# Meander Structure Analysis Techniques Using Artificial Neural Networks
## 2 Materials and Methods
### Dataset  
In total, 369 different combinations of the presented MS (Figure 1) were collected with different sets of \(L_{\rm c}\), \(N\), \(l\), \(2a\), and \(c\) geometric dimensions. The gap \(l\) between the adjacent conductors varied between 0.2 mm and 1.8 mm with a step of 0.05 mm (33 different combinations). The width \(L_{\rm c}\) of the meander conductors varied from 0.2 mm to 1 mm with a step of 0.05 mm, except for samples where \(L_{\rm c}\) was equal to 0.25, 0.35, 0.45, 0.75, 0.85, and 0.95 mm (11 different combinations). Six additional samples were collected when \(l~{}=~{}0.2\) mm and \(L_{\rm c}\) equaled 0.25, 0.35, 0.45, 0.75, 0.85, and 0.95 mm. Therefore, the overall number of samples was equal to \(11~{}\times~{}33~{}+~{}6~{}=~{}369\). All other \(N\), \(2a\), and \(c\) parameters were kept constant but were added to the network training in order to maintain the same structure of the dataset for future plans. Such a decision was made due to the long data collection procedure and the fact that variations in several parameters were sufficient to research our specified scientific uncertainties for the potential usage of ANNs to predict an MS's characteristics. The \(S_{11}\) and \(S_{21}\) characteristics were obtained during a computer-based simulation in Sonnet(r). The \(t_{\rm d}\) values were found during the additional calculations. A 120 min simulation was required on average in order to obtain the EM characteristics of a single MS. A cumulative simulation duration exceeding 738 h was required in order to collect this dataset of 369 unique MSs. The input matrix for each individual MS consisted of \(L_{\rm c}\), \(N\), \(l\), \(2a\), and \(c\) geometric dimensions and a frequency \(f\). The simulations in Sonnet(r) were carried out in the 0.1-10 GHz frequency range with a frequency step of 25 MHz (397 frequency samples overall). Therefore, the size of the prepared input matrix for each individual MS with a unique combination of parameters was equal to \([6\times 397]\). The target matrix of one particular model of the meander structure was equal to \([3\times 397]\). The target matrix consisted of the \(S_{21}\), \(S_{11}\), and \(t_{\text{d}}\) parameters. The overall size (146,493) of the input and target matrices was obtained by multiplying the 369 unique MSs by the number of samples of each unique MS (397). The overall dimensions of the collected input and target matrices were equal to \(6\times 146\),493 and \(3\times 146\),493, respectively. The collected dataset was divided into training, validation, and testing data in the following approximate percentages, depending on the neural network used: 70%, 10%, and 20%. In addition, the top view of every particular unique meander structure was saved for CNN training. In general, 369 top view images of unique MSs were collected. The original \(2298\times 1318\), 24 bit depth top view image of every unique MS was converted to a \(1024\times 1024\), 8 bit depth image to increase contrast and facilitate the CNN learning process. Examples of black and white top view images of the meander structures with a different set of \(L_{\text{c}}\) and \(l\) geometric dimensions are presented in (Figure 2). In all, 70% of the data from the collected dataset were used for training, 10% were used for validation, and 20% were used for testing. The next three subchapters will present the artificial methods used for analysis of the presented meander structure. It should also be emphasized that the collected dataset imposed limitations of the research. These limitations were independent of the chosen neural network structures. The prediction of frequency characteristics would only be possible to carry out in the 0-10 GHz frequency range, while \(l\) varied in the 0.2-1.8 mm range and \(L_{\text{c}}\) varied in the 0.2-1 mm range, and all other parameters were constant (\(2a=10\) mm, \(c=6\) mm and \(N=14\)). The parameters of the cross-sectional structures and the parameters of the used materials were not included in the training dataset.