# Meander Structure Analysis Techniques Using Artificial Neural Networks
## 1 Introduction  
Microwave devices have experienced a remarkable increase in demand, especially over the past decade, driven by rapid advances in wireless communications. This rise is driven by the increasing need for compact microwave devices that provide high performance and seamless integration into modern systems. Traditionally, microwave devices' design methodology is based on designers' experience and creativity, often involving iterative cycles of electromagnetic simulations and experimental testing until the desired specifications are met [1, 2, 3]. However, as circuit complexity increases and the need for faster development cycles based on innovative intelligent methods increases, intelligent methods are tasked with address complex circuit design and reducing computational resources and processing times, among other challenges [4, 5, 6]. In this context, the evolution of microwave devices represents not only technological progress but also a paradigm shift toward intelligent adaptive design methods, which are promising for revolutionizing the field. Artificial neural networks (ANNs) have been extensively used in the field of microwave devices in the past decade due to their ability to autonomously learn complex patterns and relationships from data [7, 8, 9]. ANNs excel at capturing nonlinearities and handling high-dimensional data, which are often encountered in real-world problems [10]. Theapplication of neural networks is widely distributed for the analysis and parametric synthesis of microwave devices [11; 12; 13] and also for optimization techniques in computer-based modeling of nonlinear microwave devices [14; 15]. ANNs are widely used for modeling antennas [16], antenna arrays [17], filters [18], phase shifters [19], delay lines [20], and other devices [21; 22]. ANNs are also used in microwave-based systems to automate the local tasks of nonlinear functions, which may speed up and simplify the design process [23; 24]. Multilayer perceptron (MLP) networks with backpropagation are commonly employed for the analysis and synthesis of microwave devices in order to map between the related geometric dimensions of microwave devices and their electrodynamical parameters [25; 26]. For example, the optimal geometrical parameters of custom-designed resonators were determined with a feedforward MLP network in order to reduce undesirable coupling in an antenna [27]. A similar MLP network was used to obtain the desired operating frequency, bandwidth, and insertion loss parameters for interdigital filters and a compact dual-band diplexer in [28]. Advanced types and structures such as deep neural networks (DNNs), recurrent neural networks (RNNs), convolution neural networks (CNNs), and Transfer Learning are used in order to approach the modeling problems of microwave devices in which electrodynamical characteristics change dynamically [29; 30; 31; 32]. The parameters of the matching circuit for the matching of antenna impedance were determined using a DNN [33]. The \(S_{11}\) parameter was used in the input of the DNN, while the DNN predicted the values of the series and parallel capacitors of the impedance matching circuit in the output. A nonlinear microwave device modeling technique, which is based on the time delay neural network (TDNN), was used to analyze the DC, small-signal, and large-signal data from different models of transistors in [34]. According to the authors, the TDNN approach has advantages in accuracy over the static modeling technique of MLP networks when the number of delay buffers increases. The most recent and scientifically uncertain direction of research is to study the possible mapping of the geometric dimensions and electrodynamic parameters of microwave devices by learning the image content [35]. For example, a feature mapping between images and the values of nonlinear phase shifts in optical fiber communication systems with polarization division multiplexing is presented in [36]. The initial signals were converted into future maps which were fed into the CNN input.