# Quad-Band Uniformly Spaced Array Antenna Using Diverse Patch and Fractal Antennas
## 3 Results  
Graphs of the reflection coefficients of the proposed element antennas are shown in Figure 6. The bow tie fractal (iteration 3), fat bow tie fractal (iteration 2), fat bow tie, and bow tie patch antenna have center frequencies of 2.47 GHz, 3.71 GHz, 4.4 GHz, and 5.08 GHz, respectively. The shift of the center frequencies due to integrating with the feed network is considered in the early stage of the element design. The reflection coefficientsat the center frequencies are \(-10.6\) dB, \(-11.4\) dB, \(-18.6\) dB, and \(-18.5\) dB for the bow tie fractal, fat bow tie, and square patch antenna, respectively. The radiation pattern of each element antenna is shown in Figure 7. It is shown that most radiation occurs on the boresight \(z\)-axis, peak gain being simulated as 5.4 dBi, 7.2 dBi, 6.6 dBi, and 8.18 dBi for the bow tie fractal, fat bow tie fractal, fat bow tie, and square patch antenna, respectively. The peak gain of the bow tie fractal decreases as its iteration number increases, which inherently reduces aperture area compared to the typical bow tie antenna. The arrangement of the array antenna takes the form of interleaving different types of element antennas. The distances between elements depend on the operating frequencies of each array antenna. In order to evaluate the effect of the array disposition, mutual coupling between two elements [27] is investigated. Figure 8a,b describes the scenarios  
Figure 6: Reflection coefficients of different element antennas: bow tie fractal patch antenna, fat bow tie fractal antenna, fat bow tie antenna, and square patch antenna. Figure 7: Radiation patterns of the element antennas. Upper left: bow tie fractal patch; upper right: fat bow tie fractal patch; lower left: bow tie patch; lower right: square patch. of mutual coupling between two identical elements or between two adjacent elements. For the purpose of evaluation, the feed network is removed and each individual element is fed by a separate microstrip line. The mutual coupling level between two antennas is simulated, and the results are shown in Figure 8c. The graphs show maximum values of \(-25\) dB for case 1 at 2.44 GHz, \(-47.8\) dB for case 2 at 2.43 GHz, \(-26.7\) dB for case 3 at 4.35 GHz, \(-23.2\) dB for case 4 at 3.69 GHz, \(-35\) dB for case 5 at 3.7 GHz \(-28.5\) dB for case 6 at 5.05 GHz. Case 1, case 3, case 4, and case 6 are related to mutual coupling between two identical elements. It is shown that all coupling levels are low with the array disposition. Among these, case 1 and case 4 with \(d=0.5\lambda\) at 2.44 GHz and \(d=0.64\lambda\) at 3.7 GHz show slightly higher levels of \(-25\) dB and \(-23.2\) dB, which is caused by the relatively short distance between the two antennas. Case 2 and case 5 each have two different elements, which generates a very low coupling level of below \(-30\) dB. The impedance-matching and radiation pattern of the quad-band array antenna is evaluated. Figure 9 presents a graph of the reflection coefficients for the antenna ports 1/2/3/4 presented in Figure 2b. The reflection coefficients are obtained as \(-10.3\) dB at 2.44 GHz for port 1, \(-14.7\) dB at 4.37 GHz for port 2, \(-12.3\) dB at 3.7 GHz for port 3, and \(-27.5\) dB at 5.05 GHz for port 4, which shows appropriate matching properties. The radiation patterns of the proposed array antenna are provided in Figure 10. The antenna boresight is on the \(z\)-axis. The peak gain is 11.1 dBi at 2.44 GHz for port 1, 13.8 dBi at 4.37 GHz for port 2, 13.5 dBi at 3.7 GHz for port 3, and 14.4 dBi at 5.05 GHz for port 4. The peak gain for port 1 is degraded as a result of the relatively low gain of the element antenna, as mentioned previously. For port 2 and port 4, the sidelobe levels are high compared to the other two ports. This is because the higher frequency increases the electrical length of interspacing, causing an unwanted grating lobe.