How fast will an FSM run? Could making our logic too fast cause our FSM to fail? In this chapter, we will see how to answer these questions by analyzing the timing of our finite-state machines and the flip-flops used to build them.
Finite-state machines are governed by two timing constraints – a maximum delay constraint and a minimum delay constraint. The maximum speed at which we can operate an FSM depends on two flip-flop parameters (the setup time and propagation delay) along with the maximum propagation delay of the next-state logic. On the other hand, the minimum delay constraint depends on the other two flip-flop parameters (hold time and contamination delay) and the minimum contamination delay of the next-state logic. We will see that if the minimum delay constraint is not met, our FSM may fail to operate at any clock speed due to hold-time violations. Clock skew, the delay between the clocks arriving at different flip-flops, affects both maximum and minimum delay constraints.
PROPAGATION AND CONTAMINATION DELAY
In a synchronous system, logic signals advance from the stable state at the end of one clock cycle to a new stable state at the end of the next clock cycle. Between these two stable states, they may go through an arbitrary number of transitions.
In analyzing timing of a logic block we are concerned with two times. First, we would like to know for how long the output retains its initial stable value (from the last clock cycle) after an input first changes (in the new clock cycle).We refer to this time as the contamination delay of the block – the time it takes for the old stable value to become contaminated by an input transition. Note that this first change in the output value does not in general leave the output in its new stable state. The second time we would like to know is how long it takes the output to reach its new stable state after the input has stopped changing. We refer to this time as the propagation delay of the block – the time it takes for the stable value of the input to propagate to a stable value at the output.
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