Electronics Guide

Defining NRZ: Levels, Symbols, and Encoding

An NRZ waveform occupies one of two voltage levels during each bit interval. The signaling family is defined by three things: the timing grid on which symbols are placed, the rule that maps bits to levels, and the electrical means by which the two levels are produced on the physical medium.

Unit Interval, Symbol Rate, and Transition Time

The bit interval is universally called the unit interval (UI). The unit interval is the reciprocal of the symbol rate: a link running at 10 gigabits per second in NRZ has a unit interval of 100 picoseconds, and a 32 gigabit-per-second link has a unit interval of 31.25 picoseconds. Because each symbol carries exactly one bit, the bit rate and the symbol rate (baud rate) are numerically equal in NRZ. That identity does not hold for multi-level schemes, where the bit rate exceeds the baud rate.

Transition time matters as much as level accuracy. Edges that are too slow consume timing margin and blur the boundary between adjacent symbols; edges that are far faster than the channel requires radiate needlessly and aggravate crosstalk and reflections. Specifications therefore constrain rise and fall times as a fraction of the unit interval rather than in absolute terms, so the same rule scales across generations of a standard. Because rise time and bandwidth are two views of the same limit, a common engineering approximation relates the two directly: for a simple single-pole response, the usable bandwidth in hertz is roughly 0.35 divided by the ten-to-ninety-percent rise time in seconds.

NRZ-Level and NRZ-Inverted

NRZ comes in two principal variants that differ in how they map bits to levels:

• NRZ-Level (NRZ-L): The absolute level encodes the bit directly. A high level represents one logical value and a low level represents the other. This is the form most engineers mean when they say simply "NRZ."
• NRZ-Inverted (NRZI): The information is carried by transitions rather than absolute levels. In the conventional definition, a transition at the bit boundary encodes a logical one and the absence of a transition encodes a logical zero; the complementary convention, in which the logical zero produces the transition, is equally valid and is the one USB adopts. Because NRZI conveys data through change rather than state, it tolerates a swapped or inverted pair without loss of meaning, which is why it appears in USB at low, full, and high speed and in fiber standards such as FDDI.

The transition-based nature of NRZI does not by itself solve the transition-density problem. A long run of the non-transitioning symbol still produces a flat waveform, so NRZI is nearly always paired with a mechanism that forces edges. USB inserts a stuffed bit after six consecutive ones so that the encoded stream cannot remain static, and FDDI uses a 4B/5B block code whose five-bit symbols are chosen to bound the run length before NRZI encoding is applied.

Single-Ended and Differential Realizations

The physical realization of the two levels depends on the signaling family. Single-ended logic such as legacy CMOS swings between ground and the supply rail, referencing every decision to a shared ground that is rarely quiet at high speed. Modern high-speed links almost always use differential signaling, in which two complementary conductors carry equal and opposite swings and the receiver senses only the difference between them. Differential NRZ rejects common-mode noise, cancels much of the far-field radiation of the pair, and defines the logic state by the sign of the differential voltage rather than by an absolute level referenced to ground.

Two driver styles dominate. Low-voltage differential signaling drives a nominal 3.5 milliamperes through a 100-ohm differential termination, producing a differential swing near 350 millivolts at modest rates and very low power. Current-mode logic and its variants, used in multi-gigabit serializer-deserializer (SerDes) macros, source a switched tail current into on-die termination and typically produce a few hundred millivolts of differential swing with the bandwidth needed for tens of gigabits per second. The electrical layers of PCI Express, USB SuperSpeed, SATA, and most Ethernet copper interfaces are differential NRZ built on this second style.

NRZ Versus RZ Signaling

Return-to-zero (RZ) is the natural counterpart to NRZ. In an RZ code the signal asserts the active level for only part of each bit interval and then returns to a neutral or zero level before the interval ends. A common form returns to zero at the midpoint, so each logical one appears as a pulse occupying half the unit interval. The defining contrast is straightforward: NRZ holds its level across the whole bit, while RZ inserts a forced return to a reference level within every bit.

This difference produces a clear set of trade-offs:

• Transition density: RZ guarantees at least one transition per asserted bit, which embeds timing information directly in the waveform and eases clock recovery. NRZ provides no transition during runs of identical bits, so long runs carry no timing edges.
• Bandwidth: Because an RZ pulse is narrower than an NRZ symbol, RZ concentrates its energy at higher frequencies and therefore requires roughly twice the bandwidth of NRZ for the same bit rate. NRZ is the more bandwidth-efficient of the two.
• Energy and amplitude: For a given peak level, RZ delivers less energy per bit because the active level is present for only part of the interval. To match the energy of NRZ, an RZ transmitter must use a larger peak amplitude, which raises driver power and stresses the linearity of the output stage.
• Implementation: NRZ is simpler to generate and consumes the least bandwidth, which is why it dominates electrical interconnects. RZ persists in specialized optical systems, where its well-defined pulses suit certain detection schemes and where the bandwidth penalty is more readily absorbed. Long-haul optical transport made extensive use of RZ and chirped-RZ pulse shapes before coherent detection with digital signal processing displaced them.

The bandwidth advantage is decisive for bandwidth-limited copper channels, and it is the primary reason NRZ, rather than RZ, became the default binary format for high-speed serial links. RZ survives mainly where its timing-rich, pulse-defined character outweighs its appetite for bandwidth.

Binary Line Codes Beyond NRZ

NRZ and RZ do not exhaust the ways two-state data can be placed on a wire. Several other binary line codes trade bandwidth for guaranteed timing content or guaranteed balance, and understanding them clarifies exactly what NRZ gives up and what it gains.

• Manchester (biphase) coding: Every bit interval contains a mid-bit transition whose direction encodes the value. The result is a self-clocking, perfectly direct-current-balanced waveform that needs no scrambler and tolerates alternating-current coupling without wander. The cost is severe: the fundamental frequency doubles, so Manchester requires about twice the bandwidth of NRZ for the same bit rate. Classic 10 megabit-per-second Ethernet used Manchester coding, as do many low-rate control, telemetry, and radio-frequency identification links where robustness matters far more than spectral efficiency.
• Alternate mark inversion and its descendants: Here logical ones alternate between positive and negative pulses while zeros remain at the reference level. The alternating polarity forces the long-term average to zero and permits simple error detection through bipolar violations, at the price of a three-level waveform carrying only one bit per symbol. Telephone-carrier systems adopted this family and layered on substitution rules, such as bipolar with eight-zero substitution and high-density bipolar of order three, to guarantee transitions during long strings of zeros.
• Block-coded NRZ: Rather than change the waveform, this approach keeps NRZ on the wire and reshapes the data beforehand. Codes such as 4B/5B, 8b/10b, and 64b/66b expand the payload slightly and choose transmitted patterns that bound run length and control balance. Modern high-speed links almost universally take this route, because it preserves the bandwidth efficiency of NRZ while supplying the timing and balance guarantees that Manchester coding buys with bandwidth.

The pattern across these codes is consistent. Timing content and direct-current balance are not free; they are purchased either with bandwidth, as in Manchester and RZ coding, with additional signal levels, as in alternate mark inversion, or with coding overhead, as in block-coded NRZ. High-speed serial design chose the last option because bandwidth is the scarcest resource on a copper channel.

The Two-Level Eye Diagram

The eye diagram is the central diagnostic tool for evaluating binary signaling quality. It is constructed by overlaying many short segments of the received waveform, each aligned to the recovered clock and spanning one or two unit intervals. As thousands of bit transitions are superimposed, the accumulated traces form a pattern resembling a human eye. For NRZ, the diagram shows a single eye opening, because two levels create exactly one gap between them. A PAM-4 signal, by contrast, produces three stacked eyes.

Reading the Eye

The shape of the single NRZ eye encodes a great deal of information about the health of the link:

• Eye height: The vertical opening measures the voltage margin between the one and zero levels at the sampling instant. A taller eye means more noise can be tolerated before a sampled value crosses the decision threshold. Noise, crosstalk, and attenuation all reduce eye height.
• Eye width: The horizontal opening measures the timing margin. A wider eye means the sampling clock can drift further from the ideal instant without error. Jitter and inter-symbol interference (ISI) narrow the eye width.
• Crossing points: The points where rising and falling edges intersect indicate the transition threshold and reveal duty-cycle distortion. Crossings that sit above or below the center point signal asymmetry between rise and fall behavior.
• Edge slope and thickness: Sharp, thin edges indicate clean transitions; smeared or thick edges indicate jitter, reflections, or bandwidth limitation in the channel.

An ideal NRZ eye is wide open, symmetric, and centered, with crisp edges and a large clear region in the middle where the receiver places its single decision threshold and its sampling clock. As data rates rise and channels attenuate high frequencies, the eye progressively closes. The principal advantage of binary signaling appears clearly here: with only two levels spanning the full signal swing, the NRZ eye is intrinsically taller than any individual eye in a multi-level scheme, giving binary links their characteristic robustness.

Masks, Bathtub Curves, and Bit Error Rate

Qualitative inspection is not enough for compliance work, so the eye is evaluated against quantitative criteria. A mask is a forbidden polygon placed inside the eye; a conforming signal keeps every trace outside it, which guarantees a minimum voltage and timing opening simultaneously. Most interface standards publish transmitter and receiver masks measured at defined test points and after a specified reference equalizer.

Margin is characterized more completely by bathtub curves. A timing bathtub plots measured bit error rate against the horizontal position of the sampling instant across the unit interval, and a voltage bathtub does the same for threshold position. Each curve is flat and low in the center and rises steeply toward the edges, so the width of the floor at a target error rate states the true margin. Because measuring a very low error rate directly would take far too long, the steep flanks are fitted and extrapolated to the target.

For a signal impaired mainly by Gaussian noise, the error rate follows the ratio of eye opening to noise, commonly expressed as a quality factor. The relationship is steep: a quality factor near seven corresponds to an error rate near one in a trillion, and small changes in eye height move the error rate by orders of magnitude. That steepness is why binary links can meet the customary one-in-a-trillion target without coding while multi-level links, whose eyes are three times smaller, generally cannot.

Bandwidth and Spectral Content

The spectrum of an NRZ signal follows directly from its pulse shape. An ideal NRZ symbol is a rectangular pulse one unit interval wide, and the Fourier transform of a rectangular pulse is a sinc function. A random NRZ data stream therefore exhibits a continuous power spectral density that follows a squared-sinc envelope: energy is greatest near direct current, falls to a first null at a frequency equal to the symbol rate, and continues with diminishing side lobes at higher frequencies.

Nyquist Frequency and Practical Bandwidth

For engineering purposes the most important feature is the Nyquist frequency, which for NRZ equals half the bit rate. The fundamental of the fastest possible pattern, an alternating sequence of ones and zeros, falls exactly at this Nyquist frequency. A 10 gigabit-per-second NRZ link has a Nyquist frequency of 5 gigahertz; a 32 gigabit-per-second link has a Nyquist frequency of 16 gigahertz. As a practical rule, a channel must pass content up to at least the Nyquist frequency to keep the eye open, and capturing the sharp edges that hold jitter low requires usable bandwidth somewhat beyond it, often cited as roughly the third harmonic of the Nyquist rate. A complementary rule of thumb places the knee frequency, above which channel response has little further effect on fidelity, at approximately 0.5 divided by the ten-to-ninety-percent rise time.

Channel loss climbs steeply with frequency, so the Nyquist frequency is the single number that governs whether a binary link is feasible. Doubling the bit rate of an NRZ link doubles the Nyquist frequency and typically far more than doubles the insertion loss the equalizer must undo, because dielectric loss rises roughly in proportion to frequency and conductor loss with its square root, while skin effect, surface roughness, and via resonances add further penalties.

Spectral Consequences for System Design

Several spectral characteristics shape NRZ system design:

• Significant low-frequency and direct-current content: Long runs of identical bits place energy near zero frequency. Channels that cannot pass direct current, such as those with alternating-current coupling capacitors, distort these low-frequency components and cause baseline wander.
• No discrete clock line: A random NRZ spectrum is continuous and contains no spectral spike at the symbol rate. The timing must be recovered from the data transitions rather than extracted as a tone, which makes transition density important.
• Spectral nulls at integer multiples of the symbol rate: The squared-sinc envelope falls to zero at the symbol rate and its harmonics, a property that scrambling and pulse shaping exploit and that filtering must respect.
• Broad, continuous emission: Because the energy is spread rather than concentrated in tones, scrambled NRZ produces a relatively smooth emission profile, which usually eases electromagnetic compliance compared with a repetitive pattern that concentrates energy at a few frequencies.

The comparatively compact spectrum of NRZ, with most of its energy below the Nyquist frequency, is precisely what makes it bandwidth-efficient relative to RZ and Manchester coding and what allows binary links to operate over real copper channels with manageable equalization.

Run Length and DC Balance

Two closely related properties govern the practical behavior of an NRZ stream: run length and direct-current balance. A run is a sequence of consecutive identical bits, and the run length is the number of bits in that sequence. Direct-current balance refers to the degree to which ones and zeros occur with equal frequency over a window of time, keeping the average level near a constant midpoint.

Why Uncontrolled Runs Hurt

• Clock-recovery starvation: Because NRZ embeds no clock tone, the receiver's clock and data recovery circuit relies on transitions to stay locked. A long run of identical bits supplies no edges, allowing the recovered clock to drift and accumulate phase error until the next transition.
• Baseline wander: When a link is alternating-current coupled through series blocking capacitors, a sustained run of one polarity discharges the accumulated charge and lets the waveform droop toward its long-term average. The eye effectively shifts vertically, eroding margin and causing errors on the bits that follow. The severity depends on the ratio of the coupling time constant to the longest run, which is why standards specify both a capacitor range and a bounded run length.
• Worst-case ISI and emissions: Certain repeating patterns concentrate energy in ways that maximize inter-symbol interference or electromagnetic emissions, stressing the channel more than random data would. Compliance testing deliberately uses such patterns, along with pseudorandom sequences, to expose the worst case rather than the typical one.

Scrambling, Block Codes, and Bit Stuffing

Designers control these effects through coding rather than by changing the NRZ format itself:

• Scrambling: A linear-feedback shift register exclusive-ORs the data with a pseudorandom sequence, breaking up long runs and statistically balancing ones and zeros without adding overhead bits. PCI Express and many Ethernet variants scramble their NRZ payloads for this reason. Scrambling is a statistical guarantee rather than an absolute one, so it is normally combined with framing that supplies periodic transitions.
• Block line codes: Codes such as 8b/10b map every eight payload bits to ten transmitted bits chosen to hold the run length to no more than five identical bits and to keep the running disparity bounded, delivering a hard guarantee of balance. The cost is twenty-five percent overhead. Higher-rate links therefore favor lower-overhead schemes: 64b/66b adds a two-bit synchronization header for about three percent overhead, PCI Express generations three through five use 128b/130b at roughly 1.6 percent, and USB adopted 128b/132b for its 10 gigabit-per-second generation and beyond.
• Bit stuffing: Where a block code would be too costly, a stuffing rule inserts a forced transition after a defined number of identical bits. USB uses exactly this approach at its lower speeds, inserting a zero after six consecutive ones so the NRZI stream can never remain static for long.
• Transition-rich framing: Periodic synchronization symbols, comma characters, and training sequences insert guaranteed transitions that refresh clock recovery and let the receiver re-establish symbol alignment even when the payload is momentarily run-heavy.

The guiding principle is that NRZ delivers maximum bandwidth efficiency but provides no inherent guarantee of transitions or balance; the surrounding coding layer supplies those guarantees so that clock recovery and alternating-current coupling remain reliable.

Equalization and the NRZ Link Budget

Beyond a few gigabits per second, no practical copper channel passes the NRZ Nyquist frequency without substantial attenuation, and the unequalized eye at the receiver is often completely closed. Modern binary links do not avoid this condition; they compensate for it. Equalization applies the inverse of the channel response so that the sampled waveform is once again a clean two-level signal.

Transmitter Equalization

The transmitter typically implements a feed-forward equalizer, a short finite-impulse-response filter operating on the outgoing bit stream. Because the total launch amplitude is capped, the filter works by de-emphasis: it attenuates the sustained portion of a long run relative to the first bit after a transition, so the high-frequency content arrives at the receiver in better proportion to the low-frequency content. A tap before the main cursor corrects precursor inter-symbol interference and one or more taps after it correct postcursor interference. Transmitter equalization is cheap and effective but cannot raise the signal above the noise, because it works by reducing low-frequency energy rather than boosting high-frequency energy.

Receiver Equalization

At the receiver, a continuous-time linear equalizer provides an analog high-frequency boost that partially cancels the channel roll-off. Because it is linear, it amplifies crosstalk and noise along with the signal, so its gain must be chosen carefully. A decision-feedback equalizer then removes residual postcursor interference by subtracting the known contribution of previously decided bits from the incoming waveform. Decision feedback is attractive because it cancels interference without amplifying noise, but it can propagate a wrong decision into subsequent bits and its feedback loop must settle within a single unit interval, which becomes the limiting design problem at the highest rates.

These blocks are adapted rather than fixed. During link training, the two ends exchange defined patterns while the receiver measures residual error and requests transmitter tap adjustments, converging on a setting matched to the specific channel. Adaptation continues at a slower rate during normal operation to track temperature and supply drift.

Where the Budget Runs Out

Equalization extends the reach of binary signaling but does not extend it indefinitely. Each decibel of insertion loss removed by equalization costs power, silicon area, and noise amplification, and the requirement grows faster than the data rate. PCI Express illustrates the ceiling clearly. Generation 5 transmits 32 gigatransfers per second per lane using NRZ, placing the Nyquist frequency at 16 gigahertz. Retaining NRZ at generation 6 would have doubled that to 32 gigahertz, where the loss of a realistic server channel was estimated to exceed 60 decibels, far beyond what a practical equalizer can recover. The specification therefore adopted PAM-4 at 32 gigabaud, keeping the Nyquist frequency at 16 gigahertz while doubling throughput. The general lesson holds across standards: NRZ remains the better choice until the Nyquist frequency lands where the channel loss becomes unrecoverable, and only then does a multi-level format pay for itself.

Comparison With PAM-4

The dominant alternative to NRZ in modern high-speed links is PAM-4, a four-level scheme that carries two bits per symbol. Comparing the two clarifies why each occupies its niche. The fundamental relationship is that PAM-4 conveys twice the data per symbol, so for a given bit rate its symbol rate is half that of NRZ, which in turn halves the required channel bandwidth. This bandwidth saving is the entire reason PAM-4 displaced NRZ at the highest data rates.

The cost of that saving appears in noise margin. PAM-4 packs four levels into the same peak-to-peak swing that NRZ uses for two, so the spacing between adjacent PAM-4 levels is only one-third of the full swing. Each of the three PAM-4 eyes is correspondingly smaller, and the reduction in vertical margin amounts to an intrinsic signal-to-noise penalty of about 9.5 decibels relative to NRZ for the same swing and the same target error rate. The contrast can be summarized as follows:

• Bits per symbol: NRZ carries one bit per symbol; PAM-4 carries two.
• Bandwidth for a given bit rate: PAM-4 requires roughly half the bandwidth of NRZ, because its symbol rate is half.
• Eye diagram: NRZ shows one tall eye; PAM-4 shows three small eyes stacked vertically, and the three are generally unequal because driver and channel nonlinearity compress the outer levels.
• Noise margin: NRZ enjoys roughly a 9.5 decibel advantage in signal-to-noise ratio because its single eye spans the whole swing.
• Receiver complexity: NRZ needs one decision threshold; PAM-4 needs three, plus tighter transmitter linearity, more elaborate equalization, and almost always forward error correction.
• Bit error rate: Raw NRZ links routinely meet an error rate of one in a trillion without coding, whereas PAM-4 typically operates at a far higher raw error rate and relies on forward error correction to reach comparable reliability.
• Latency and power: The coding, deeper equalization, and digital signal processing that PAM-4 requires add latency and power that a binary receiver avoids entirely.

PAM-4 is not the only step beyond binary. PAM-3, which uses three levels and encodes eleven payload bits into seven ternary symbols, occupies a middle ground: it gains less bandwidth efficiency than PAM-4 but suffers a smaller margin penalty. Version 2.0 of the USB4 specification adopted PAM-3 at 25.6 gigabaud to reach 40 gigabits per second per lane, the first use of multi-level signaling in the USB family after decades of binary operation.

The choice among these formats is therefore a direct trade of bandwidth against margin and complexity. When the channel can comfortably pass the NRZ Nyquist frequency, binary signaling delivers superior margin and a simpler, lower-latency, lower-power receiver. When the channel cannot pass that frequency without ruinous loss, a multi-level format buys back the needed bandwidth at the price of margin, complexity, and coding latency.

NRZ in Practice: Representative Standards

The reach of binary signaling is easiest to appreciate through the interfaces built on it. The following examples show both how far NRZ has been pushed and where each family eventually reached its limit.

• PCI Express, generations 1 through 5: All five generations use differential NRZ, rising from 2.5 gigatransfers per second per lane to 32 gigatransfers per second. Early generations used 8b/10b; generations 3 through 5 switched to 128b/130b with scrambling to cut the overhead. Generation 6 moved to PAM-4 with forward error correction and flow-control-unit-based framing.
• Serial ATA: The storage interface runs at 1.5, 3, and 6 gigabits per second using NRZ with 8b/10b coding. Its modest rates and short cable runs make binary signaling an easy fit, and the interface has never needed a multi-level successor.
• USB: Low, full, and high speed use NRZI with bit stuffing. SuperSpeed and its successors use NRZ at 5, 10, and 20 gigabits per second per lane with 8b/10b or 128b/132b coding. Only USB4 version 2.0 departs from binary signaling, adopting PAM-3.
• Ethernet electrical and optical lanes: Backplane and cable variants standardized NRZ lanes at 10.3125 gigabits per second and later at 25.78125 gigabits per second, the rates that carried 10, 25, 40, and 100 gigabit Ethernet. An early 400 gigabit variant even used sixteen parallel NRZ lanes of 26.5625 gigabits per second over multimode fiber. Once per-lane rates climbed to 50 gigabits per second and beyond, IEEE 802.3 adopted PAM-4 with Reed-Solomon forward error correction as the standard lane format.
• Short-reach optics: Directly modulated and electro-absorption-modulated laser transmitters carry NRZ comfortably at 10 and 25 gigabits per second per wavelength, which is why those rates dominated data-center optics for a decade before PAM-4 took over at 50 gigabits per second per lane.
• Embedded and industrial interfaces: Low-voltage differential signaling links, display interfaces, sensor buses, and countless board-level connections operate at rates where the channel is effectively transparent. In this domain NRZ faces no serious competition, and no multi-level format offers any advantage worth its cost.

Where NRZ Remains Preferred

Despite the rise of PAM-4 in the fastest interfaces, NRZ remains the preferred binary format across a vast range of applications. Its persistence reflects genuine engineering advantages rather than mere legacy inertia.

• Moderate data rates over manageable channels: Wherever the channel can pass the NRZ Nyquist frequency without excessive loss, which in practice covers per-lane rates up to roughly 25 to 32 gigabits per second over short, well-designed copper, NRZ is the obvious choice. Its larger eye and simpler receiver win decisively over multi-level alternatives.
• Latency-sensitive links: Because raw NRZ can meet stringent error rates without forward error correction, it avoids the encode-and-decode latency that PAM-4 systems usually incur. Applications that prize the lowest possible latency favor binary signaling for this reason.
• Power-constrained and cost-constrained designs: NRZ receivers need only a single threshold and far less equalization and digital signal processing than multi-level receivers, which translates directly into lower power and lower silicon cost. Consumer interfaces and embedded systems benefit accordingly.
• Robustness in noisy environments: The superior noise margin of a two-level signal makes NRZ resilient where crosstalk, ground bounce, or supply noise would close the smaller eyes of a multi-level scheme. Binary signaling is also far more tolerant of transmitter nonlinearity, since only the sign of the signal must be correct, not its proportionality.
• Established and interoperable standards: Many widely deployed interfaces, including USB through its binary generations, SATA, PCI Express through generation 5, and numerous Ethernet electrical layers, are defined around NRZ. Its maturity, well-understood compliance methodology, and broad interoperability keep it entrenched.

The recurring theme is that binary signaling is the natural choice whenever bandwidth is not the binding constraint. Multi-level signaling is adopted only when the channel forces the issue; until that point, the simplicity, margin, low latency, and low power of NRZ make it the default. Both NRZ and PAM-4 are members of the same pulse-amplitude-modulation family, and the engineering decision between them rests on whether the channel has enough bandwidth to let the simpler, more robust binary format do the job.

Summary and Key Takeaways

NRZ is the canonical binary baseband line code and the foundation against which advanced modulation schemes are measured. The essential points are these:

• Definition: NRZ holds a constant level for the full bit interval and does not return to zero between identical bits. It is PAM-2, carrying one bit per symbol, so its bit rate and baud rate are equal.
• NRZ versus RZ and Manchester coding: Codes that force a transition within every bit enrich timing content and guarantee balance but roughly double the required bandwidth. NRZ is the more bandwidth-efficient format and dominates electrical links for that reason.
• The eye diagram: Two levels produce a single eye whose height measures voltage margin and whose width measures timing margin, quantified in practice through masks and bathtub curves. The intrinsically tall NRZ eye is the visible source of binary signaling's robustness.
• Spectrum and bandwidth: The NRZ spectrum follows a squared-sinc envelope with its first null at the symbol rate and its key fundamental at the Nyquist frequency, equal to half the bit rate. Significant low-frequency content makes baseline wander a concern on alternating-current-coupled channels.
• Run length and direct-current balance: NRZ guarantees neither transitions nor balance on its own, so scrambling, block codes such as 8b/10b and 128b/130b, and bit stuffing bound run length and keep the average level centered for reliable clock recovery and coupling.
• Equalization: Transmitter de-emphasis, continuous-time linear equalization, and decision feedback extend binary signaling well past the point where the raw channel closes the eye, but the cost grows faster than the data rate and eventually sets a ceiling.
• Comparison with PAM-4: PAM-4 doubles bits per symbol and halves bandwidth but sacrifices roughly 9.5 decibels of margin, adds two more decision thresholds, and usually requires forward error correction. PAM-3 offers an intermediate trade adopted by USB4 version 2.0.
• Where NRZ wins: Binary signaling remains preferred wherever bandwidth is sufficient, latency must be low, power and cost are constrained, or noise immunity is paramount, which together cover most interconnects below the highest data rates.

Understanding NRZ is the prerequisite for understanding everything that builds upon it. The multi-level, partial-response, and coded schemes that extend throughput all start from the two-level baseband signal and add complexity to overcome the bandwidth ceiling that NRZ eventually meets. As long as a channel offers enough bandwidth to keep the single eye open, binary NRZ remains the simplest, most robust, and most widely used signaling format in electronics.

Related Topics

To extend your understanding of binary signaling and its relationship to advanced modulation, explore these related topics: