RMS to Peak-to-Peak Jitter conversion

To converter between RMS and peak-to-peak random jitter, the bit-error-rate (BER) must be specified.

 

$Jitter_{P-P}=\alpha \times Jitter_{RMS}$

where $\alpha$ is determined by $\frac{1}{2}erfc(\frac{\alpha}{2\sqrt{2}})=BER$

The following table is to depict the scaling factor for different BER.

If some one wants to save a copy of the table to his or her personal computer, please click the link to download: google sheet link.

RMS noise value of comparator

The comparator offset is mean value of output normal distribution. RMS noise value is the one standard deviation of the normal distribution.

For an error rate $10^{-12}$, the input must exceed the input offset by up and down $\alpha/2$ times the RMS noise level. For example, the offset of an comparator is $3mV$. The RMS noise is $1mV$, so the high output logic level the required input voltage is $3mV + 14.069 /2 \times 1mV = 10mV$. For the low output logic level, the input must be below $-4mV$.