# Meander Structure Analysis Techniques Using Artificial Neural Networks
## 2 Materials and Methods
### Investigated Meander Structure  
The applied research on the possible usage of ANNs for the prediction of the parameters of microwave devices was conducted using a meander structure (MS) (Figure 1) from our previous article [44]. The introduced meander structure was designed for signal synchronization by delaying signals. Meander structures are used to create longer electrical paths within a confined space, effectively increasing the signal's travel time without significantly enlarging the physical size of the circuit. These structures are commonly found in microwave circuits, delay lines, phase shifters, and antennas. The main electrodynamical parameters for the analysis of the meander structures were \(S_{11}\) (reflection coefficient), \(S_{21}\) (transmission coefficient), \(\Delta f\) (operating frequency range), \(t_{\text{d}}\) (delay time), and \(Z_{\text{c}}\) (characteristic impedance) [45; 46]. The meander structure (Figure 1) was designed for a delay system, and therefore the most relevant \(S_{11}\), \(S_{21}\) and \(t_{\text{d}}\) characteristics will be predicted. The \(\Delta f\) could be seen from the \(S_{21}\) characteristic, and the  
Figure 1: A 3D view of the MS with \(L=14.8\) mm, \(2a=10\) mm, \(c=6\) mm, \(L_{\text{c}}=0.4\) mm, \(l=0.4\) mm, \(l_{\text{s}}=0.221\) mm, and \(h_{\text{c}}=0.035\) mm, where 1 is the meander shape conductor and 2 is the dielectric substrate. \(Z_{\rm c}\) characteristic's impedance matching in the line can be seen from the \(S_{11}\) characteristic. Therefore, the list of \(S_{11}\), \(S_{21}\), and \(t_{\rm d}\) was sufficient to analyze the meander structure. The electrodynamical parameters of the presented MS depended on its geometric dimensions and the materials used in it. The width of the meander strip \(L_{\rm c}\), the number of central meander strips \(N\), the gap between adjacent meander strips \(l\), the length of the central meander strip \(2a\), and the length \(c\) of the meander conductors near the connectors have a direct influence on the electrodynamical parameters of the meander structure. The characteristic impedance \(Z_{\rm c}\) is mainly dependent on the ratio of the width \(L_{\rm c}\) of the meander strip and the height of the substrate. The operating frequency range \(\Delta f\) and thus \(S_{11}\) and \(S_{21}\) are mainly dependent on the width \(l\) of the gap between the meander strips. The provided meander structure has limitations. The gap between adjacent meander conductors was selected to allow the MS to work in the 0-10 GHz frequency range. The number of meander strips was selected in the range from 10 to 20 to have approximately 1 ns for its delay time. The exact dimensions of the initial model of the meander structure (Figure 1) from which the data gathering was started were the following: the total length of the meander structure \(L=14.8\) mm; the width of the central part of the meander structure \(2a=10\) mm; the length of the additional conductors near the connectors \(c=6\) mm; the width of the meander conductors \(L_{\rm c}=0.4\) mm; the gap between adjacent conductors \(l=0.4\) mm; the thickness of the substrate \(h_{\rm s}=0.221\) mm; and the thickness of the conductors \(h_{\rm c}=0.035\) mm. An FR4 material was used for the substrate, where \(\epsilon_{\rm r}=4.3\) and \(tan\delta=0.02\). Copper was used for the conductor, whose inductance was equal to 5.8107 S/m. The general dimensions of the meander structure were \(16.24\times 17.35\times 0.291\) mm. Data for the investigation were collected using the full-wave Sonnet(r)commercial software package (Sonnet 13.52, Sonnet Software, Syracuse, NY, USA). Sonnet(r) is based on the method of moments (MoM). The MoM belongs to a family of techniques which use a differential form of Maxwell's equations. The calculations when using the MoM are time-consuming. Calculating the particular model (Figure 1) takes approximately two hours. It is important to search for new methods that will allow real-time analysis of MSs.