# A Four-Port Dual-Band Dual-Polarized Antenna for Ku-Band Satellite Communications
## 2 Antenna Design and Working Mechanism
### Working Mechanism  
The proposed antenna is developed based on the design concept presented in [15]. This antenna, however, has a large size and a high frequency ratio of approximately 2. Therefore, this work aims to design a compact shared-aperture DBDP antenna with a smaller frequency ratio in order to meet the requirements for the downlink and uplink bands of the Ku band. The following sections describe the key steps involved in designing the proposed antenna. Figure 3a illustrates the design steps for the LB antenna. Two reference designs, including Ant.1 with no protruding stub and Ant.2 with one protruding stub, are also investigated to compare with the proposed one. The simulated \(|S_{11}|\) and \(|S_{21}|\) are shown in Figure 3b,c, respectively. As observed, the protruding stubs help to improve the impedance matching of the LB antenna significantly (see Figure 3b). Moreover, high isolation between two orthogonal polarizations \(|S_{21}|\) of the LB antenna is retained mostly by implementing three protruding stubs (see Figure 3c). Referring to Figure 3a, the LB antenna exhibits a \(-10\) dB impedance bandwidth (IBW) covering the entirety of the desired frequency band of 10.7-12.75 GHz. The simulated current distributions observed at two resonant frequencies of 10.2 GHz and 13 GHz when the LB antenna is excited by **P1** are illustrated in Figure 3d. At each resonant frequency, two currents appear, one in the clockwise direction and another in the anti-clockwise direction, demonstrating the fundamental \(TM_{11}\) mode operating over the operating bandwidth [18; 19]. The HB antenna is designed according to the procedure shown in Figure 4, and the simulated \(|S_{33}|\) of the HB antenna according to each procedure is shown in Figure 5 (the \(S\)-parameters of the LB antenna are not shown here for brevity). In addition, the simulation showed that the HB antenna design procedure had a minor impact on the LB antenna's performance. As a starting point, a capacitive fed microstrip patch antenna (HB-Ant.1) is selected and designed as shown in Figure 4a. The miniaturization of the patch is achieved by cutting off four small squares from each corner. As shown in Figure 5, HB-Ant.1 exhibits poor impedance matching for the frequency of interest from 13.75 to 14.5 GHz. Thus, it is necessary to improve the impedance matching of HB-Ant.1. To improve the impedance matching, a plus-shaped parasitic patch is introduced and located above the driven patch of HB-Ant.2. As illustrated in Figure 5, the impedance matching of HB-Ant.2 is improved for the frequency range of 14.1-15.2 GHz. In HB-Ant.3, one more plus-shaped parasitic patch is added, significantly improving the reflection coefficients (see Figure 5). At this point, instead of increasing the patch sizes to extend the impedance matching range further  
Figure 3: (**a**) Design evolution of the LB antenna. (**b**) \(|S_{11}|\). (**c**) \(|S_{21}|\). (**d**) Simulated current distributions at 10.2 GHz and 13 GHz. to cover the frequency of 13.75-14.5 GHz, four rectangular slots are cut off from each parasitic patch of HB-Ant.4. The \(|S_{33}|\) of HB-Ant.4 indicates that it operates from 13.6 to 15.7 GHz (see Figure 5). Moreover, the reflection coefficient of the driven patch is significantly enhanced by applying arc-shaped slots in the final step. Through the inclusion of additional slots, the compactness of the HB antenna can be achieved without increasing its physical dimensions. According to Figure 5, the proposed HB antenna shows a \(-\)10 dB IBW, covering the entire desired frequency range of 13.75-14.5 GHz. An overview of the shorting pin's function is also presented in Figure 6. As shown in Figure 6a, the HB antenna's resonance does not change significantly as a result of the shorting pin. With the shorting pin, the HB antenna still exhibits a wideband operating frequency band covering the entire designed frequency range of the Tx band.