## 1 Introduction
In [32], the RBF-ANN model is used to model the small-signal behavior of the microwave transistors. Especially, the intermodulation distortion behavior of MESFETs is modeled using RBF in [32], which the results of this study show to be very accurate and efficient via an RBF-ANN approach. Moreover, it is claimed in [33] that using regular MLP in modeling nonlinear behavior of microwave devices was failed to converge to right solutions, but the RBF network improved the results to the right solution. Additionally, it is shown in [34; 35; 31] that the ANN approach can help to improve the microwave devices functionality and achieve the desired frequency parameters. In addition, there are several works that have designed the RRC by combining of the aforementioned techniques. Some of these research results are explained in the following discussion. In [36], slow-wave broadside-coupled microstrip lines are used to create a compact rat-race coupler with a wide response. Benefiting from the slow-wave line and slow-wave coupled-line structure, an ultra-compact rat-race coupler with a planar structure is realized. This coupler has a 94% size reduction, compared with conventional RRC, but it offers no harmonic suppression. This coupler has a complex structure, which complicates the design process. In [37], the potential of space-filling curves in the miniaturization of hybrid couplers with fractal structures is demonstrated. This structure has been achieved through the replacement of straight transmission lines segments by space-filling curve segments with the same electrical characteristics. The reported RRC has an 87% size reduction compared with conventional RRC, but has no harmonic suppression. A microwave RRC, with a 56% size reduction and high port isolations, is introduced in [36]. Two short-circuited stubs are used in this RRC structure to reduce circuit size, but this structure also has no harmonic suppression. In [38], a compact microwave RRC with harmonic eliminations is designed. In this coupler, stub-loaded transmission lines are used instead of long conventional lines, providing an 85% size reduction compared with conventional RRC. This coupler works at 2.4 GHz and provides harmonic suppression bands up to 24 GHz, suppressing the 2 nd-10 th harmonics. A defected ground structure (DGS) is used to design a small RRC coupler with harmonic suppression in [39]. With this structure, a 54% size reduction is obtained and only the3 rd harmonic is suppressed. However, the applied DGS structure has some drawbacks. The fabrication process for these structures can be complex and expensive, which can increase the overall cost of the device and need extra steps in the fabrication, which is undesirable [40]. In [41], C-SCMRC resonators are used in the RRC, resulting in a 55% size reduction and 2 nd and 3 rd harmonic suppression. The applied C-SCMRC resonators have the same electrical characteristics as conventional microstrip lines at the operating frequency, but suppress them at higher frequencies. The applied resonators in this RRC reduce size but increase insertion loss parameters, which is undesirable. A rat-race coupler with a filtering response is presented in [42]. This is based on coupled-line structures that can suppress the 2 nd harmonic. Applied coupled lines in this RRC provide wideband responses with 35% fractional bandwidth and 2 nd harmonic suppression. The insertion loss of this coupler is high, which is not desirable. Overall, compact rat-race couplers with harmonic suppression capabilities have been extensively researched in recent years. Various approaches have been proposed for this task, including one involving the introduction of frequency-dependent phase shifts and use of novel coupler structures. The development of these compact couplers has significant potential for reducing the size and cost of microwave and radio frequency (RF) systems, while also maintaining a high performance. This paper presents a novel design of a compact RRC with harmonic suppression for microwave circuits.