608 Chapter 20
Note that, at state 15, the pattern starts to repeat. This sequence is known as the
maximum-length sequence. The fact that the outputs states are predictable illustrates that
the output of the code generator is not really random at all but is a pseudo-random binary
sequence (PRBS). The sequence does, however, have some very “ random ” qualities—like
a very nearly equal number of 1 s and 0 s (think of it a coin-tossing machine)! Practically,
this lack of true randomness does not matter provided that the sequence is long enough
to appear random in any particular application. In every case of an n-stage, chain code
generator, the longest (maximal length) sequence of 1 s and 0 s repeats after (2 e n – 1)
states. Note that, as illustrated in Figure 20.6 , a pathological condition can occur if all
outputs power up in an identical 0 state—in which case 0 s will propagate indefi nitely
around the chain code generator, resulting in no output. Practical circuits have to include
provision to prevent this situation from ever occurring. Indeed it is precisely because
of the necessity to avoid this “ forbidden ” all zeros state that the output of the chain
code generator illustrated in Figure 20.6 consists of a cycle of 15 (rather than the more
intuitively expected 16) states.
It can be shown mathematically that the output binary sequence from the chain code
generator has a frequency spectrum extending from the repeat frequency of the entire
sequence up to the clock frequency and beyond. The noise is effectively fl at (within
0.1 dB) to about 0.12 of the clock frequency (Fc). The noise source is –3 dB at 0.44 Fc
State Output (A,B,C,D)
8 1,1,0,1
9 1,1,1,0
10 1,1,1,1
11 0,1,1,1
12 0,0,1,1
13 0,0,0,1
14 1,0,0,0
15 0,1,0,0
16 0,0,1,0
17 1,0,0,1
18 1,1,0,0
etc.