# Timing Analyses in FWE Evaluation
## 2 Problem Statement and Issues
### The Fiberglass Fabrics Effect  
Based on previous coupled line models, we created circuits with two separate lines to analyze the impact of glass fiber fabrics. These circuits feature composite substrates and will be simulated using N4000-13 material for lengths of 120 mm and 250 mm at 1 GHz and 10 GHz rates, with the results analyzed using eye diagrams, as illustrated in Figure 13. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Substrate** & **Frequency (GHz)** & **Jitter (ps)** \\ \hline FR4 & & 2.2284 \\
**N4000-13** & 1 & 1.8578 \\
**FR4** & & 6.4644 \\
**N4000-13** & 10 & 1.9901 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Jitter values for stripline lines extracted from simulation results. Figure 14 shows the results obtained by overlapping the eye diagrams of the signal at the circuit input and the results obtained after passing through the transmission line. Analyzing the images, we notice that, as the rate of the transmitted signal increases, the eye diagram closes. Therefore, at rates of 10 GHz and interconnection lengths of 250 mm, the eye diagram is completely degraded. The input signal is represented in blue and the signal at the end of the line is represented in pink. For low rates, such as 1 GHz, the eye diagram maintains both its amplitude and jitter level, and at high interconnection values. Next, we implemented the two uncoupled lines circuit stripline technology, but with pseudo-random signal source, and the eye diagrams associated with the circuit are shown in Figure 12. It can be observed, again, that as the transmitted signal rate increases, the eye diagram closes, so at 10 GHz and an interconnection length of 250 mm, the eye diagram is completely degraded, represented in pink in Figure 14 in all four cases at the far end of the evaluated interconnection. For lower rates, such as 1 GHz, the eye diagram maintains both its amplitude and jitter level for longer interconnections lines. Figure 13: (**a**) Eye diagram for two non-coupled microstrip lines for L = 120 mm and Rate = 1 GHz. (**b**) Eye diagram for two non-coupled microstrip lines for L = 250 mm and Rate = 1 GHz. (**c**) Eye diagram for two non-coupled microstrip lines for L = 120 mm and Rate = 10 GHz. (**d**) Eye diagram for two non-coupled microstrip lines for L = 250 mm and Rate = 10 GHz. A comparison can be made on the same system of the shape of the eye diagram obtained at the far end of the interconnection by overlapping the graphs maintaining the rate and length of the interconnection for circuits with homogeneous and composite substrate, respectively. First, the result obtained for the use of microstrip technology is illustrated. We notice that the circuit with homogeneous substrate, represented by red in Figure 15, behaves better than the circuit made with inhomogeneous substrate, represented by pink. In the case of the second circuit, the eye closes faster, and the presence of distortions is observed. The following is an illustration of the overlap of eye diagrams for stripline technology. Figure 14: (a) Eye diagram for two non-coupled stripline lines for L = 120 mm and Rate = 1 GHz. (b) Eye diagram for two non-coupled stripline lines for L = 250 mm and Rate = 1 GHz. (c) Eye diagram for two non-coupled stripline lines for L = 120 mm and Rate = 10 GHz. (d) Eye diagram for two non-coupled stripline lines for L = 250 mm and Rate = 10 GHz. Figure 15 shows that in the case of the composite substrate, represented in red, the eye diagram shows a higher jitter value compared to the circuit that has a homogeneous substrate, represented in pink. Time domain analysis and frequency domain analysis are two distinct approaches in the study of signals and systems. Time domain analysis is a method that examines the behavior of signals over time, focusing on how the signal varies over time and the temporal relationships between different signal events. The primary advantages of this analysis include detecting specific events within a time interval and evaluating the system's response over time.