## 3 Measured Results Discussion  
In order to verify the accuracy of the simulated results of Ant. 3, the proposed tri-band patch antenna as shown in Figure 8 is fabricated, and the test items related to reflection coefficient, antenna gain, radiation efficiency, and radiation pattern are also carried out.  
Regarding the reflection coefficient of the proposed tri-band patch antenna, the comparison curve between the simulated result and the measured result is depicted in Figure 9. The measured S\({}_{11}\) shows that the fabricated antenna operates in three frequency bands of \(f_{1}\): 1.79-1.81 GHz, \(f_{2}\): 3.74-4.0 GHz, and \(f_{3}\): 4.93-5.44 GHz. Compared with the simulated results, both\(f_{1}\) and \(f_{3}\) show signs of moving towards a lower frequency, which is mainly due to errors introduced during the assembly and testing.  
The reasons for the existence of more than three reflection nulls in Ant. 3 can be summarized as follows. Part of the reflection nulls of Ant. 3 is caused by the off-center feeding technology. The benefit of the off-center feeding technology is that Ant. 3 can work in a slot-like mode, which is similar to the principle that etches a slot with a specific shape on the radiating patch to achieve the notch effect. On the other hand, by loading the parasitic patch on the circular radiating patch of the antenna in the corresponding frequency band, the current on the circular patch and the current on the parasitic patch cancel each other out, and a notch response is also introduced.  
Figure 8: Photography of the fabricated patch antenna: (**a**) top view of Substrate 1; (**b**) top view of Substrate 2; (**c**) top view of the assembled antenna; (**d**) test process of the fabricated antenna.  
Figure 7: (**a**) E-field distribution of the Ant. 3 at 5.38 GHz. (**b**) Sketch of the operation mechanism at TM\({}_{03}\) mode.  
Meanwhile, Figure 10 shows the measured results of antenna gain and radiation efficiency. As shown in Figure 10a, the measured maximum gains of the antenna in \(f_{1},f_{2}\), and \(f_{3}\) are, respectively, 6.35 dBi, 6.15 dBi, and 9.42 dBi, which are lower than the simulated gains of 7.20 dBi, 6.74 dBi, and 10.62 dBi. In terms of radiation efficiency, Figure 10 presents the compared results of measurement and simulation. The results show that the measured efficiencies in the three frequency bands are 89.2%, 86.9%, and 85.6%, respectively, and are lower than the simulated results of 98.0%, 93.6%, and 94.7%. The measured antenna gain and radiation efficiency both show partial attenuation, which is mainly due to the loss introduced by the 0.5 mm foam layer and the error in the welding and assembly process.  
Figure 10: Simulated and measured gains and radiation efficiencies of the designed antenna: (**a**) gain; (**b**) radiation efficiency.  
Figure 9: Comparison of simulated results and measured results of the S\({}_{11}\).  
In order to visually reveal the pattern diversity of the designed antenna, Figure 11 shows the measured results of the radiation pattern at 1.80 GHz, 3.80 GHz, and 5.35 GHz. As shown in Figure 11a, the patterns which show broadside directional radiation on the _xoz_ and _yoz_ planes are obtained at 1.80 GHz, while an omnidirectional radiation pattern is achieved on the _xoy_ plane at 3.80 GHz. Figure 11c shows the antenna pattern at 5.80 GHz with the characteristics of three adjacent beams on the _xoz_ plane, which is caused by the introduction of higher-order modes. Based on the above analysis, the proposed Ant. 3 can be utilized for multi-service applications in wireless communication due to the characteristics of multi-mode operation, pattern diversity, and expanded bandwidth.  
Figure 11: Simulated and measured radiation patterns of the designed antenna in xoy, xoz, and yoz planes: (**a**) 1.80 GHz; (**b**) 3.80 GHz; (**c**) 5.35 GHz.