###### Abstract
Typically, artificial neural networks (ANNs) are used as a powerful and effective tool for small-signal behavioral modeling due to their outstanding learning and generalization abilities [46; 47; 48; 49; 50; 51; 52]. Another valuable behavioral approach consists of using the standard recurrent neural networks (RNNs) and their advanced variants, such as long-short term memories (LSTM) and gated recurrent units (GRU), which are an extension of the traditional ANNs that became more popular in the recent years due to their superior performance [53; 54; 55]. Compared to LSTM, the GRU model has a simpler structure and uses fewer training parameters, thereby resulting in a faster computation time and improved memory usage. Undoubtedly, there are pros and cons to each modeling approach. Therefore, there is no universally best modeling approach but a variety of situations where one or the other approach is better suited, depending on the given constraints and requirements. With the aim to highlight the advantages and disadvantages of each modeling approach, the present article is focused on developing a comparative analysis. The device under test (DUT) considered in this study is a multi-finger on-wafer GaN HEMT transistor grown on a SiC substrate with a gate length of 0.25 \(\upmu\)m and a gate width of 1.5 mm (i.e., 10 \(\times\) 150 \(\upmu\)m). The multi-finger layout, also known as interdigitated, is typically used in the realization of transistors for high-power applications. This is because the multi-finger structure, which consists of the parallel connection of multiple gate fingers, allows for enlarging the size of the total gate periphery and, thus, the output current. At the same time, the multi-finger structure allows making the extrinsic gate resistance smaller and better the microwave noise performance and the maximum frequency of oscillation (\(f_{\text{max}}\)). Due to the lack of a native GaN substrate, GaN HEMT transistors are commonly realized using various foreign substrates, such as sapphire, silicon (Si), and silicon carbide (SiC). Compared to sapphire and Si, SiC is more expensive, but its excellent thermal conductivity makes it the material of choice for enhancing the power handling capability of GaN HEMTs. An efficient heat spreading is a mandatory requirement, especially when considering a large device operating at high power and high temperature, as in the present study. The \(S\)-parameters of the DUT were measured with a frequency range spanning from 200 MHz to 65 GHz and at four values of the ambient temperatures (\(T_{a}\)), namely 35 \({}^{\circ}\)C, 90 \({}^{\circ}\)C, 145 \({}^{\circ}\)C, and 200 \({}^{\circ}\)C. The importance of investigating the impact of the temperature on the behavior of the GaN HEMTs lies in the fact that the device performance can considerably vary with the selected working thermal condition [56; 57; 58; 59; 60]. The bias point was fixed at \(V_{DS}\) = 30 V and \(V_{GS}\) = -3.1 V, corresponding to a dissipated power of 5.1 W when \(T_{a}\) is set to 35 \({}^{\circ}\)C. To model the measured \(S\)-parameters, three different strategies are considered here: the equivalent-circuit approach, ANNs, and GRUs. The models are compared in terms of accuracy, generalizability, complexity, compactness, and usefulness. The equivalent circuit is a physically meaningful representation, enabling the achievement of deeper insightsinto the device physics, and is suitable to be used as a starting point for building both large-signal and noise models, which play a crucial role in a successful design of high power amplifiers (HPAs) and low noise amplifiers (LNAs). ANNs have good learning ability and generalization capabilities, allowing for achieving accurate predictions even for data different from those used in training. The approach based on GRUs allows for accurately fitting the small-signal behavior of the DUT, thus achieving a faithful reproduction of the experiments.