight minutes on the bench. Convinced the fault is electrical noise on the supply, an engineer fits a

100\,\mathrm{nF}

decoupling capacitor right at the chip's supply pins. The failure rate is unchanged. ((a)) Find the error in the engineer's diagnosis and name the mechanism actually responsible. ((b)) A colleague instead inserts a second flip-flop, clocked by the same clock, between the sensor and the state machine (a two-flop synchroniser). This gives the resolving flip-flop's output up to a full extra clock period,

T_{\rm clk} = 50\,\mathrm{ns}

, of settling time it did not have before. Taking the flip-flop's resolution time constant as

\tau = 2.5\,\mathrm{ns}

, find the least extra settling time that would stretch the eight-minute mean time between failures beyond ten years, and say whether the synchroniser provides it.

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