# RMS to Eye-closure Jitter Calculator

RMS to Eye-closure Jitter Calculator | Back to Development Calculators

Assuming only random noise, you've quantified the time-interval error (TIE) jitter in a signal as an RMS value. You want to determine, if a bit-error ratio (BER) bathtub plot were to be measured for this signal, what the plot's eye closure is at a specified BER (that is, BERS).

Note that TIE is the short-term variation of a digital signal's significant instants from their ideal positions in time, where a "significant instant" refers to the time a rising or falling edge crosses a threshold voltage (Vt).

The figure below illustrates one unit interval (UI), which is the duration of one bit in a data signal. The location of each edge in the signal is randomly distributed with a standard deviation of σ. Note that since the distribution's mean is zero, its RMS value equals σ. The eye closure is computed as Nσ, where N is a crest factor determining how much of the distribution's tail needs to be included for the BER to equal BERS. The calculator computes this eye closure after solving the following equation for N, where DTD is the signal's data-transition density. For data signals, DTD is defined as the ratio of transitions (or, edges) to the number of bits. For clock signals, set DTD=1.

Enter numbers below using integers or scientific notation (for example, enter 123 as 123, 1.23e2, or 1.23E2).

## RMS to Eye-closure Calculator

 Specified BER, BERS Data-transition Density, DTD TIE Random Jitter in ps RMS (e.g. σ) Calculate   Reset Crest Factor, N = Eye Closure in ps Peak-peak = Nσ =

The following table is provided for quick reference.

 BERS Crest Factor (N) DTD = 0.5 DTD = 1 1e-1 1.683 2.563 1e-2 4.108 4.653 1e-3 5.756 6.180 1e-4 7.080 7.438 1e-5 8.215 8.530 1e-6 9.223 9.507 1e-7 10.138 10.399 1e-8 10.982 11.224 1e-9 11.768 11.996 1e-10 12.508 12.723 1e-11 13.208 13.412 1e-12 13.874 14.069 1e-13 14.511 14.698 1e-14 15.122 15.301 1e-15 15.710 15.883 1e-16 16.277 16.444 