SIPI

Calculators / 04

Bit Rate, Unit Interval and Nyquist Frequency Calculator

Data rate → UI, Nyquist, bandwidth exact
Spectrum of random data, and what the edge leaves of it

Most channel numbers start here. The unit interval sets the time budget, the Nyquist frequency sets where loss is quoted, and the rise time sets how far above Nyquist the spectrum really reaches. PAM4 sends two bits per symbol, so at the same data rate it has twice the UI and half the Nyquist frequency of NRZ.

Reading the numbers

Every value is in the address bar as you change it, so a link reproduces the calculation exactly. Type values with SI prefixes — 100n, 2.2p, 16G — or drag the sliders; a bare number keeps the prefix already shown.

The formulas

UI = bits per symbol / data rate,    fNyquist = 1 / (2 · UI) NRZ carries one bit per symbol, PAM4 two.
f3dB = 0.35 / tr A single pole rises 10–90% in 2.2τ, so f₃dB = 2.2 / (2π·tr): the 0.35 is 2.2/2π.
Go deeper — assumptions, how it is checked, and sources

Assumptions. Random, equiprobable symbols, whose spectrum has a sinc² envelope with nulls at multiples of the symbol rate. The edge is modelled as one pole; a Gaussian edge gives 0.34, and real edges sit between the two. Trace delay uses the effective Dk you enter.

How it is checked. UI times symbol rate is exactly 1; PAM4 at the same bit rate has twice the UI and half the Nyquist of NRZ; the data spectrum is 1 at DC and zero at the symbol rate; and the edge filter is 3 dB down exactly at 0.35/tr.

Source. H. Johnson and M. Graham, High-Speed Digital Design, Prentice Hall, 1993, ch. 1 (rise time and bandwidth).

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