# A Two-Port Dual-Band Dual-Circularly-Polarized Dielectric Resonator Antenna
## 2 Antenna Design and Analysis
### Working Mechanism  
The design goal of this work is to obtain a compact two-port DRA antenna that can generate the dual-band dual-circularly-polarized response. There are two main stages in the design process of the proposed antenna; the first is the realization of the two-port dual-band DRA operating in two close frequency bands, and the second is the realization of circular polarization at each of the operating bands with an opposite sense of circular polarization. The following sections describe in detail the design process of the proposed DBDCP DRA. Figure 2 shows the evolution toward the dual-band DRA design (first step). We start with a square DR, with a diagonal length of \(a_{2}\) and a height of \((d_{1}+d_{2})\), fed by two 50-\(\Omega\) microstrip feedlines through a cross-slot-coupled aperture etched on the ground plane (Design 1). To realize the dual-band operation, the bottom portion of the square DR is replaced by a cross-shaped DR (Design 2). The simulated results of S-parameters of these two DRAs are illustrated in Figure 3. As observed, Design 1 exhibits a poor impedance matching over the frequency of interest when excited by P1. Meanwhile, when excited by P2, Design 1 produces two impedance bandwidths of 4.35-4.65 GHz and 4.85-5.75 GHz with corresponding dips found at 4.0 GHz and 5.5 GHz. Using the dielectric waveguide model (DWM) [22], the resonant frequencies of the main square DR are estimated to be 3.88 GHz TE\({}_{111}\) and 5.45 GHz TE\({}_{113}\). These mode frequencies attained by the DWM closely correspond to those anticipated in simulation. By introducing the cross-shaped DR at the bottom portion, a good impedance matching from 3.35 to 4.25 GHz is achieved in Design 2 when excited by P1 [see Figure 3a]. As a result, Design 2 exhibits dual-band operation. When excited by P1, it operates in the lower frequency band of 3.35-4.25 GHz, and when excited by P2, it operates in the upper frequency band of 5.2-6.2 GHz. Figure 2: Evolution toward to the dual-band DRA design. The second step focuses on achieving circular polarization at each operating band with opposite polarization sense. The evolution of this step is shown in Figure 4, and its simulated results of the \(S\)-parameters and ARs are presented in Figure 5a and b when P1 and P2 excited, respectively. A pair of symmetrical corner truncations with length \(b\) are removed from Design 2 in the first step to build Ant. I. This is a common method for generating two orthogonal degenerate mode pairs of the fundamental TE\({}_{111}\) and higher order TE\({}_{113}\), responsible for realizing the CP waves. Figure 5 shows that Ant. I achieves dual-band operation with poor AR performance within the \(-10\) dB impedance bandwidth (IBW) at the LB when P1 is excited and a narrow 3 dB AR bandwidth at the UB when P2 is excited. To improve CP performance, one diagonal length is extended, as illustrated in Figure 4, forming Ant. II (here \(a_{3}>a_{2}\)). Simulated results (black dashed line) show that Ant. II achieves a clear improvement in the CP performance for both operating bands. In the UB with P2 excited, the 3 dB AR bandwidth is entirely covered by the \(-10\) dB IBW (see Figure 5b). However, in the LB with P1 excited, the overlapped 3 dB AR bandwidth \(/-10\) dB IBW is still narrow. To obtain a better AR performance, two diagonal grooves are etched into the cross-shaped DR and a longitudinal groove is engraved into the hexagonal DR from its top, forming the proposed DRA. Clearly observing from the simulated results (red solid line) in Figure 5a,b, the proposed antenna provides a dual-band operation with a good dual-CP performance for both operating bands. For the LB when P1 is excited, the proposed antenna exhibits a \(-10\) dB IBW of 3.35-4.42 GHz, which entirely covers the 3 dB AR bandwidth of 3.52-4.28 GHz. Meanwhile, for the UB with P2 excited, the proposed antenna yields a \(-10\) dB IBW of 5.0-6.0 GHz covering the entire 3 dB AR bandwidth of 5.1-5.95 GHz. This satisfies the design goal of this work.