Tektronix 071-0590-00 user manual SNR = 20 log S / N rms

BERT Technical Articles

Standard Mathematical Tables published by the Chemical Rubber Co, or use the software product Mathcad produced by MathSoft.

It is usually convenient to measure signal strength and noise in dB. Let the signal-to-noise ratio in dB be defined as

SNR = 20 log(S / Nrms). (12)

Then with Equation (11) we can find BER as a function of SNR. This is plotted in Figure 4. In Figure 4a the BER axis is a log scale. In Figure 4b the BER axis has a specially distorted scale so the plot appears as a straight line. This will help in determining whether noise is Gaussian, and it will help in extrapolating data. Suppose a system has a SNR of 18 dB. According to Figure 4, the corresponding bit error ratio is 10−16. At a baud of 1 Gbit/s, this would yield an error only once every 4 months on average. To get an estimate of this error rate in a reasonable time, testing with stress is necessary.

10 1													10 2
10 2
103
BER
10 4													10 3
105
106													BER
10		7											10 4
108													10 5
109
10 10													10 6
10 11													10 7
10 12													10 8
10 13													10 9
10 14													10 10
10 15													12
													10
10	16		8	9	10	11	12	13	14	15	16	17	10 14
		7											18
							SNR (dB)						10 16	8	9	10	11	12	13	14	15	16	17	18
(a)													7
													(b)					SNR (dB)

Figure 4. Bit-Error-Rate (BER) is plotted here as a function of the signal-to-noise ratio (SNR), where SNR is S/Nrms in decibels (electrical), S is the distance from the signal (1 or 0) to the decision threshold and Nrms is the rms value of the Gaussian noise introduced by the first receiver state (a). In (b), the log scale was distorted, so the plot is a straight line.

The stress that we propose is attenuation of the received signal S. Most of the system noise arises in the input stage of the data receiver, and the attenuator won't affect this noise. Then if there is no AGC, the attenuator reduces S. If there is an AGC, S is held constant and the noise increases. In any case, the ratio of S to Nrms changes with the attenuation; 6 dB of electrical attenuation decreases the signal-to-noise ratio by 6 dB. In general, the signal-to-noise ratio with stress is

SNR = SNR0 – Attenuation,(13)

where SNR0 is the signal-to-noise ratio without stress (attenuator set to 0 dB).

In order to properly extrapolate data taken with stress, we need to know what a plot of BER versus Attenuation looks like for a given SNR0. Suppose that SNR0 is 18 dB. Then for Attenuation = 0 the

SNR is also 18 dB, and from Figure 4 we find BER = 10−16 (see point at Attenuation = 0 in Figure 5). As the Attenuation is increased to 6 dB, then SNR is reduced to 18 – 6 = 12 dB. According to Figure 4,

this corresponds to BER = 3.5×10−5 (see point at Attenuation = 6 dB in Figure 5). The complete plot of

B-36 GB1400 User Manual