Calculators / 03
BER, Q-Factor and Total Jitter Calculator
Random jitter has no hard edge — its Gaussian tail reaches every distance with some probability. A target BER picks the distance: how many standard deviations out the tail has thinned to that probability. That multiplier, Q, is why a 1 ps RMS jitter costs about 14 ps of eye at 10−12.
Reading the numbers
- Total jitter is DJ plus 2·Q times RJ: the deterministic part once, and the random tail on both sides of the eye.
- Transition density. Random data changes state on about half its bits, so only half the bits can fail at an edge: ρ = 0.5, the convention the bathtub panels use. The multiplier tables quote Q for ρ = 1; at 10−12 that is 2Q = 14.07.
- A closed eye here means the extrapolated jitter alone exceeds the UI — before any amplitude noise.
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. RJ is Gaussian and DJ is well described by its dual-Dirac value DJ(δδ), which is a model-fitted quantity and is smaller than the peak-to-peak DJ a scope reports. Extrapolating a Gaussian to 10−15 assumes nothing else lives out there.
How it is checked. Q(0) = ½; Q is antisymmetric about 0; the two numerical branches of the tail agree where they meet at x = 3; the inverse round-trips; and at 10−12 the multiplier matches the published 14.069.
Source. INCITS TR-35-2004, Fibre Channel — Methodologies for Jitter and Signal Quality Specification (MJSQ).