Examples 2.2
The specification for a Class 1 telephone link is a
guaranteed flat bandwidth of 300 Hz to 3400 Hz and a minimum signal to noise ratio of 40 dB.
The specification for a Class 2 telephone link is a guaranteed flat bandwidth from
600 Hz to 2800 Hz and a minimum signal to noise ratio of 30 dB. A company has a requirement to
send data over a telephone link at a bit rate of 20 kbps without error. Would you advise
the company to rent the more expensive Class 1 service or the cheaper Class 2 service?
Justify your decision.
Solution
The ShannonHartley equation gives us the required
relationship between channel capacity in bps, bandwidth and signal to noise ratio as
follows:
Channel capacity C = B.log2(S/N + 1) bps
For the Class 1 line, B = 3400 300 = 3100 Hz
and S/N = 40 dB, thus:
C = 3100.log2(10000 + 1)
= 41.2 kbps
Note, it is essential to convert the S/N value
from dB to a ratio for use in the ShannonHartley expression.
For the Class 2 line, B = 2800 600 = 2200 Hz
and S/N = 30 dB, thus
C = 2200.log2(1000 + 1) bps
= 21.9 kbps
These calculations show that both the Class 1 and Class 2 line will meet the
specification of 20 kbps error-free transmission however, the
performance of the Class 2 line is very close to the Shannon bound, and allows little
margin for error. In practice, it is unlikely that a modem could be realized that would
give the desired result on the Class 2 line.