Page 5 · Energy vs frequency

Spectra

Computed power spectra of NRZ, Manchester, MLT-3 and PAM4, what block codes and scrambling do to them, and why that matters for channel loss, AC coupling and EMI.

Why the spectrum matters

Where a code puts its energy decides three things: how much of the signal the channel loses (loss grows with frequency), whether the signal survives AC coupling (energy near DC is blocked), and how much it radiates (emission limits are set per frequency band). Comparing spectra is the quickest way to see what a code buys.

Computed from 200,000 random bits, each curve normalized to the same total power, plotted against frequency as a fraction of the bit rate. NRZ peaks at DC with nulls at multiples of R_b. Manchester has nothing at DC and peaks near 0.75 R_b. MLT-3 squeezes most energy below 0.25 R_b. PAM4 halves the symbol rate, so its main lobe ends at 0.5 R_b.

Reading the curves

Scheme	Shape	Energy below 0.5 R_b	Consequence
NRZ (random or scrambled)	sinc²(f/R_b): peak at DC, first null at R_b	77%	90% of power lies below the bit rate; energy at DC means AC coupling removes some signal unless the data is balanced
Manchester	zero at DC, broad peak near 0.75 R_b, extends to 2 R_b	16%	Only 1% below 0.2 R_b (NRZ: 38%): ideal for transformers, but needs twice the bandwidth
MLT-3	concentrated low, peak near 0.12 R_b; 80% below 0.25 R_b	90%	Lets 125 MBd fit through a cable rated for ~30 MHz and stay inside emission limits
PAM4 (same bit rate)	sinc² with first null at 0.5 R_b	90%	Half the bandwidth of NRZ for the same data, the whole point of using it

What block codes do to the spectrum

8b/10b looks like NRZ at the 10-bit line rate, except that its bounded running disparity removes energy near DC. The spectrum has a notch below roughly 1/20 of the line rate, which is why 8b/10b links can use small AC-coupling capacitors and transformers.
Scrambled codes (64b/66b, 128b/130b) look like random NRZ: a smooth sinc² with some energy at low frequency. AC-coupling capacitors are made large (100–200 nF) so the high-pass corner sits far below where that energy matters.
Unscrambled repetitive data puts power into discrete spectral lines at the repetition frequency and its harmonics. One line holding all the energy breaks an emissions limit that a spread-out spectrum would pass, which is the EMI case for scrambling.
Spread-spectrum clocking attacks the same problem from the clock side: modulating the line rate by up to 0.5% smears every spectral line across a band, lowering peak emissions by several dB.

The general formula

S(f) = (1/T) · |P(f)|² · S_a(f)For linear modulation, the spectrum is the pulse shape's spectrum |P(f)|² times the spectrum of the symbol sequence S_a(f). A rectangular pulse of width T gives sinc²(fT). Random independent symbols give a flat S_a. Codes shape S_a: Manchester and 8b/10b carve a notch at DC; MLT-3 correlates symbols so energy collects at low frequency; a longer T (PAM4) narrows sinc² itself.

Thirty-second version

NRZ is a sinc² with most of its energy below the bit rate and some at DC. Manchester moves it all away from DC at the cost of double bandwidth. MLT-3 squeezes 125 MBd into ~30 MHz. PAM4 halves the bandwidth for the same bit rate. 8b/10b adds a notch at DC; scrambling makes the spectrum smooth and line-free, which helps EMI.