Timing

In previous sections, we have been concerned primarily with whether the circuit works — ideally, using the fewest gates. However, as any seasoned circuit designer will attest, one of the most challenging issues in circuit design is timing: making a circuit run fast.

An output takes time to change in response to an input change. This is the timing specification we are talking at the start of this chapter. Figrue 2.66 shows the delay between an input change and the subsequent output change for a buffer. The figure is called a timing diagram; it portrays the transient response of the buffer circuit when an input changes.

We measure delay from the 50% point of the input signal, A, to the 50% point of the output signal, Y. The 50% point is the point at which the signal is half-way (50%) between its LOW and HIGH values as it transitions.

Propagation and Contamination Delay

Combinational logic is characterized by its propagation delay and contamination delay.

• The propagation delay, $t_{\text{pd}}$, is the maximum time from when an input changes until the output or outputs reach their final value.

• The contamination delay, $t_{\text{cd}}$, is the minimum time from when an input changes until any output starts to change its value.

For example, Figure 2.67 illustrates a buffer's propagation delay and contamination delay in blue and gray, respectively.

The figure shows that A is initially either HIGH or LOW and changes to the other state at a particular time; we are interested only in the fact that it changes, not what value it has. In response, Y changes some time later.

The arcs indicate that Y may start to change $t_{\text{cd}}$ after A transitions and that Y definitely settles to its new value within $t_{\text{pd}}$.

Critical Path

Propagation and contamination delays are also determined by the path a signal takes from input to output.

There are two paths in a combinational circuit:

1. The critical path, which is the longest and therefore the slowest, path from input to output.

2. The short path, which as its name suggested, is the shortest path from input to output.

And we have that,

1. The propagation delay of a combinational circuit is the sum of the propagation delays through each element on the critical path.

2. The contamination delay is the sum of contamination delays through each element on the short path.

Glitches

So far we have discussed the case where a single input transition causes a single output transition. However, it is impossible that a single input transition can cause multiple output transitions. These are called glitches or hazards.

Although glitches usually don't cause problems, it is important to realize that they exist and recognize them when looking at timing diagrams.