# Compact Four-Port Circularly Polarized MIMO X-Band DRA
## 2 Single-Element Analysis  
Figure 1 illustrates the 2D and 3D layout of the CPDRA. The antenna contained a DR of deformed shape, so that the CP field could be obtained as shown in Figure 1. The simplest deformed shape of the DR that is generally used in obtaining the CP response is the stair-shaped geometry [20; 22; 24]; so, this was also utilized here to fulfil the aim of this research work, i.e., implementing a compact CP MIMO antenna. The DR was composed of material with a permittivity of 10.2, and added above the substrate of the thickness of 0.762 mm. The dimensions of the DR could be selected using the dielectric waveguide model (DWM) by considering the rectangular geometry, and can then be deformed for obtaining the desired polarization and response [23; 25]. The sim  
by considering the fabrication tolerances, as the prototype was fabricated with multiple layers of dielectric material. The power was coupled to the DR using a rectangular slot with dimensions of 5.8 \(\times\) 0.6 mm in aperture. A 50 \(\Omega\) microstrip line of 0.6 mm width was used as the transmission line. The microstrip line was terminated with a \(\lambda\)/4 triangular transformer stub for obtaining an appropriate impedance matching. The proposed DR and the ground had a curvature with a radius \(R_{d}=1.5\) mm and \(R_{g}=2.5\) mm. The reason for chamfering the ground plane and reducing its dimensions was for preserving the isolation between ports, and keeping the desired phase differences between the orthogonal modes to generate the CP field. These values were optimized to achieve the desired frequency response.  
This antenna was fabricated, and the results obtained from the simulation using CST microwave studio were validated by the measurement as illustrated in Figure 2. The antenna displayed an impedance bandwidth of 38% (8.5-12.5 GHz), along with the 3 dB AR passband extended from 9.1 to 10.1 GHz offering 10.4% AR bandwidth. The axial ratio bandwidth was not dependent upon impedance matching and was related to the orthogonal modes [10; 12; 13]. The DWM model does not consider the effect of the type of feed; hence, the effect of variation in the dimensions of the coupling slot is reported in Figure 3, so that one can infer the conclusions for obtaining the desired response by maintaining the phase difference between the generated orthogonal modes. Figure 4a,b show the E-field distribution at the top of the DR in a \(z=h\) plane at frequencies of 9.64 and 11.88 GHz, respectively. The field distribution in the antenna corresponded to modes TE\({}_{11\delta}^{y}\) and TE\({}_{11\delta}^{z}\) at frequencies of 9.64 and 11.88 GHz, respectively. This confirmed the generation of two orthogonal degenerate modes, which is required for obtaining the CP field. These modes provide circular polarization at a frequency of 9.77 GHz. The field was drawn at a frequency of 9.77 GHz at different time instants, as shown in Figure 5. The field vectors rotated in the counterclockwise direction, confirming the generation of the dominant right-hand CP field, which was later confirmed during the study of the radiation pattern.  
Figure 1: Single-element DRA layout: (**a**) 2D front view; (**b**) 2D back view; (**c**) 3D view; (**d**) fabricated prototype with single DR element.  
Figure 3: Effect of parameters \(L_{\rm s}\) on (**a**) S\({}_{11}\) and (**b**) AR and the effect of \(w_{\rm s}\) on (**c**) S\({}_{11}\) and (**d**) AR, for single-element DRA.  
Figure 2: (**a**) Simulated and measured S-parameter response; (**b**) AR for single-element DRA.