In a certain digital data transmission system the probability of a bit error as a function of timing jitter is given by 

where z is the signal-to-noise ratio, |ΔT|, is the timing jitter, and T is the bit period. From observations of an eye diagram for the system, it is determined that |ΔT|/T = 0.05 (5%).

(a) Find the value of signal-to-noise ratio, z₀, that gives a probability of error of 10^-6  for a timing jitter of 0.

(b) With the jitter of 5%, tell what value of signal-tonoise ratio, z₁, is necessary to maintain the probability of error at 10^-6. Express the ratio z₁/z₀ in dB, where [z₁ / z₀]_dB =10 log₁₀ (z₁/z₀). Call this the degradation due to jitter.

(c) Recalculate parts (a) and (b) for a probability of error of 10^-4. Is the degradation due to jitter better or worse than for a probability of error of 10^-6?

Transcribed Image Text:

ΙΔΤ| ( 1- 2 j exp(-z) +jexp PE :-