## 3 Experimental Verification of the Monolithic Rotman Lens Design
### Experimental Results
However, the phase variations by frequency remained fairly in line with predictions. Figure 11: Simulated scattering parameters in amplitude (**left**) and adjacent port phase difference (**right**) of the double-ridged waveguide \(10\,\times\,10\) Rotman lens prototype for (**a**) port 1, (**b**) port 3 and (**c**) port 5 (reflection coefficient in _black_; coupling coefficients in _shades of blue_; transmission coefficients in _shades of red_; operating frequency bands in _light grey_). The phase error versus frequency was evaluated in simulation and measurement for selected ports, and the results are reported in Figure 13. The simulated results are very similar to those reported in Figure 5, as the transitions included in all ports have no impact on the phase difference. The measured phased error is about twice the predicted one, with a standard deviation below 10\({}^{\circ}\) and a peak-to-peak error below 38\({}^{\circ}\). Variations of up to 10\({}^{\circ}\) in peak-to-peak error were observed across the operating band, while the RMS values were more stable versus frequency. As expected from simulations, the phase error is slightly worse in the lower frequency band. The values remain nevertheless acceptable considering the test setup. The accurate characterization of such large beamformers may benefit from automation, which will be considered in future works. Figure 12: Measured scattering parameters in amplitude (**left**) and adjacent port phase difference (**right**) of the double-ridged waveguide 10 \(\times\) 10 Rotman lens prototype for (**a**) port 1, (**b**) port 3 and (**c**) port 5 (reflection coefficient in _black_; coupling coefficients in _shades of blue_; transmission coefficients in _shades of red_; operating frequency bands in _light grey_). Finally, synthesized array factors obtained with the scattering parameters of the \(10\times 10\) Rotman lens prototype are reported in Figure 14, assuming a linear array with a spacing of 6.28 mm as discussed in Section 2.2. Numerical results are reported for the frequencies at the edge of the bands considered, i.e., 17.3 GHz, 20.2 GHz, 27.5 GHz and 30 GHz. The results are not normalized to report the losses with reference to the ideal 10-element array factor adding 10 dB to the elementary pattern gain. The losses obtained were slightly higher than those reported in Figure 10 because phase errors also translate into a maximum gain degradation. The average difference in peak array factor between simulation and measurement was 0.9 dB in the lower frequency band and 1.2 dB in the upper band. The difference typically tends to increase toward the outer ports. For example, at 30 GHz, the difference was only 0.8 dB for port 5, but 1.4 dB for port 1, the outermost feeding port. These results are in line with previously reported numerical results [38] indicating that phase aberrations increase with the pointing angle despite the presence of the off-axis focal point. This is because secondary effects not accounted for in the simplified ray-tracing models become predominant. Nevertheless, the results reported confirm the good stability of the patterns across the wide frequency band analyzed, both in terms of pointing direction and side lobe levels, confirming the potential of this design for wide-band and dual-band applications in the K/K\({}_{\text{a}}\)-Band.