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Synchronization and Arbitration in Digital Systems by David J. Kinniment

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2

Modelling Metastability

Asynchronous data originating from outside a clocked system has to be synchronized to the clock before it can be used. This usually involves a choice made on the basis of the arrival time of the data, which is a continuous variable, and the result of the decision, which clock edge to use, is discrete. In this situation it is possible to have very small input time differences between the data available signal and the clock. Such choices are difficult as the input energy to the synchronizer circuit falls towards zero when the time difference becomes small, and the response time of the circuit then approaches infinity. In fact there is always a point at which the synchronizer time response can become longer than the available time, and the synchronizer circuit fails because its output has not reached a stable state [4,5].

Asynchronous systems have a similar problem where the system must decide which of two or more asynchronous requests for a common processing resource is to be granted first. In this case the circuit that makes the decision is called an arbiter, and the input energy to the arbiter is also derived from the time differences between the inputs. Again, this time difference is a continuous variable and can also approach zero, with the result that the arbitration time can approach infinity [5,6]. In both cases the decision element, usually a flip-flop, has become metastable, and the resolution time of metastability in a flip-flop is important to ...

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