# C Band 360\({}^{\circ}\) Triangular Phase Shift Detector for Precise Vertical Landing RF System
## 3 Circuit Design
### Theoretical Design
The VTGT and VTADJ voltages are obtained from resistive voltage dividers and the reference voltage VREF (2.3 V). The estimated VTGT value recommended by the manufacturer is about 0.8 V over the entire frequency band, which represents a compromise between output voltage noise and maximizing dynamic range. The value is set by the 2.2 k\(\Omega\) and 1.2 k\(\Omega\) resistors. The VTADJ value improves temperature compensation and is frequency dependent. The estimated VTADJ value recommended by the manufacturer at 5 GHz is about 0.92 V, which is set by the 1 k\(\Omega\) and 1.5 k\(\Omega\) resistors (Table 4 in [45]). Next, the rest of the circuits that are part of the basic detector scheme are selected (Figure 6): the hybrid circuit (C5060) and the switch (PE42553). The hybrid circuit presents a phase shift of the coupled output (Q) of +90\({}^{\circ}\) with respect to the direct output (I), introduces branch losses of 3.5 dB, and has a phase unbalance of 3.8\({}^{\circ}\) and 1 dB of amplitude. The switch is absortive and has insertion losses of 1 dB. A circuit that adjusts the levels of the control signals between the Arduino Uno (0-5 V) and the switch (0-3.3 V) is introduced (Figure 8a). A filter (DEA16537) with 1 dB losses is connected to the input of each branch. The set of devices connected between the input and the reference point (Test Port 1) introduce a total theoretical attenuation of 18.5 dB, considering directional coupler losses negligible. Three amplifiers (SE5005L) with a typical gain of 30 dB have been distributed along each branch, resulting in a maximum gain of 71.5 dB. When the variable attenuators are at maximum attenuation (28 dB), the gain is reduced to 15.5 dB. Since the signal level at the reference point is 0 dBm, the dynamic range of the input signal varies from \(-\)71.5 dBm to \(-\)15.5 dBm. The circuit is prepared to be controlled by an external device (control connector) or manually (DIP Switch: Dual In-line Package Switch). The switches allow the circuit branches to be turned on independently and select the direct or phase-shifted output of the hybrid circuit to generate the IQ-\(\beta\) products. In addition, the control connector includes the outputs of the phase detectors (Table 1). Table 2 includes the state relationship of the switches and the phase detector output voltages (IQ-\(\beta\) products). The values selected to obtain the phase shifts between the RF inputs have been highlighted in green. \begin{table}
\begin{tabular}{l l l l} \hline \hline  & **Type** & **Low (0 V)** & **High (3.3 V)** \\ \hline P1-S1 (Branch 1) & In & Off & On \\ \hline P2-S2 (Branch 2) & In & Off & On \\ \hline P3-S3 (Branch 3) & In & Off & On \\ \hline P4-S4 (Switch 1) & In & Phase-shifted & In phase \\ \hline P5-S5 (Switch 2) & In & Phase-shifted & In phase \\ \hline P6-S6 (Switch 3) & In & Phase-shifted & In phase \\ \hline P7 (\(V_{d_{12}}\)) & Out & & \\ \hline P8 (\(V_{d_{23}}\)) & Out & & \\ \hline P9 (\(V_{d_{31}}\)) & Out & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Control connector pin assignment: truth table for the input pins and voltages at the output pins.