Calculators / 04
Bit Rate, Unit Interval and Nyquist Frequency Calculator
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
- Loss budgets are usually quoted at Nyquist — half the symbol rate — because that is the fastest pattern, 1010…, the channel must pass.
- 0.35/tr is where a single-pole edge is 3 dB down. If it sits well above Nyquist, the edge, not the data rate, decides how much bandwidth matters.
- UIs in flight is how many symbols are on the trace at once: when it passes one, a reflection lands on a later bit.
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
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).