# Bent and Branched Microstrip-Line Antennas for Circular Polarization
## 3 Branched Line Antenna
### Modified Antenna  
Figure 1d shows an antenna configuration. The antenna is created using the branched line antenna in Section 3.1: We add \(N-1\) loops and segments on feedline \(F\)-\(T\)'s other side (the +\(y\) side). Each additional segment is connected to the line center of length \(d\) (=1\(\lambda_{0}\)). For CP beam formation in the +z-axis direction, each additional loop \(\#n^{\prime}\) is rotated by 180\({}^{\circ}\) concerning the original loop \(\#n\) to compensate for an excitation phase difference of 180\({}^{\circ}\) (= \(d/2\)\(\times\) 360\({}^{\circ}/\lambda_{0}\)). The other configuration parameters are the same as those of the original antenna with \(N=4\), resulting in 7 (=\(N+N-1\)) loops and segments. First, the antenna is analyzed for a direct feed using vertical wire \(F\)-\(F^{\prime}\) shown in Figure 1e. After confirming CP beam formation, we replace the direct feed with an electromagnetic-coupling one shown in Figure 7 to obtain impedance matching. The feed parameters are selected so that they do not deteriorate the radiation characteristics for the direct feed and are determined to be (\(\ell_{1}\), \(\ell_{2}\), \(\ell_{3}\), \(\ell_{4}\)) = (0.08\(\lambda_{0}\), 0.02\(\lambda_{0}\), 0.18\(\lambda_{0}\), 0.08\(\lambda_{0}\)). The simulated radiation pattern is shown with solid and dotted lines in Figure 8. It is observed that the antenna radiates a CP beam in the +\(z\)-axis direction. The HPBW is 12\({}^{\circ}\), and the gain is evaluated to be 16.6 dBi. It is emphasized that the gain is increased by 2.0 dB compared with that of the original antenna. Figure 6: Simulated radiation pattern in \(\phi\) = 0\({}^{\circ}\) plane for a branched line antenna with \(N=4\). Figure 7: Electromagnetic-coupling feed for impedance matching. Solid lines in Figure 9 show the simulated frequency responses of the gain, axial ratio, and VSWR. It is found that a CP wave bandwidth for a 3 dB axial-ratio criterion is 2.5%, where the gain is almost constant with a VSWR of less than 2. For reference, the gain and axial ratio of the original antenna are also shown with dotted lines. The CP wave bandwidth is almost the same as that of the modified antenna. It can be said that the modified antenna has a gain enhancement of 2.0 dB without deterioration in the CP wave bandwidth of the original antenna. The increased gain is explained using the radiation mechanism of a line antenna with loops [2; 5]. Let us focus on a periodical bend of \(\#n\) shown in Figure 1b. Radiation from the  
Figure 8: Radiation pattern in \(\phi=0^{\circ}\) plane for a modified branched line antenna with \(N=4\). Figure 9: Frequency responses of branched line antennas with \(N=4\): (**a**) axial ratio and gain; (**b**) VSWR for 50 \(\Omega\). periodical bend is decomposed into partial radiation from the loop part and partial radiation from parts other than the loop. It is known that partial radiation from the loop part becomes dominant in the broadside (z-axis) direction for a loop perimeter of \(1\lambda_{0}\). This radiation mechanism holds for other periodical branches of \(\#n\) shown in Figure 1c,d. Note that partial radiation from the loop part is CP due to a traveling-wave current along the loop. Keeping the abovementioned radiation mechanism in mind, we consider the gains of modified and original branched line antennas. Remember that each antenna is designed for a broadside beam, where the phase of partial radiation from each loop part is the same. This means that the gain depends on the number of loops. The modified antenna has more loops than the original one, resulting in a larger gain. In summary, the increased gain of the modified antenna is due to more loops than the original one. A final consideration is given to validating the simulated results. For this, we fabricate a modified antenna at \(f_{0}=3\) GHz using a ground plane of \(9\lambda_{0}\times 3\lambda_{0}\). The prototype's photographs are shown in Figure 10. Small circles and dots in Figures 8 and 9 show the experimental results.