NRZ Codes

The basics of Non-Return-to-Zero line coding and its spectral properties.

The Principle of NRZ

Non-Return-to-Zero (NRZ) is one of the simplest and most direct families of . The name itself reveals its core principle: the signal level does not return to zero in the middle of a bit period. A specific level (e.g., a positive or negative voltage) is maintained for the entire duration of the bit, designated as $T$ .

Variant 1: Unipolar NRZ

In the unipolar (one-pole) version, a logical '1' is represented by a positive voltage level, while a logical '0' is represented by a zero-volt level.

Logical '1' → $+V$
Logical '0' → $0V$

While simple, this method has a significant drawback: the presence of a strong , especially during long sequences of '1's. This makes it unsuitable for many transmission systems.

Variant 2: Bipolar NRZ

The bipolar (two-pole) version improves upon the unipolar scheme by using voltage levels of opposite polarity. This is the more common form of NRZ.

Logical '1' → $+V$
Logical '0' → $-V$

By using symmetrical positive and negative voltages, the DC component is significantly reduced, assuming that '0's and '1's appear with roughly equal probability in the data stream.

Interactive NRZ Encoding Example

Binary Input

Enter binary sequence (0s and 1s only)

Voltage Level (V): 5V

Bit Duration (ms): 1000ms

Show Unipolar NRZ

Show Bipolar NRZ

Current Bit: 1

Unipolar: 1 → +V, 0 → 0V

Bipolar: 1 → +V, 0 → -V

DC Component

Unipolar:3.75V

Bipolar:0.00V

Spectral Information

Clock Frequency:1.00 Hz

Main Lobe Bandwidth:0 - 1.00 Hz

Spectral Analysis and Key Drawbacks

The greatest strength of NRZ codes is also the source of their biggest weakness. An analysis of the bipolar NRZ signal's reveals two critical characteristics:

Spectral Efficiency: The main lobe of the spectrum, which contains most of the signal's energy, is relatively narrow, extending from DC to the clock frequency, $f_{clk} = 1/T$ . This makes NRZ efficient in its use of bandwidth compared to other codes like Manchester.
Synchronization Problem: The spectrum has a power null (zero) precisely at the clock frequency. This means there is no energy at this critical frequency component. This, combined with the lack of signal transitions during long runs of identical bits ( $1111...$ or $0000...$ ), makes it extremely difficult for the receiver to perform and maintain synchronization. If the receiver loses sync, it will start reading bits incorrectly, resulting in a cascade of errors.

Summary of NRZ Properties

Advantages

Simplicity: Very easy and inexpensive to implement in hardware.
Good Bandwidth Efficiency: The main spectral lobe is narrow (extends to $f_{clk}$ ), requiring less bandwidth than many other codes.

Disadvantages

Poor Synchronization: Long strings of '0's or '1's provide no signal transitions, leading to potential loss of synchronization.
Null at Clock Frequency: The absence of a spectral component at the clock frequency makes clock recovery difficult and unreliable.
Presence of DC Component: Heavily dependent on data content. Long runs of one bit create a DC level, which is problematic for AC-coupled systems.

Due to these significant drawbacks, raw NRZ coding is seldom used for direct transmission in modern baseband communication systems. It often serves as the initial binary sequence that is then processed by a scrambler or a more robust line coding scheme to overcome its limitations.