The Problem with Non-Stop Signals

While simple line codes like NRZ (Non-Return-to-Zero) are easy to implement, they suffer from a major flaw: a long, uninterrupted sequence of identical bits ($11111111$) creates a constant voltage level on the line. With no changes in the signal, the receiver can lose its timing reference, a phenomenon known as loss of synchronization.

Return-to-Zero (RZ) coding was developed to solve this very problem by forcing a change in the signal during each bit that carries energy.

How Unipolar RZ Works

The simplest variant is Unipolar RZ. It modifies the NRZ signal by making the pulse for a logical '1' last for only a fraction of the bit duration, typically one-half. After the pulse, the signal "returns to zero" for the remainder of the bit period.

Encoding Rules

The signals representing the symbols are defined as follows, where $T$ is the bit duration:

• Logical '1': Represented by a positive pulse $+V$ for the first half of the bit duration ($0.5T$), followed by a return to $0V$ for the second half.
  Formula: $g_1(t) = +V \cdot \Pi(t; 0.5T)$
• Logical '0': Represented by a zero voltage level for the entire bit duration.
  Formula: $g_0(t) = 0$

Interactive RZ Encoding Example

The RZ Spectrum: A Double-Edged Sword

The unique structure of the RZ signal has a profound impact on its frequency spectrum, bringing both a significant advantage and a major disadvantage.

Spectrum Analysis

• Advantage - Clock Recovery (++): The spectrum of an RZ signal contains a distinct, discrete spectral line (a spike) at the clock frequency ($f_{clk} = 1/T$). This acts like a built-in "metronome" that the receiver's circuitry can easily lock onto using a simple filter. This makes clock recovery from an RZ signal much more reliable than from an NRZ signal.
• Disadvantage - Increased Bandwidth (--): The price for this improved synchronization is a wider bandwidth requirement. Because the pulses are shorter (half the bit duration), the signal's main spectral lobe is twice as wide as that of an NRZ signal, extending to $2f_{clk}$. This makes RZ coding less spectrally efficient.
• Disadvantage - DC Component (-): The unipolar version of RZ has a data-dependent DC component, which can be problematic for some transmission systems.
• Limitation - Long Zero Sequences (-): A long string of zeros still produces a flat, zero-voltage line, which can lead to a loss of synchronization, just like in NRZ. More advanced codes like AMI and HDB-3 were created to solve this specific issue.