# Timing Analyses in FWE Evaluation
## 2 Problem Statement and Issues
### Implementation of Circuits with Two Coupled Lines
Using the FR4 substrate designed in stripline technology and with a pseudo-random signal source at the input port, we represented the overlapping eye diagrams for the output port of the circuits, as shown in Figure 11. The results correspo \begin{table}
\begin{tabular}{c c c} \hline \hline
**Substrate** & **Frequency (GHz)** & **Jitter (ps)** \\ \hline
**FR4** & 1 & 1.633 \\
**N4000-13** & 1 & 1.117 \\
**FR4** & 2.1276 \\
**N4000-13** & 10 & 1.2659 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Jitter values for microstrip lines extracted from simulation results. with substrate FR4 are illustrated in blue, while those corresponding to the circuit with substrate N4000-13 are in pink. The simulations were performed at the same frequency rates and the same transmission line lengths as in the case of microstrip technology for proper comparison. Analyzing the results presented above, we notice that even in the case of stripline technology for large rates and lengths, the signal is degraded. We notice that the performance degrades even for smaller rates and line lengths for the circuit with FR4 substrate compared to the circuit on N4000-13 substrate. Therefore, comparing all the results obtained in Figures 9 and 11, we notice a better behavior at high frequencies and lengths for circuits with substrate N4000-13 compared to circuits with substrate FR4. We chose to increase the length of the line and to study the behavior of the circuits in this case, because its increase leads to the occurrence of the attenuation phenomenon due to the loss tangent of the dielectric. On the other hand,  
Figure 11: (**a**) Rise time, fall time, and corners on the eye diagram for two coupled striplines, FR4 substrate for L = 250 mm and Rate = 1 GHz. (**b**) Rise time, fall time, and corners on the eye diagram for two coupled striplines, FR4 substrate for L = 250 mm and Rate = 10 GHz. (**c**) Rise time, fall time, and corners on the eye diagram for two coupled striplines, FR4 substrate for L = 250 mm and Rate = 10 GHz. increasing the transmission rate of symbols reduces the transmission time of the signals. We demonstrated that as the frequency rate increased from 1 GHz to 30 GHz, the signal transmission time decreased from 2000 ps to approximately 67 ps in both cases. The same simulations were carried out for the rise time, the fall time, and the corners of the eye, and for the stripline technology, as shown in Figure 12. The same lengths and frequency rates were used as in the previous case. Figure 11a,b show the results for the FR4 substrate and Figure 11c,d show the results for the N4000-13 substrate in stripline technology. In all four figures, the rising time is represented with light blue, the falling time is represented with green, and the corners of the eye are represented with orange. We notice that the performance of the circuits has not changed much. At a rate of 1 GHz, we still have a fast transition, which indicates a very low jitter value, and with the increase in the frequency rate, the jitter value also increased. As the rate increases, we see how the transitions on the upper and lower levels exceed the eye mask. Results were obtained for time and amplitude for the transition of rise and fall time for the FR4 and N4000-13 materials for the lines designed in stripline technology for different data rates. The corresponding rise and fall time values can be extracted in a similar manner. For 1 GHz, we obtained 152.98 ps for rise time and 152.9 ps for fall time, respectively, for FR4, and for N4000-13, we gained better values of 140.41 ps and 140.45 ps. For higher data rates (10 GHz), the values decreased as follows: 41.14 ps and 41.99 ps for FR4 and 24.06 ps and 24.03 ps for N4000-13. A few parameters are available for analysis, extracted from jitter measurements. Among these, the most important is the time variation of the voltage. As we have two intervals or two eye crossings for representation, both rise and fall times will include, in pairs, values for each unit interval.