## 2 Design and Analysis of Proposed Hybrid DRA
### Composition and Field Analysis of the Proposed HDRA  
The proposed design and composition of the hybrid DRA is illustrated in Figure 2a-d. Initially, a conventional probe-fed DRA is created for a frequency of 4 GHz, based on the fundamental resonance Equation (1) referenced in [32]. This design is chosen to transform the traditional cylindrical DRA into a hybrid model that incorporates a probe-feed mechanism, aiming to achieve resonances at 5 GHz, circularly polarized (CP) radiation, and improved gain. A substrate is then introduced between the ground and the DRA to support the ring patch. An independent resonance study of the conventional DRA, the substrate-integrated DRA, the ring patch, and the proposed DRA is carried out to analyze orthogonal mode generation and the variation of S\({}_{11}\), as depicted in Figure 3. The fundamental resonance of the conventional probe-fed cylindrical DRA is observed at 3.9 GHz, while the resonance for the substrate-integrated DRA is shifted to 4.15 GHz. The ring patch resonates at 4.9 GHz with a lower return loss of \(-3\) dB. The combination of the ring patch and the cylindrical element, both utilizing a common probe feed, resonates at  
Figure 1: Proposed HDRA Configuration with dimensions (Ls = 60, Ws = 45, h = 0.787, Ph = 8.4, DR = 10, Dh = 10.16). All the dimensions are in “mm”. 5 GHz, producing two orthogonal modes that result in CP radiation. This study reveals a lower resonance due to the high dielectric constant of the dielectric resonator element and a higher resonance attributed to the ring patch on a lower dielectric substrate. The impact of ring patch and cylindrical DR elements with common coax feed creates the asymmetry that helps to generate two orthogonal modes with approximate equal magnitudes and a 90\({}^{\circ}\) phase-shift between them, that is, HEM\({}^{x}\)\({}_{811}\) (YZ Plane) and HEM\({}^{y}\)\({}_{181}\) (XZ Plane) desired for CP radiation. With this asymmetric nature of feed arrangement, the DR is excited to operate in the HEM\({}_{118}\) mode (Ref. Equations (1)-(3)) with a fundamental resonant frequency of 4.9 GHz. \[f_{r,\;HE_{116}}=\frac{6.321c}{2\pi d\sqrt{\in_{r,eff}+2}}\left[0.27+0.36\frac {d}{2H_{eff}}+0.02\left(\frac{d}{2H_{eff}}\right)^{2}\right] \tag{1}\]  
Figure 3: \(S_{11}\) Comparisons of all the composition stages to generate CP radiation. Figure 2: Evolution of the proposed antenna (**a**) Conventional DRA (without substrate) (**b**) DRA (with substrate) (**c**) Probe-fed ring patch and (**d**) Proposed hybrid DRA with probe at 0 deg. If a multi-segmented antenna is considered, the resonance frequency will be affected by the layers of the substrate (\(\mathrm{H_{S}}\)) and dielectric (HD) materials. Accordingly, the effective height (\(H_{\mathit{eff}}\)), and permittivity (\(\in_{r\mathit{eff}}\)) [33; 34] of the hybrid CDRA are calculated by Equations (2) and (3). \[H_{\mathit{eff}}=H_{DR}+H_{\mathit{S}ub} \tag{2}\]  
Similarly, the effective relative permittivity \(\in_{r\mathit{eff}}\) in Equation (3) is given by,  
\[\in_{r\mathit{eff}}=\ \frac{H_{\mathit{eff}}}{\frac{H_{DR}}{\varepsilon_{r \mathit{CDRA}}+\frac{H_{\mathit{S}ub}}{\varepsilon_{r\mathit{,}ub}}}} \tag{3}\]  
where \"d\" (D/2) is the radius of the cylindrical DR element. The circular field rotation for the YZ and XZ planes confirms the CP radiation, as illustrated in Figure 4. It is observed that the E-Field is subverted into the DRA in the YZ plane, while in the XZ plane, it emerges from the DRA. This interaction results in two perpendicular modes at different phases, demonstrating CP radiation. To achieve the desired resonance frequency around 5 GHz, optimizing the dimensions of the probe feed length (Ph) and the height (Dh) of the dielectric resonator is crucial, as illustrated in Figures 5 and 6. Specifically, an increase in the height of the coaxial pin causes the resonance frequency band to shift from higher to lower frequencies. Conversely, an increase in the DR height helps fine-tune the resonance to the targeted 5 GHz for WLAN applications.