## 1 Introduction  
With the exponential growth in smart wireless devices, compact and low-cost microstrip antennas, especially circularly polarized (CP) patch antennas, are increasingly being deployed in a wide range of devices and applications, such as radio frequency identification (RFID), near-field communication (NFC), wireless local area network (WLAN), and global navigation satellite system (GNSS). Antenna polarization indicates the direction of electric field vectors in the time domain at a fixed position in space. There are two types of polarization: linear polarization and circular polarization [1]. Circular polarization consists of two linear components of electric field that are perpendicular to each other and equal in magnitude, but have a 90\({}^{\circ}\) phase difference. For circular polarization, the electric field rotates in a circle around the direction of propagation [1]. Right-hand circular polarization (RHCP) antennas (clockwise rotation) are commonly used in modern wireless devices. The extent of circular polarization is determined by the axial ratio (AR), which is the proportion of the maximum and minimum semi-axes of the orthogonal electric field components. A perfect CP has an AR of 0 dB; however, in reality an AR \(\leq\) 3 dB is technically acceptable. Attempts have been made to realize circular polarization using patch antennas. The dual-fed circularly polarized patch antenna (DCPA) with an external polarizer could achieve near-perfect circular polarization [2]. In DCPA, there are dual feeding points with equal magnitude and a 90\({}^{\circ}\) phase difference. In [3], a DCPA with a hybrid coupler achieved a near-perfect CP with a reflection coefficient or return loss bandwidth (RLBW) of 21.76% (1.31-1.63 GHz) and 7.45% ARBW (1.55-1.67 GHz), while a DCPA with a U-slot radiatingpatch and power divider achieved a 32.08% RLBW (1.091-1.508 GHz) and 21.28% ARBW (1.150-1.424 GHz) [4]. In [5], the Wilkinson network-fed quasi-cross-shaped coupling slot antenna realized a 21.2% RLBW (2.82-3.49 GHz) and 17.43% ARBW (2.88-3.43 GHz), while a DCPA with multiple feeding probes could achieve a 31.6% RLBW (1.2-1.65 GHz) and 20.83% ARBW (1.29-1.59 GHz) [6]. Despite the near-perfect circular polarization, DCPA suffers from fabrication challenges and structural complexity. As a result, single-fed circularly polarized patch antennas (SCPA) are alternatively adopted to realize circular polarization without an external polarizer. Unlike DCPA, the SCPA is straightforward and easy to fabricate by manipulating the feed line, patch shape, ground slot, and/or partial ground plane. In the realization of SCPA, a single-fed patch antenna is manipulated to perturb the LP field to generate a CP field. In [7], LP perturbation was realized by the truncation of the single-fed patch. In [8], slits were cut into the circular patch to perturb LP for CP generation, and the proposed method could achieve a 4.92% RLBW (1.011-1.062 GHz) and 2.40% ARBW (1.028-1.053 GHz). In [9], a corner-truncated patch with an coaxial probe feed was used to generate CP with a 11.2% RLBW (1.92-2.16 GHz) and 5.85% ARBW (1.99-2.11 GHz), while a patch with a fractal boundary could realize a 12.7% RLBW (2.35-2.67 GHz) and a 2.12% ARBW (2.376-2.427 GHz) [10]. These findings reveal that LP perturbation by manipulating the radiating patch can achieve a very narrow ARBW. To improve the ARBW, a circular patch with multiple vias between the radiator and ground plane was proposed and the scheme could achieve a 19.82% RLBW (2.09-2.55 GHz) and 25.2% ARBW (2.1-2.72 GHz) [11]. A coplanar waveguide (CPW) feed with a slot ground could achieve a 72% RLBW (2.26-4.85 GHz) and 66.48% ARBW (2.44-4.87 GHz) [12]. An inverted L-shaped patch with a cross-slot ground plane for the L-band spectrum could achieve a 34% RLBW (1.3-1.83 GHz) and 19.86% ARBW (1.36-1.66 GHz) [13]. An inverted L-shaped structure is commonly used in realizing CP antenna.