Digital Baseband Transmission

Tip

Exam Focus

High-yield items: what line coding is and the four goals (DC balance, clock recovery, limited bandwidth, error indication); NRZ-L / NRZ-I / RZ / Manchester / Differential Manchester rules and waveforms for one common bit sequence; AMI operation and the bipolar violation (BPV); the HDB3 four-zero substitution ($000V$ vs. $B00V$ by pulse-count parity) used on E1; the line-code comparison table; and the regenerative repeater with 3R (re-amplify, reshape, retime).

Baseband Transmission

In baseband transmission a digital waveform is sent through a low-pass physical channel without translating it onto a sinusoidal RF carrier. Copper Ethernet, short digital buses and wired PCM links are baseband systems.

A practical baseband link chains: binary source and framing $\to$ line encoder $\to$ pulse-shaping filter and line driver $\to$ physical channel $\to$ receive/equalization filter $\to$ timing recovery and decision circuit $\to$ line decoder.

Why Raw Bits Need Line Coding

An abstract bit sequence has no defined voltage, polarity or transition timing. A line code assigns a physical waveform to each bit (or bit transition). A good line code should provide:

• Low or zero DC component (vital for transformer-coupled lines).

• Enough transitions for clock recovery (self-clocking).

• Limited bandwidth and low high-frequency content.

• Low baseline wander during long identical runs.

• Some error indication where possible.

• Simple encode/decode and robustness to polarity reversal when needed.

No single code optimises every property; the choice is a trade-off.

Line Coding

Unipolar NRZ, polar NRZ-L, NRZ-I, polar RZ, AMI, Manchester, Differential Manchester and HDB3 for $1\,0\,0\,0\,0\,1\,1\,0$, time-aligned to one bit grid. NRZ-I uses a start transition for $1$ (initial level $-V$); Manchester uses $1$: low-to-high and $0$: high-to-low at mid-bit; Differential Manchester always transitions at mid-bit and uses a start transition for $0$ (initial level $+V$). Plain AMI leaves the four-zero run transition-free; HDB3 uses the odd-count substitution $000V$ with $V=+$.

Term	Meaning
Bit interval $T_b$	Duration of one input bit; bit rate $R_b=1/T_b$
Signal element	Shortest waveform element placed on the line
Baud / symbol rate $R_s$	Signal elements per second
DC component	Spectral component at $f=0$
Self-clocking	Regular transitions let the receiver recover timing
Baseline wander	Drift of the decision reference during long low-frequency runs

Key line-coding terms.

Binary data does not imply one bit per signal element: Manchester deliberately uses two half-bit elements per bit.

Unipolar and Polar Codes

NRZ-L (Non-Return-to-Zero Level). Absolute level carries the bit ($1\to+V$, $0\to-V$); the level is held for the whole bit and never returns to zero. Simplest receiver and lowest bandwidth, but long equal runs have no transitions, data imbalance gives DC/baseline wander, and polarity reversal swaps $0$ and $1$.

NRZ-I (Non-Return-to-Zero Inverted). A transition at the bit start means $1$; no transition means $0$. Information is change, so complete line-polarity inversion does not alter decoding, and a run of $1$s gives regular edges — but a long run of $0$s is still transition-free.

Return-to-Zero (RZ). Polar RZ holds the level for the first half of $T_b$ then returns to $0$ ($1\to+V$ then $0$; $0\to-V$ then $0$). Guarantees a transition every bit, so timing improves; costs three levels and roughly twice the high-frequency span of NRZ.

Manchester. A compulsory mid-bit transition carries both clock and data; under the common IEEE convention $1\to$ low-to-high and $0\to$ high-to-low at mid-bit. Self-clocking with zero DC per bit; costs about twice the NRZ signalling bandwidth. The convention (0/1 direction) must be stated.

Differential Manchester. There is always a mid-bit transition (clock); data is the presence/absence of a start-of-bit transition ($0\to$ start transition, $1\to$ none). Self-clocking, zero DC and immune to conductor reversal, at high transition activity.

Bipolar AMI

AMI (Alternate Mark Inversion) is a three-level bipolar code: a binary $0$ is $0\,V$, and successive binary $1$s (marks) alternate polarity $+V,-V,+V,-V,\dots$ regardless of the zeros between them.

Data: 1 0 1 1 0 0 1 0AMI: +$-$+$-$

Advantages. Alternating marks cancel, so there is no ideal DC and reduced low-frequency energy (transformer-friendly); less transition activity than Manchester; two same-polarity marks form a bipolar violation (BPV) that flags an error or a deliberate substitution; and complete line-polarity reversal does not change mark/space decoding.

Limitation. A long run of zeros gives no pulses, so the clock-recovery circuit can drift and the baseline can wander. HDB3 fixes this for E1.

HDB3 (High-Density Bipolar 3)

HDB3 is an AMI scrambling rule that replaces every run of four zeros by a pattern containing a deliberate bipolar violation, guaranteeing at most three consecutive zero intervals.

Note

Law — HDB3 substitution rules

Symbols: $B$ = a balancing pulse with normal AMI polarity (opposite the preceding nonzero pulse); $V$ = a violation pulse with the same polarity as the preceding nonzero pulse (an intentional BPV). Count ordinary nonzero pulses since the previous substitution:

$$0000 \;\to\; \begin{cases} 000V & \text{if the count is \textbf{odd}}\\[2pt] B00V & \text{if the count is \textbf{even}} \end{cases}$$

Odd $\Rightarrow$ a single $V$ restores an even pulse count; even $\Rightarrow$ $B$ and $V$ share polarity so the substitution stays DC-balanced.

Count since last $V$	Replace $0000$	Pulses	Reason
Odd	$000V$	one violation	Restores even pulse count / resets counter
Even	$B00V$	$B$ then $V$ (same polarity)	Keeps long-term DC balance

HDB3 four-zero substitution by pulse-count parity.

Odd-count example. Previous ordinary mark $+$, one mark since last violation, data $1\,0000\,110 \to$ line $+\,0\,0\,0\,V\,-\,+\,0$ with $V=+$ (same polarity as the preceding pulse); ordinary marks then resume alternating from $V$. Even-count example. Previous nonzero pulse $+$, even count: $0000 \to B00V = -\,0\,0\,-$, where the second $-$ repeats $B$ and is the violation. Decoding: the receiver spots the illegal AMI polarity pattern, replaces the whole $000V$ or $B00V$ group with four zeros, and resumes ordinary AMI. HDB3 keeps near-zero DC, supplies timing transitions, and is the standard E1/PCM-30 line code (T1 typically uses B8ZS instead).

Line-Code Comparison

Exact occupied bandwidth depends on pulse shape, filtering and the bandwidth definition; the table gives the standard relative comparison used in exams.

Code	Levels	DC / low-freq	Clock recovery	Rel. BW	Special use
NRZ-L		Can be significant	Poor on equal runs	Lowest	Simplest links
NRZ-I		Can be significant	Good 1s, poor 0s	Low	Polarity-insensitive
Polar RZ		Lower, not always $0$	Good	High	Simple timing
Manchester		Zero DC	Excellent	$\approx 2\times$ NRZ	Classic Ethernet
Diff. Manchester		Zero DC	Excellent	$\approx 2\times$ NRZ	Polarity-insensitive
AMI		No ideal DC	Poor on long $0$s	Moderate	BPV error flag
HDB3		No ideal DC	Good	Moderate	E1 line systems

Comparison of common baseband line codes.

Selection. NRZ when bandwidth/simplicity dominate and a separate clock/scrambler exists; Manchester when embedded clocking outweighs bandwidth; Differential Manchester when polarity reversal must not matter; AMI for transformer coupling and BPV monitoring with controlled zero runs; HDB3 for self-timed AMI-compatible E1 transport.

Regeneration and Synchronization

Digital pulses suffer attenuation, additive noise, dispersion and intersymbol interference (ISI). A regenerative repeater does not merely amplify the analog waveform — it makes a fresh binary decision and launches a clean pulse, so noise does not accumulate indefinitely (provided each hop’s error probability stays low).

Regenerative repeater: an equalizer reshapes the distorted input, recovered clock retimes the decision, and a decision circuit regenerates clean pulses. Below: noisy received waveform, the regenerated clean output, and an E1 PCM frame (32 timeslots; TS0 sync, TS16 signalling).

Caution

Key Formula — 3R regeneration

A regenerative repeater performs, in order: Re-amplification (restore amplitude), Reshaping (threshold decision restores standard levels/edges) and Retiming (recovered clock places new transitions at correct bit instants).

Synchronization levels. Bit/clock locates each decision instant (line coding chiefly assists this); word/codeword groups bits into samples/characters; frame locates channel slots/boundaries; and carrier recreates the phase/frequency reference for coherent passband detection.

Solved Examples

Note

Example — Line-coding rules and waveforms (10 marks)

Line coding maps source bits to physical voltage/pulse elements on a baseband channel, trading bandwidth, DC content, clock transitions, polarity tolerance and complexity. For the common sequence $1\,0\,0\,0\,0\,1\,1\,0$ ($T_b$ = bit interval): NRZ-L holds $+V/-V$ (simplest, lowest BW, but no edges on equal runs and polarity-sensitive); NRZ-I encodes a $1$ as a start transition (polarity-insensitive, but zeros give no edges); polar RZ returns to zero mid-bit (guaranteed edge, three levels, wider spectrum); Manchester uses a mid-bit direction (self-clocking, zero DC, $\approx 2\times$ BW); Differential Manchester clocks at mid-bit and encodes data as a start transition (self-clocking, zero DC, polarity-immune). The common-sequence figure shows all five as labelled rows, together with Unipolar NRZ, AMI and HDB3; reproduce the five relevant rows and compare DC, timing, polarity and bandwidth.
Practice target: 18–20 min; state one convention, reproduce every waveform for the same sequence, then compare the four properties.

[!NOTE]

Example — AMI operation and properties (5 marks)

AMI is three-level bipolar: $0\to 0\,V$; successive $1$s alternate $+V,-V,\dots$ For $1\,0\,0\,0\,0\,1\,1\,0$ with first mark $+$ the line is $+,0,0,0,0,-,+,0$. Alternating marks cancel, so there is no ideal DC and reduced low-frequency energy (transformer-friendly) with modest transition activity. Two same-polarity marks are a bipolar violation that flags an error (not a complete error-detecting code). Its weakness is a long zero run: no edges $\Rightarrow$ clock drift and baseline wander — solved by HDB3.
Practice target: 8 min; encode one 8-bit sequence, then state DC, transformer, polarity, BPV and long-zero properties.

[!NOTE]

Example — HDB3 substitution rules in PCM lines (5 marks)

AMI loses transitions on long zero runs. HDB3 replaces each $0000$ by a pattern with a deliberate violation, leaving at most three zeros. $B$ = normal AMI polarity (opposite the preceding pulse); $V$ = same polarity as the preceding pulse. Counting ordinary marks since the last violation: odd $\to 000V$, even $\to B00V$. Odd example: first $1$ sent as $+$, then for $1\,0000\,110$ one mark has occurred, so $000V$ with $V=+$; line $= +,0,0,0,+,-,+,0$. Even example: previous pulse $+$, even count $\Rightarrow 0000 \to B00V = -,0,0,-$ (second $-$ is the violation). The decoder removes $B$/$V$ and restores four zeros. HDB3 keeps near-zero DC and timing; standard on E1 (not to be confused with T1’s B8ZS).
Practice target: 8–9 min; define $B$ and $V$, write the odd/even table, and work both polarity cases without altering the data zeros.

[!NOTE]

Example — Regenerative repeater and 3R (5 marks)

Cable loss lowers amplitude, noise perturbs level and dispersion spreads pulses (ISI). A regenerative repeater estimates the symbols and launches a new standard waveform (unlike an analog amplifier it does not reproduce all input noise). Its equalizer limits noise and compensates the channel; a clock-recovery circuit extracts timing; at the eye-centre sampling instant a decision circuit compares against thresholds; a pulse generator on the recovered clock sends a clean pulse. This is 3R: re-amplify, reshape, retime. E.g. a noisy $+0.31\,V$ sample is decided $+V$ and reborn as a nominal $\pm 1\,V$ pulse, so noise does not accumulate — unless a sample crosses the threshold, giving a bit error that is then regenerated perfectly.
Practice target: 8–9 min; draw equalizer, clock recovery, sampler and pulse generator, then distinguish all three Rs from analog gain.

[!NOTE]

Key Point — Revision — Digital Baseband

• Line coding maps abstract bits to a physical voltage/pulse waveform.

• NRZ: low bandwidth but weak clock recovery on long identical runs.

• Manchester: mid-bit transition, zero DC, self-clocking, $\approx 2\times$ BW.

• Differential Manchester encodes data by transitions $\Rightarrow$ polarity-immune.

• AMI: $0\to 0\,V$, $1$s alternate; same-polarity mark $=$ BPV.

• HDB3: $0000\to 000V$ (odd count) or $B00V$ (even count); used on E1, not T1.

• Regenerative repeater does 3R: re-amplify, reshape, retime.