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# A digital link analysis

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An underground twisted pair line is one mile long. The line is used to send a 1.50 Mbps signal as a polar binary NRZ voltage waveform. A logical 1 is transmitted as a +1.0 V pulse and a logical 0 is transmitted as a -1.0 V pulse. At the output of the receiver's sampling gate the pulses have peak amplitudes of +100 mV and -100 mV. Assume an ideal link and correct synchronization of the clock in the receiver.

a. What is the main cause of bit errors on this digital link?

b. At the receiver, what is the rule that is used to decide whether to output a 1 or a 0?

c. A logical 1 is transmitted over the link. A noise spike of +150 mV is added to the signal at the instant it is sampled by the receiver. Will this cause a bit error?

d. Observation of the voltage at the output of the sampling gate of the receiver shows that voltage spikes of 150 mV amplitude are being added to the signal pulses at an average rate of six spikes per second, with an equal number of positive and negative spikes. What is the bit error rate on the link?

e. What change at the transmitter would make this link error free?

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#### Solution Preview

(a) Dispersion over the link (i.e. the non uniform attenuation of frequency components that constitute the perfect (assumed) square pulse waveform) will both alter the waveform height (amplitude) and spread out the pulse energy (flatten the shape of the pulse) over the time interval. This dispersion effect will become more pronounced the further the pulse has to travel along the link. This results in pulse energy merging from one pulse into the period occupancy of an adjacent pulse. When the interfering pulse energy becomes great enough (i.e. equal or greater than the actual pulse energy to be measured in a time interval) then an ...

#### Solution Summary

From a description of a digital link the bit errors on the link are deduced and analysed and questions on its QoS addressed

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## Baseband link equipped with an equalizer: maximum pulse rate, bit rate, average power and voltage

A baseband link is equipped with an equalizer such that its operating bandwidth is 1.00 MHz. Over this bandwidth the attenuation is constant at 25 dB and the phase shift is linear with frequency. The link is used for the transmission of digital signals. The transmitter and receiver have ideal RRC filters with roll off factor r = 1.0. The transmitter pulses are binary ASK using on-off keying (OOK).

a. What is maximum pulse rate (i.e. symbol rate) for this link?

b. What is the bit rate of the signal?

c. If the filters in the transmitter and receiver are changed for ideal RRC filters with roll off factor r = 0.25, what is the maximum symbol rate for this link?

d. The transmission line has an impedance of 600 ohms and is terminated in a load of 600 ohms. The transmitter delivers an average power of 0.1 W to the input of the line. What is average power at the receiving end of the line? What is the average voltage of the received pulses?

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