Line Codes — NRZ / RZ / Manchester / AMI / MLT-3

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Type a binary stream (or hex, or random). Pick a code. See the same bits encoded as voltage levels over time. Compare all six codes side-by-side for the same bit stream to understand the trade-off: DC balance, clock recovery (transitions per bit), and bandwidth (theoretical first-null). Long-form history "why NRZ → RZ → Manchester" lives in the deep-dive blog.

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Bit stream

Source:

Binary:

N bits (random):

Bit stream:

Code

Line code:

Manchester conv.:

Voltage + time

V_dd (V):

Bit period T_b:

Samples / bit:

⚠ Why so many codes? NRZ is the simplest but has DC drift and long runs of 1s (or 0s) give no clock-recovery transitions. RZ adds transitions for every 1 but is still DC-unbalanced. Manchester gives a transition every bit AND is DC-balanced, but at 2× the bandwidth. AMI and MLT-3 trade off complexity for narrower spectra. See the deep-dive blog for the full history.

① Time-domain voltage waveform v(t)

The y-axis is voltage (in V, scaled to ±V_dd). The x-axis is time in bit periods. Vertical grid lines mark bit boundaries; horizontal grid lines mark the voltage levels of the selected code (e.g., NRZ uses ±V_dd, AMI uses 0 and ±V_dd, MLT-3 cycles through 4 levels).

Same bit stream, six different voltage-level encodings. Watch the trade-off: NRZ is the simplest, RZ has a transition for every 1, Manchester has a transition every bit and is DC-balanced, AMI is DC-balanced at half the BW of Manchester, MLT-3 has the narrowest spectrum but the most levels.

Code

Selected code

—

Voltage levels

—

Rates

Bit period T_b

—

Bit rate R_b = 1/T_b

—

Baud (= R_b for binary codes)

—

Signal quality

DC component (mean v)

—

DC-balanced?

—

Transitions / bit (clock recovery)

—

1st-null BW (= x · R_b)

—

DC-balanced = mean voltage ≈ 0 (good for AC-coupled channels, no baseline wander). Transitions/bit ≈ 1 means the receiver can recover the clock from a long stream (no long runs of constant level).

Why these codes? (the trade-offs)

① NRZ-L: 2 levels, ±V_dd. Simple, but DC-unbalanced and no clock-recovery on long runs of 1s or 0s.
② NRZ-I: 2 levels. DC-balanced only if equal number of 1s and 0s. Differential encoding = no polarity ambiguity at the receiver.
③ RZ: 2 levels, but the "1" pulse returns to 0 mid-bit. Self-clocking for every 1, but still DC-unbalanced.
④ Manchester: always one transition per bit → self-clocking. DC-balanced by construction. Cost: 2× the bandwidth of NRZ.
⑤ AMI: 3 levels, "1"s alternate polarity → DC-balanced. Bandwidth half of Manchester. Used in T1 / E1.
⑥ MLT-3: 3 levels, but 4-state cycle. Lowest spectral content of the set. Used in 100BASE-TX Ethernet.

📖 Deep-dive blog (planned)

The history of why we go NRZ → RZ → Manchester → AMI → MLT-3 is a sequence of trade-offs. Each step solves a problem the previous one couldn't. The blog will walk through this evolution with the full derivation, eye diagrams, and how each code interacts with the channel (transformer coupling, baseline wander, jitter).

The DC-balance problem — why AC-coupled channels and transformer isolation make a non-zero mean voltage a problem; how baseline wander destroys SNR over long packets.
The clock-recovery problem — why long runs of 1s (or 0s) make it impossible for the receiver PLL to lock; the bit-error floor that results from bad clock recovery even at infinite SNR.
The bandwidth problem — why NRZ at bit rate R_b has first-null at R_b, but RZ at 2R_b; the engineering trade-off between spectral efficiency and timing margin.
Manchester vs. Differential Manchester — the two variants and where each is used (10BASE-T vs. token ring).
AMI in T1 / E1 — why the telecom backbone uses AMI, and how B8ZS / HDB3 extend it to handle long zero runs.
MLT-3 in 100BASE-TX — how a 3-level code achieves a 4× spectral reduction and why that matters for running gigabit Ethernet over Category-5 twisted pair.
PAM-4 / PAM-8 (the next step) — multi-level pulse-amplitude modulation; how Ethernet went from 2-level NRZ (100M) to 4-level PAM-3/4 (1G / 10G) to keep up with bandwidth-limited channels.

Posts are planned. Tool ships first; deep-dives follow.