## 2 Design Method
### Arbitrary Termination Impedance Reflection-Type Phase Shifter
To select the optimum circuit parameters of the proposed arbitrary termination impedance reflection-type phase shifter, Figure 6b,c illustrate the calculated phase shift range and phase deviation error according to the variations of \(Z_{r}\) and \(\theta_{r}\). In these figures, the color bars represent phase shift range and phase deviation error values. As can be observed in Figure 6b, higher phase shift ranges can be achieved by increasing \(Z_{r}\) while keeping \(\theta_{r}\) fixed, or vice versa. However, the maximum phase shift range of 245\({}^{\circ}\) can be achieved, and further increasing \(Z_{r}\) and/or \(\theta_{r}\) results in a decreasing phase shift range. Meanwhile, once the phase shift range reaches its maximum value, further increases in \(Z_{r}\) and/or \(\theta_{r}\) result in a continued increase in phase deviation error up to a certain point before it starts to decrease, as demonstrated in Figure 6c. Therefore, appropriate \(Z_{r}\) and \(\theta_{r}\) can be selected through a trade-off between the desired values of phase shift range and phase deviation error. In this paper, the arbitrary termination impedance reflection-type phase shifter was designed to achieve a phase shift range of over 180\({}^{\circ}\) while maintaining a phase deviation error of less than \(\pm\)8\({}^{\circ}\) across the operational BW of 200 MHz at the center frequency (\(f_{0}\)) of 2.45 GHz. For the validation of the proposed arbitrary termination impedance reflection-type phase shifter, Figure 7 shows the simulated \(S\)-parameters of the three proposed reflection-type phase shifters where the input port is terminated with 50 \(\Omega\) and the isolation port is terminated with three different \(Z_{4}\), as shown in Table 2. To see the phase shift range and phase deviation error tendencies, each proposed reflection-type phase shifter is terminated with three different reflection loads, specifically three different pairs of \(Z_{r}\) and \(\theta_{r}\). As can be seen from Table 2, a high-phase shift range (>200\({}^{\circ}\)) and low-phase deviation error (<\(\pm\)7.4\({}^{\circ}\)) within the desired BW can be achieved by selecting \(Z_{r}\) = 50 \(\Omega\) and \(\theta_{r}\) = 45\({}^{\circ}\). This result reveals that by carefully selecting \(Z_{r}\) and \(\theta_{r}\), the proposed arbitrary termination impedance reflection-type phase shifter can simultaneously provide a high-phase shift range, a low-phase deviation error, and a good RL. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \(\mathbf{Z_{i}}\), \(\mathbf{Z_{z}}\), \(\mathbf{Z_{3}}\) & \(\mathbf{Z_{4}}\) & \(\mathbf{C_{J}}\)/ \(\mathbf{L_{4}}\) & \(\mathbf{Z_{4}}\) & \(\mathbf{Z_{B}}\) & \(\mathbf{Z_{C}}\) & \(\mathbf{Z_{0}}\) & \(\mathbf{Z_{z}}\) & \(\mathbf{\theta_{r}}\) (\(\uparrow\)) & **PSR (\(\uparrow\))** & **PDE (\(\uparrow\))** \\ \hline
50 & 80 & 0 & 35.36 & 50 & 44.72 & 63.25 & 30/50/80 & 30/45/60 & 157.8/2145.2332 & 3.8/74/39.8 \\ \hline
50 & 45 + \(j10\) & \(\mathcal{C}_{4}=6.5\) pF & 35.36 & 50 & 33.54 & 47.43 & 30/50/80 & 30/45/60 & 157.8/2145.2332 & 3.8/74/39.8 \\ \hline
50 & 60 – /70 & \(L_{4}=4.55\) nH & 35.36 & 50 & 38.73 & 54.77 & 30/50/80 & 30/45/60 & 157.8/2145.2332 & 3.8/74/39.8 \\ \hline \end{tabular}
\end{table} 
Table 2: Simulated values of phase shift range = \(\Delta\phi_{\mathrm{max}}\) and phase deviation error = \(\phi_{err}\) within BW of 200 MHz at \(f_{0}\) = 2.45 GHz for different \(Z_{4}\), \(Z_{r}\), and \(\theta_{r}\). \(Z\) are units in [\(\Omega\)] (PSR: phase shift range; PDE: phase deviation error). Figure 6: Parametric study of reflection load: (**a**) capacitance variation according to DC–bias voltage, (**b**) phase shift range according to \(Z_{r}\) and \(\theta_{r}\) at \(f_{0}\) = 2.45 GHz, and (**c**) phase deviation error according to \(Z_{r}\) and \(\theta_{r}\) within BW of 200 MHz (PSR: phase shift range; PDE: phase deviation error). Figure 7: Simulated S-parameters of ATI reflection-type phase shifter.