**3.1.1 Random Jitter (RJ)**

210 Modern Metrology Concerns

is minimum, for a simulation time of 1 s. In each mentioned points the condition expressed

*<sup>X</sup> n* <sup>0</sup> *n n T nT X X* 0 0 ,s *Xm f* , Hz 957087 1628027 <sup>13</sup> 1.00 10 5878815.277633602 1000000 1701023 <sup>17</sup> 2.78 10 5878815.277629991 1042913 1774019 <sup>13</sup> 1.00 10 5878815.277626677

<sup>0</sup> 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 <sup>1</sup> -1

1 2 3 4 5

Masurement Time (s)

In order to evaluated the jitter effect on the non-electrically detectable stop event for frequency measurement method based on the direct comparison of two regular independent trains of narrow pulses and rational approximations. Deterministic and random components of jitter are modeled and, are added in both pulse trains one deterministic jitter component and random jitter in each case. Simulation results are presented when both pulse

Table 1. Simulation results of frequency measurement process.

Fig. 3. Frequency offset from the simulation process for 1 s.

trains start in phase and when start with a phase shift.

**3.1 Jitter effect in frequency measurement** 

This condition is repeated with time, and we can see five points where absolute value of

in (30) is fulfilled.


0

0.5

, Frequency offset

1

1.5 x 10-11

Random Jitter RJ is caused the common influence of a large number of very small independent contributor or various device-originated noise sources (such as thermal and flicker noise). By the central limit theorem, the distribution of a large number of uncorrelated noise sources approaches a probability Gaussian distribution and is given by [14]

$$J\_{Rf}\left(\mathbf{x}\right) = \frac{1}{\sigma\sqrt{2\pi}}e^{-\left(\frac{\mathbf{x}^2}{2\sigma^2}\right)}\tag{31}$$

where *σ* is the standard deviation of the jitter distribution or the RMS value, and *JRJ* is the probability that leading edge (or trailing edge) will occur at time *x*, where *x* is the deviation from the mean value of the time reference point (time point related to 50% amplitude point on pulse edge). In Fig. 4a), is shows the histogram for random jitter.
