# Timing Analyses in FWE Evaluation
## 2 Problem Statement and Issues
### Implementation of Circuits with Two Coupled Lines
These might be different and will be seen as jitter--eye transition variation voltage. Measurements of rise and fall times are set between 20% and 80% and can be modified. The measurement of the transition contains individual values for different means as follows: left and right mean, left and right sigma (standard deviation), and left and right lower and upper peaks. In Figure 11d, the curves in light green and blue contain the above-mentioned measurement points, but another type of representation of these transitions is in a tabular form. On each line in the table, we have the values for the two standard deviations, two means, and return on the first instance. This explains the coincidence of the first and last line in each section, for each substrate, and for each frequency. Results were obtained of the simulations for the corners of the eye for the same materials and frequency rates as above, for stripline technology. The results were presented for each substrate and for the two frequencies, the values of crossing points for time (ps) and associated voltage (V) were obtained. For better understanding, we can explain the corners values on Figure 11a, the orange measurement trace (hexagonal shape). We have  
Figure 12: N4000-13 two-line uncoupled circuit and substrate designed in microstrip technology and pseudo-random signal source. six plus one (as return) crossing points as follows: starting from the left crossing point, two level one edges, right crossing point, and two level zero edges, and return on the left crossing point. The values are given by the mean, but another representation could have been the standard deviation, for example. For 1 GHz, the results for the eye diagram conclude to the same observation for corners tabular representation, meaning that both substrates present similar behavior, having values for the corners with the same mean seen in Figure 11, with similar eye opening. Increasing the rate, we can observe a degradation on the eye opening in Figure 11, also highlighted by the values of the corners with a higher range of minimum and maximum values means for N4000-13 compared to those of FR4. The results for transitions and eye corners in the case of stripline interconnections are illustrated in Appendix B. Table 2 shows the peak-to-peak jitter at the same frequencies for FR4 and N4000-14 materials for stripline technology for 1 GHz and 10 GHz. Again, the results demonstrate the better stability, with an increase of frequency for N4000-13 compared to the traditional FR4 substrate, as jitter increased for both substrates with the frequency but, for FR4, the increase was 65.53% and only 6.65% for N4000-13. We notice that in this case we also have a lower jitter value for the circuit with the N4000-13 substrate. This means that regardless of the design technology, microstrip or stripline, FR4 substrate circuits achieve a higher jitter value that will degrade circuit performances. Minimizing jitter in a system brings several benefits. Firstly, it enhances the overall reliability of signal transmission by reducing timing uncertainties, ensuring that data arrives at their destination consistently and predictably. This is particularly crucial in applications where precise timing is essential, such as telecommunications and data networking. Secondly, a low jitter value contributes to improved signal integrity, reducing the likelihood of timing errors and distortion. This is especially important in high-speed digital communication systems, where even small variations in signal timing can lead to data corruption. On the other hand, minimizing jitter is a key to achieving stable and accurate synchronization between different components within a system. In scenarios like audio and video streaming or real-time data processing, maintaining a low jitter level helps prevent synchronization issues and ensures a smooth and seamless user experience.