# Timing Analyses in FWE Evaluation
## 1 Introduction  
The necessity of high-speed paths puts distinctive constraints on dielectrics, with a smaller dielectric constant, DK, due to the inverse proportionality between the velocity and the square root of the dielectric constant. One main issue is the costs of the overall system, which will rise due to substrate cost; thus, using the N4000-13 substrate with low loss at higher frequencies, given by the loss tangent of the dielectric, Df, is more costly in comparison to a common substrate like FR4. The cost of the design will also increase because a good estimation of the electromagnetic and signal integrity is needed. All new IoT applications, 5G networks, and high-speed circuits need low latency and low jitter even for high data rates; thus, timing analysis is necessary while minimizing power consumption. High-speed circuits impose constraints on PCB substrates with lower dielectric constants, where lower permittivity allows higher velocity and, thus, maximum data rates. However, this can significantly increase system costs, as both analog and digital applications require PCB material selection based on dielectric properties. Common dielectric materials like FR4 exhibit reduced performance and significant frequency-related issues. This paper is an extension of [1] written as a partial result of the research carried out by the same group of authors, where several primary results were obtained and presented, while in this work, the topic has been expanded by conducting a new series of simulations and measurements and extracting several interesting conclusions based on the larger set of results. Since it proves that the subject is of interest, we consider that its development is valuable. While in [1], we highlighted the presence of FWE only through the study of insertion and reflection parameters; here, we aim to demonstrate the presence of FWE through time domain analyses using eye diagrams. In [2], the authors presented a new delay deviation measure to quantify the delay in single-ended links, and they evaluated the differential skew exceedance to estimate the unpredictability in differential links. Those measured were calculated by varioussimulations and several interesting results were highlighted. It is important to say that the development of the study depends on the trace width and separation. In [3], specimens of varying thicknesses were tested at different stress levels, and various analyses, including acoustic emission, infrared thermography, and micro-CT, were conducted. The study also observed thermoelastic effects, crack diversion, and delamination at elevated stress levels, with thicker specimens showing increased crack growth and susceptibility to manufacturing defects. Numerical and experimental results indicated that specimen thickness influences crack growth patterns. The authors of [4] explored the impact of fiber hybridization on the tensile fracture of 3D woven textile composites. It was the first investigation of its kind in this context. The hybridization led to increased modulus with higher carbon fiber volume fractions but a proportional decrease in strength (78% of the baseline glass). Fiberglass can still maintain 80% of its original strength, a significant improvement over nonhybrid materials with no hybridization. Cases showed a residual strength higher than the initial strength, like the thick unsymmetrical and functionally graded in the warp direction. In general, the warp direction retained a residual strength comparable to the weft. Unsymmetric samples displayed coupled behavior, influenced by thermally induced shrinkage. These findings highlight the tradeoff involved in hybridization methods. In [5], the authors investigated the impact of fabric areal weight on the mechanical properties of carbon-fiber-reinforced polymer composite laminates. Three different twill weaves with areal weights of 380, 630, and 800 g/m\({}^{2}\) were used to create laminates.