Two-Dimensional One-Body 3 × 3-Way Hollow-Waveguide Nolen Matrix Using a Two-Plane Unequal Division Coupler

This article proposes a 2-D one-body
$3\times3$
-way hollow-waveguide Nolen matrix employing an innovative two-plane coupler with unequal output division working from 27.65 to 28.85 GHz, corresponding to a 4.1% fractional bandwidth. This is the first time a 2-D one-body beam-switching matrix is demonstrated having a number of beams other than
$2^{n}$
. The diagram and working principle of the entire 2-D
$3\times3$
-way Nolen matrix, combining three types of couplers and various phase shifters, are reported. Specifically, a rigorous theoretical analysis is provided to explain the working mechanism of the novel two-plane unequal division coupler. The reflection and port-to-port isolation coefficients of this 2-D
$3\times3$
-way Nolen matrix, as well as the realized gain, are verified by measurements with the output ports radiating directly into free space. The maximum insertion loss and power imbalance of this 2-D
$3\times3$
-way Nolen matrix are 0.86 and 2.5 dB, respectively, across the operating bandwidth. The maximum realized gain is obtained for the boresight beam, with 15.5 dBi in measurement compared to 15.7 dBi in simulation. The minimum realized gain in measurement is 12.0 dBi corresponding to Beam 6, which is a 2-D tilted beam at an angle of 42° with reference to boresight, with a scan loss of 3.5 dB, while the simulated minimum realized gain is 12.7 dBi, obtained for Beam 9 at an angle of 36° with reference to boresight, with 3-dB scan loss.