# Timing Analyses in FWE Evaluation
## 2 Problem Statement and Issues
### Implementation of Circuits with Two Coupled Lines
(**d**) Eye diagram for two coupled lines, stripline technology for L = 250 mm and Rate = 10 GHz. (**e**) Eye diagram for two coupled lines, stripline technology for L = 60 mm and Rate = 30 GHz. (**f**) Eye diagram for two coupled lines, stripline technology for L = 250 mm and Rate = 30 GHz. Based on the simulation results concerning the corners of the eye, we observed that the transition takes place through the corners of the eye, which again suggests a minimum jitter value. For a rate of 10 GHz, we can see that the mask is exceeded both for the upper level and for the lower level. Values were obtained for the transition on rise time and fall time for both materials at the two rates at which the simulations were performed (1 GHz and 10 GHz) for microstrip lines. The corresponding rise and fall time values can be extracted similarly. For 1 Hz, we obtained 143.67 s for rise time and 143.71 s for fall time, respectively, for FR4, and for N4000-13, we gained better values of 136.26 s and 136.21 ps. For higher data rates (10 GHz), the values decreased as follows: 29.45 ps and 29.46 ps for FR4 and 20.13 ps and 20.08 ps for N4000-13. Values were obtained for time and amplitude for the eye mask. The simulations were carried out for FR4 and N4000-13 materials at a rate of 1 GHz and 10 GHz for microstrip 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 10a, the orange measurement trace (hexagonal shape). We have 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 10, with similar eye opening. Increasing the rate, we can observe a degradation on the eye opening in Figure 10, 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 are illustrated in Appendix A. Another measurement in the time domain is the jitter metric that is computed on the eye diagram. Jitter refers to the deviation or variability in the timing of signals in a communication system. It is a phenomenon characterized by small, rapid, and unpredictable variations in the timing of signal edges. Jitter can occur in various electronic and communication systems, affecting the accuracy and stability of signal transmission. In digital communications, jitter can lead to timing errors, signal distortion, and decreased system performance. Thus, managing and minimizing jitter is crucial in ensuring reliable and efficient data transfer, especially in high-speed communication systems. Jitter can be determined by the peak-to-peak value or by the root mean square value. Table 1 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. It was determined from the maximum between the values on the horizontal axis (time in ps) of the two crossing points of the eye diagram, with each one considered as the difference from the upper and lower peak values. The results demonstrate a slightly 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 23.25% and 11.76% for N4000-13.