# Timing Analyses in FWE Evaluation
## 1 Introduction
Dielectrics are made up of molecules and atoms; thus, the effect of an applied electromagnetic field cannot move at macroscopic distances. Evaluation has found that the applied electric field can shift the orientation of the interrelated charges inside the material [24; 25]. The eye diagram is an illustration of overlays of thousands or millions of bits corresponding to the transmitted signal. The arrangement of bits 0 and 1 can influence the integrity of the signal propagation if collective transitions from 0 to 1 or 1 to 0 happen in a tight period. The purpose of eye diagram representation is to describe the propagation over a given channel, for a given rate of the source signal and special parameters: levels of 0/1 s, eye opening or height and width of the eye, eye amplitude, bit rate, transitions, rising and falling edges, and jitter. Those are the major high-speed signal parameters in signal examination that may display channel imperfections [26; 27]. Some of these parameters are illustrated in Figure 1.  
Levels 0/1, also named logical levels, represent the amplitude corresponding to these levels. The eye opening should be equivalent to the amplitude of the propagated signal, but in practice, the noise can also change the amplitude. Rise and fall times matter the most for calculating the middle values of the signal thresholds from 0 to 1 and vice versa. Jitter is the deflection of signal propagation times between the two levels [28; 29; 30]. To have a physical dielectric model, the frequency behavior needs to be known, thus, transmission models with frequency-dependent parameters are necessary [31; 32; 33; 34; 35]. In this paper, the main contribution is the study of the time and frequency domains of two materials, FR4 and N4000-13. The simulations are carried out in two design technologies (microstrip and stripline) for different values of the frequency. Secondly, for a more detailed study, we will evaluate several parameters that help us highlight the better behavior of the N4000-13 material compared to the common FR4 material. The parameters to be studied are the rise and fall times, the transition from high level to low level, and the jitter and amplitude values of the eye mask. The subject of this research is focused on high- and very high-frequency circuit design and analyses, as shown within the references cited by this work. From those references, we may highlight [2] where a well-known tool in the circuit design industry is used, particularly in the field of simulations and analyses of paths for high- and very high-frequency signals. Figure 1: Eye diagram—general representation and main parameters. Simbeor (version 2023.01--beta), a software recognized worldwide in the Printed Circuit Board (PCB) design, was developed for precise simulations of signal behavior in such environments. The purpose of our article is to demonstrate the importance of determining the occurrence of jitter in high-speed circuits and reducing it to increase the system performance. The novelty of this work lies in:  
* Highlighting the fiberglass effect on the system performances using eye diagrams;
* Checking the matching conditions via scattering parameters using Smith charts;
* Designing circuits, simulations, extracting data, and interpreting the results in this software, MWO (Microwave Office, version V22.1) from AWR DE, which is a work-oriented program for high-frequency applications; however, it is not specific for modeling certain materials, and accomplishes this behavior by implementing the equations for the substrates used in the design tool. The main contribution consists of the:  
* Implementation of the circuits in the MWO design tool from AWR-DE;
* Selection of the parameters of the specifications for two substrates, a low-cost, conventional FR4 and a high-speed-oriented substrate, N4000-13, from the data sheets;
* Implementation and analysis of the circuits;
* Extraction of data from these simulations, their analysis, and the interpretation of results. The rest of this paper is organized as follows.