# C Band 360\({}^{\circ}\) Triangular Phase Shift Detector for Precise Vertical Landing RF System
## 2 \(\pm\)90\({}^{\circ}\) Versus \(\pm\)180\({}^{\circ}\) Landing System
### Extending Phase Shift to \(\pm\)180\({}^{\circ}\)  
A 360\({}^{\circ}\) (\(\pm\)180\({}^{\circ}\)) phase detector allows one to increase the tracking area. Figure 4b shows the tracking area in the conditions set in Section 2.2 when the unambiguous range is \(\pm\)180\({}^{\circ}\). The maximum distance reaches 1338 cm, and the minimum distance increases to 332.8 cm. This means a relative increase of 3.5:1 and 11.8:1 with respect to the minimum and maximum distance for an unambiguous range of \(\pm\)90\({}^{\circ}\). A larger phase range translates into a larger tracking distance. If the frequency increases in the same proportion as the increase in the phase range, the tracking distance remains but allows using smaller antennas and, therefore, reducing the distance between receiving points (\(D\)). For example, Figure 5  
Figure 3: (**a**) Multiplier as analog phase detector and multiplier output voltage. (**b**) Non-ambiguous symmetric range when the phase shift between branches is 90\({}^{\circ}\) (\(\beta\) = 0\({}^{\circ}\)) and 90–30\({}^{\circ}\) (\(\beta\) = 30\({}^{\circ}\)).  
Figure 2: (**a**) Tracking volume (inverted cone) when the phase detector has an unambiguous detection range of \(\pm\)90\({}^{\circ}\), \(D\) = 7 cm at 2.5 GHz. (**b**) Top view.  
shows the increase in tracking volume when \(D\) = 4 cm, the frequency is 5 GHz, and the phase range is +180\({}^{\circ}\). Compared with Figure 2, the maximum distance at a height of 10 m increases from 569 m to 1730 m (3.0:1 distance ratio) and the minimum distance from 474 m to 1134 m (2.4:1 distance ratio). The increase in tracking distance is due to the reduction in distance \(D\) from 7 cm in Figure 2 to 4 cm in Figure 5.  
In this paper, we have decided to use a 360\({}^{\circ}\) phase detector with double multiplication, in phase and phase-shifted (IQ-\(\beta\) phase detector), because it can be easily extrapolated to other frequency ranges and technologies [41], as well as being quite immune to inter-branch unbalance. Its operation is similar to the IQ phase detectors (Figure 6a with \(\beta\) = 0\({}^{\circ}\)), but it does not have to fulfill the quadrature condition strictly (Figure 6a with \(\beta\) < 90\({}^{\circ}\)), which provides more flexibility in the design. Figure 6b shows the output signals of the IQ-\(\beta\) phase detector that allow the phase shift to be obtained. In both cases, the output voltages of the multiplier when the input signals are in phase and quadrature (shifted) are needed to obtain the phase shift, which implies calibration and storage of the output curves for each input amplitude and frequency. In addition to all this, the IQ-\(\beta\) phase detector obtains the phase difference from a somewhat more complex calculation procedure [42,43]. In simplified terms, the solution phase shift will be the one with the smallest difference between those obtained through the voltage \(V_{dI}\) in curve C.1 and \(V_{dQ}\) in curve C.2 (\(-\)100\({}^{\circ}\) in Figure 6b). The solution would be calculated from the voltage closest to zero volts (lower phase error versus amplitude noise) and its associated curve (circled \(V_{dI}\) in blue color).  
Figure 4: Comparison of coverage areas for \(z_{D}\) = 200 cm, \(f\) = 2.5 GHz, and \(D\) = 7 cm when the unambiguous area is (a) \(\pm\)60\({}^{\circ}\), \(\pm\)90\({}^{\circ}\) and (b) \(\pm\)180\({}^{\circ}\).  
Figure 5: (a) Tracking inverted cone for \(D\) = 4 cm at 5 GHz and unambiguous phase range of \(\pm\)180\({}^{\circ}\). (b) Top view.