# Timing Analyses in FWE Evaluation
## 3 Discussion and Future Work  
In this article, we presented the circuits made in the MWO work environment from AWR DE. We simulated circuits with two coupled lines designed in microstrip and stripline technology for two types of materials: FR4 and N4000-13. The results obtained in this article represent the continuation of the study initiated in [1] and provide further insights into how the occurrence of FWE can be prevented and how it affects circuit performance. Further developing the setup established in our previous work, we extended our research and conducted FWE studies in both time and frequency domains for different substrate materials. In the frequency domain, the simulations were based on representing the S parameters based on the Smith diagrams, which helped us assess circuit matching. These simulations were conducted for both microstrip and stripline technologies, using both FR4 and N4000-13 materials. We compared the results from various design technologies and material choices. To emphasize the findings from [1], we further explored the time domain, this time using eye diagrams. While in the previous paper the focus was placed on presenting the reflection coefficients for the common and differential mode and the insertion losses for different lengths of the microstrip line, in this paper, an emphasis was put on the time domain representation in the signal at the output of the line when the input was connected at a pseudo-random signal source. Based on the eye-diagrams obtained, we drew several interesting conclusions regarding the rise time, fall time, and jitter. Simulations were conducted for all the cases mentioned above and results were compared to provide a comprehensive understanding of FWE in circuit design. First, we checked the matching of the circuits with the help of the \(S_{ii}\) distribution parameters that we represented on the Smith chart. We noticed how these parameters were in the middle of the Smith chart, which means that the circuits are matched. To check the performance of the circuits, we performed simulations in the time domain using the eye diagram representation. We simulated the circuits at three different frequency rates (1 GHz, 10 GHz, and 30 GHz) for two line lengths (60 mm and 250 mm). Comparing these results, we noticed that the circuits designed in stripline technology offered better performances, with the simulation results being more favorable. This happened because, in the case of microstrip technology, the transmission occurs through the air, and this leads to the appearance of coupling on the neighboring line. Based on the obtained eye diagrams, we were able to extract data about the rise time and the fall time. It was highlighted that with the increase of the frequency rate (from 1 GHz to 10 GHz), the transition from the upper front to the lower levels was no longer performed through a single point, as it happened at a rate of 1 GHz. Also, we demonstrated how with the increase of the frequency rate, the upper and lower levels exceeded the eye mask. Given the results, we noticed that N4000-13 presents a lower variation of the rise and fall time for microstrip technology, 16.67%, compared to FR4 substrate's 27.50% (values obtained for 10 GHz). We noticed that the jitter values were lower for circuits with N4000-13 material compared to circuits with FR4 material. The simulations showed that for stripline technology, the jitter for N4000-13 presented a lower increase in comparison to microstrip technology (6.65% vs. 11.76%) with the increase of frequency. For microstrip, the jitter was lower compared to stripline technology, but the influence of the frequency increase had a lower impact on the N4000-13 substrate. We performed simulations in the time domain using the eye diagram for rates of 1 GHz and 10 GHz and for lengths of 120 mm and 250 mm. To highlight the influence of the high data rates, the frequency of the data source varied from 1 GHz, for small rates,to 10 GHz, for high rates.