Digital Baseband Transmission¶

Exam-ready answer

Line coding is the rule that maps source bits into physical voltage or pulse elements for a baseband channel. A useful code balances bandwidth, DC content, clock transitions, polarity tolerance and implementation complexity. Let \(T_b\) be the bit interval and \(R_b=1/T_b\).

Use the common data sequence \(1\ 0\ 0\ 0\ 0\ 1\ 1\ 0\) and the following explicit conventions:

In NRZ-L, information is the absolute level. It has simple detection and the lowest relative transition rate, but a long run of either symbol has no timing edge; unequal probabilities also create DC/baseline wander, and line-polarity reversal swaps bit meanings.

In NRZ-I, information is a change rather than a level. A run of 1s gives timing transitions and complete polarity reversal does not change decoding, but a long run of 0s remains transition-free and DC content can still occur.

In polar RZ, each pulse returns to zero halfway through the bit. The guaranteed half-bit return improves timing, but it uses three levels and shorter pulses extend the high-frequency spectrum. Its average is zero only for balanced positive/negative data, not automatically for every sequence.

In Manchester, the compulsory center transition carries clock and data; its direction carries the bit under the stated convention. Each bit has equal positive and negative half-areas, so ideal DC is zero and clock recovery is excellent. The cost is roughly twice the transition bandwidth class of NRZ. Some texts reverse the 0/1 directions, so the convention must be stated.

In Differential Manchester, the center transition supplies clock while presence/absence of a start transition carries data. It is self-clocking, has zero ideal DC and tolerates reversed conductors, but has high transition activity and bandwidth similar to Manchester.

Exact occupied bandwidth depends on pulse shaping, filtering and whether one quotes first-null, null-to-null or power containment. Qualitatively, NRZ is most bandwidth-efficient, RZ/Manchester/Differential Manchester require more high-frequency content, and transition-rich codes give better clock recovery. NRZ is used where a separate clock or scrambler exists; Manchester is associated with classic Ethernet-style links; differential coding is useful when polarity may reverse.

Practice target: 18–20 minutes; state one convention, reproduce all five waveforms for the same sequence, and compare DC, timing, polarity and bandwidth.

Exam-ready answer

Alternate Mark Inversion (AMI) is a three-level bipolar line code. A binary 0 is transmitted as \(0\,\text{V}\), while successive binary 1s, called marks, alternate polarity \(+V,-V,+V,-V,\ldots\) regardless of the number of zeros between them.

If the first mark is positive, the sequence \(10000110\) becomes

Because positive and negative marks alternate, their areas cancel over ordinary traffic. AMI therefore has no ideal DC component, reduced low-frequency energy and is suitable for transformer-coupled lines. It also uses fewer forced transitions than Manchester. A reversal of both line wires changes every pulse sign but does not change mark-versus-zero decisions.

AMI provides limited error indication. Two received nonzero marks of the same polarity violate the alternating rule; this bipolar violation (BPV) can flag a channel error. It is not a complete error-detecting code: some multiple errors preserve alternation, and a changed zero/mark may alter the expected sequence without guaranteeing a visible BPV.

Its main limitation is a long run of zeros. Such a run produces no pulse edges, so a clock-recovery circuit can drift and the decision baseline can wander. HDB3 retains AMI polarity balance but deliberately substitutes pulses into every four-zero run, allowing the receiver to recover timing and then restore the zeros.

Practice target: 8 minutes; encode one eight-bit sequence, then state DC, transformer, polarity, BPV and long-zero properties.

Exam-ready answer

AMI loses clock transitions during long zero runs. HDB3 (High-Density Bipolar 3) solves this in E1/PCM line systems by replacing each group of four data zeros with pulses that create a recognizable deliberate AMI violation. No more than three zero line intervals remain.

The symbols are:

• \(B\): a balancing pulse with normal AMI polarity, opposite to the immediately preceding nonzero pulse.
• \(V\): a violation pulse with the same polarity as the immediately preceding nonzero pulse at that point.

Count ordinary nonzero pulses since the previous substitution/violation:

Odd-count example: assume the first data 1 is sent as \(+V\). For \(1\,0000\,110\), one ordinary mark has occurred, so use \(000V\) with \(V=+V\). The complete line sequence is \(+,0,0,0,+,-,+,0\); the next ordinary marks resume alternating from the violation.

Even-count example: if the previous nonzero pulse is \(+V\) and the ordinary-pulse count is even, \(0000\) becomes \(B00V=-,0,0,-\). The second negative pulse is the deliberate violation because it repeats the polarity of \(B\).

The receiver detects these illegal AMI polarity patterns, replaces the complete \(000V\) or \(B00V\) group by four data zeros, and resumes normal AMI decoding. HDB3 preserves near-zero DC/controlled low-frequency content while supplying timing transitions. It is standard for E1; it should not be confused with B8ZS commonly used on T1 links.

Practice target: 8–9 minutes; define \(B\) and \(V\), write the odd/even table, and work both polarity cases without changing the original data zeros.

Exam-ready answer

A line code specifies the voltage levels and transitions representing bits. Selection is a trade-off among clock recovery, low-frequency/DC content, occupied bandwidth, polarity sensitivity, error indication and circuit complexity.

For the common sequence \(10000110\) with first AMI mark positive, NRZ-L levels are +,-,-,-,-,+,+,-, while AMI is +,0,0,0,0,-,+,0. The four-zero run makes plain AMI transition-free. Because one ordinary mark has occurred since the prior violation, HDB3 uses \(000V\), giving +,0,0,0,V,-,+,0 with \(V=+\). This shared sequence exposes the practical reason for substitution rather than merely listing rules.

Bandwidth qualification: rectangular NRZ pulses have the lowest transition rate; RZ halves pulse width and Manchester forces a half-bit transition, so both extend farther in frequency. AMI/HDB3 lie between these groups for typical traffic. Numerical bandwidth is not universal unless pulse shaping, roll-off and first-null/null-to-null convention are stated.

Choice: use NRZ when bandwidth and simplicity dominate and clocking is otherwise guaranteed. Use Manchester when embedded timing and zero DC justify extra bandwidth. Use Differential Manchester when conductor reversal must not matter. AMI supports transformer coupling and BPV monitoring, but HDB3 is preferred on E1 because it also guarantees timing through long data-zero runs. HDB3 substitutions are transparent: the decoder removes \(B\) and \(V\), so user data is unchanged.

Practice target: 18 minutes; reproduce the seven-row table, annotate the shared zero-run example, and state the bandwidth convention caveat.

Exam-ready answer

During baseband transmission, cable loss reduces pulse amplitude, noise perturbs level, and channel dispersion spreads each pulse into neighboring bit intervals, causing intersymbol interference and timing jitter. A regenerative repeater estimates the transmitted symbols and launches a new standard waveform; unlike an analog amplifier, it does not reproduce all input noise and distortion.

Its receive filter/equalizer first limits noise and compensates channel response. A clock-recovery circuit extracts bit timing from line transitions. At the optimum sampling instant, normally near the eye center, a decision circuit compares the sample with one or more thresholds and chooses the nearest allowed line symbol. A pulse generator driven by the recovered clock then transmits a clean, correctly timed pulse to the next span.

The process is called 3R regeneration:

1. Re-amplification: restore standard output amplitude after attenuation.
2. Reshaping: make a threshold decision and restore standard levels, pulse width and edges.
3. Retiming: remove accumulated timing displacement by launching the decided pulse on recovered clock instants.

For a binary polar example with zero threshold, a noisy center sample of \(+0.31\,\text{V}\) is decided as \(+V\) and one of \(-0.18\,\text{V}\) as \(-V\); the output is not \(+0.31/-0.18\,\text{V}\) but fresh nominal pulses such as \(\pm1\,\text{V}\). Noise therefore does not accumulate continuously over many correctly deciding repeaters. If noise/ISI pushes a sample across the threshold, however, the repeater makes a bit error and regenerates that wrong decision perfectly. Adequate line-code transitions, equalization and a wide eye opening are therefore essential.

Practice target: 8–9 minutes; draw filter/equalizer, clock recovery, sampler/decision and pulse generator, then distinguish all three Rs from analog gain.