tml.scirp.org/file/1-6801322x7.png" class="100" /> (2)
Based on Equation (2), when making the maximum radiation direction face in the z-axis direction, the element spacing should be set to be equivalent to one wavelength of the radiated electromagnetic wave. Therefore, the element spacing dp was made to vary within the range 11.00 - 13.50 mm which corresponds to 0.9 λg - 1.1 λg, and the electromagnetic field simulation software was used to calculate the changes in the maximum radiation direction. As a result of optimizing the size of the patch in the design of one element  , we obtained W = 6.90 mm and L = 3.90 mm. In Figure 3, an offset of the maximum radiation direction from the z-axis to the positive y-axis direction is defined to be positive. When the element spacing dp was 11.00 mm, the offset angle became 0˚. The radiation characteristics for this situation at 20 GHz are shown in Figure 4, and the frequency characteristics of the reflection loss are shown in Figure 5. Figure 4 shows the radiation characteristics for the yz face, for which the effects of the array are significant. The maximum value of the directional gain was 13.70 dBi. In Figure 5, it can be seen that there are several points for which the resonance frequency deviates from the design value of 20 GHz. Verifying the electric field distributions at these resonance points, we determined that the resonance point due to phase resonance based on the design value was at 20.45 GHz. Therefore, we performed optimization on the patch width W and the patch length L so that this resonance point would become 20 GHz. First, to adjust the resonance frequency to 20 GHz, we performed an analysis while varying the patch length L in the range 3.90 - 4.20 mm at intervals of 0.05 mm. The change in the resonance frequency is shown in Figure 6. The resonance frequency becomes fr = 19.98 GHz when L = 4.05 mm. Therefore, we set L = 4.05 mm, and performed an analysis while varying the patch width W in the range 3.50 - 6.50 mm at intervals of 0.50 mm in order to improve the return loss. The change in the reflection loss is shown in Figure 7. The dotted, dash-dotted, and solid lines show the cases in which W = 6.50 mm, 5.00 mm, and 4.00 mm, respectively. These results show that as the patch width W becomes smaller, the return loss improves and the resonance frequency increases. This is because the effective wavelength changes along with W because of the change in the effective permittivity directly below the patch. Furthermore, given that the maximum radiation direction changed at the same time due to the change in the patch width W, we attempted tore-op- timize the element spacing dp, patch width W, and patch length L, and obtained a resonance frequency of 20.05 GHz and return loss of −29.59 dB at the resonance frequency when dp= 11.50 mm, W = 3.90 mm, and L = 4.15 mm. The return loss for this situation is shown in Figure 8, and the frequency characteristics at 20 GHz are shown in Figure 9. Based on the results in Figure 8, it can be
Figure 3. Variation of radiation direction by space between elements.
Figure 4. Radiation characteristics of the linear array antenna for dp = 11.00 mm.
Figure 5. Return loss S11 of the linear array antenna for dp = 11.00 mm.
Figure 6. Variation of resonance frequency by patch length.
Figure 7. Variation of return loss for patch width W.
Figure 8. Return loss of the optimal design.
Figure 9. Radiation characteristics of the optimal design.
seen that resonance points exist at frequencies other than 20 GHz. The results in Figure 9 show that the maximum value of the directional gain is 13.6 dBi, and the maximum radiation direction is the z-axis direction. The radiation characteristics at the other resonance point, 18.51 GHz, are shown in Figure 10. The maximum radiation direction has changed. Since the radiation direction changes significantly depending on the frequency, it is necessary to suppress undesired resonance points in order to prevent receiving undesired signals. In the next section, we describe a method that uses impedance-matching circuits as a method to suppress undesired resonance points.
Figure 10. Radiation characteristics for undesirable resonance frequency.
3. Structure of Stub-Loaded Linear Array Antenna
3.1. Investigation of Impedance-Matching Circuit (Stub)
The 4-element linear antenna considered in the previous section had multiple resonance points. It was demonstrated that the maximum radiation direction changes for resonance points other than 20 GHz. In this section, we discuss the results of our investigation on placing an impedance-matching circuit on the CPW as a method for solving this problem. Previous studies have reported the creation of filters using short stubs for CPWs  . According to reference  , the impedance Zl of the load side separated from the transmission line of line length l can be represented by Equation (3).
To match impedances, the reactance of the parallel stub is represented as jX, and the designer should connect a circuit with jX needed to cancel the imaginary part of Zl shown in Equation (3). Here, the parameters of the stub that can be adjusted include the line length l and stub reactance jX. Considering the impedance of the stub side as viewed from the feed line, the short stub represents the case where Zl = 0 in Equation (3), so it can be expressed as shown in Equation (4).
In the 4-element linear array antenna considered here, it is necessary to adjust the impedance-matching circuit to suppress the resonances at frequencies other than the design frequency of 20 GHz. In other words, setting the line length l to λg/2 so that Zl in Equation (4) becomes zero changes the impedance at wavelengths other than λg, making it is possible to suppress the undesired resonance points at frequencies other than 20 GHz.
3.2. Design of the Stub Circuit
The stub circuit used to load the feed line on the back face of the linear array antenna under consideration is shown in Figure 11. A short stub with a shortened tip is used. The stub length is defined as Ls, and the distance from the feed point to the stub is defined as dc. The central conductor width and slit width of the stub are a = 1.80 mm and b = 0.10 mm, similar to the feed line. The adjustable parameters of the stub include the stub length and the stub arrangement positions. In this investigation, we set the stub length Ls to λg/2 = 6.10 mm, and analyzed the changes in the antenna characteristics with respect to changes in dc using the electromagnetic field simulation software. The return loss S11 at 20 GHz is shown in Figure 12. The largest return loss of −25.22 dB was obtained when dc = 37.50 mm. Next, we analyzed the changes in the characteristics with respect to changes in the stub length Ls. The changes in return loss at 20 GHz are shown in Figure 13. Because we obtained S11 = −46.5 dB when the stub length was Ls = 5.95 mm, we determined that this is the optimal value. Furthermore, the frequency characteristics of the return loss for this situation are shown in Figure 14, and the radiation characteristics are shown in Figure 15. The solid line shows the return loss frequency characteristics for the case with the stub, and the dotted line shows the characteristics for the case without the stub. Figure 14 shows that the undesired resonances are suppressed well, and that the return loss at the design frequency has been improved. On the other hand, as shown in Figure 15, the gain in the maximum radiation direction decreased.
Figure 11. Structure of the stub circuit.
Figure 12. Variation of return loss by distance between the stub and feeding point dc.
Figure 13. Variation of return loss by stub length LS.
Figure 14. Return loss of the linear array antenna with stub.
Figure 15. Radiation characteristics of linear array antenna with stub.
While the gain was 13.6 dBi without the stub, the gain was 11.2 dBi with the stub. This is believed to be caused by the stub radiating waves from the face with the feed line at the back of the antenna. In addition, the side lobes increased.
3.3. Design of Stub Circuit with Slits
In the previous section, we demonstrated that loading with the stub circuit was effective for suppressing undesired resonances, but the gain between the patch face and the opposite face with the feed line increased due to radiation from the stub. Therefore, we attached a stub circuit with a slit as shown in Figure 16. We propose a method for reducing the backward radiation by strengthening the coupling between the stubs. This is done by generating aperture coupling between the stubs by creating slits within the stubs. Since the value of λg in the stub circuits may change due to the slits, we performed optimization of the stub length Ls. Figure 17 shows the changes in the return loss with respect to the stub length Ls. When Ls = 5.70 mm, S11 = −42.53 dB, and fr = 19.99 GHz. This was chosen as the optimal value. The return loss for this situation is shown in Figure 18, and the radiation characteristics are shown in Figure 19. For return loss, the
Figure 16. Structure of stub circuit with slits.
Figure 17. Variation of return loss by stub length LS.
Figure 18. Return loss of the linear array antenna with slit stub.
Figure 19. Characteristics of te linear array antenna with slit stub.
undesired resonances were suppressed after loading with the stub as well, and no large changes were seen. For radiation characteristics, on the other hand, a gain improvement of 0.5 dBi was seen.
We investigated the design of a linear array patch antenna composed of 4-ele- ment linear array antennas using four 20 GHz band MSAs with a structure such that the signal is fed to the patch antennas from open-end CPWs without contact. To adjust the maximum radiation direction and reduce the return loss, we optimized the element spacing and the element shape, and obtained a return loss of −29.59 dB at the resonance frequency of 20.05 GHz. However, undesired resonance frequencies gave rise to frequency bands other than the design frequency of 20 GHz when a 4-element linear array antenna structure was used. To suppress these undesired resonances, we proposed a new structure in which the feed line is loaded with a short stub as a method to obtain stable performance at the design frequency. We demonstrated that this method can sufficiently suppress the undesired resonances. Furthermore, we revealed that introducing the short stub causes a new problem in which the radiation gain is reduced. To solve this problem, we proposed a design method for a new structure in which the circuit has slits between the stubs, which improved the antenna gain by 0.5 dBi.
In the future, we plan to investigate methods for further improving the maximum radiation gain of a linear array of patch antennas that is designed using the design method proposed in this paper.
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