Nolen Matrix Research Articles

Broadband Substrate Integrated Waveguide 4$\,\times\,$4 Nolen Matrix Based on Coupler Delay Compensation

A broadband Nolen matrix in substrate integrated waveguide (SIW) technology is proposed and studied in this paper. Being feeding networks, Nolen matrices usually introduce significant phase dispersion in their standard form, thus limiting effective bandwidth. In this work, broadband frequency operation is achieved with adequate coupler delay compensation, resulting in a more parallel matrix topology. Consequently, H-plane couplers with continuous aperture are preferred in the proposed design as opposed to the cross-couplers previously used in the serial configuration. The SIW couplers and phase shifters of a balanced amplitude 4×4 Nolen matrix are designed at 77 GHz for radar applications. The resulting matrix that combines these elementary building blocks is fabricated and measured, and measured characteristics are in good agreement with theoretical and simulated predictions. This first design achieves excellent results over a 11.7% frequency bandwidth centered at 77 GHz. This modified Nolen matrix combines advantages of standard Nolen and Butler matrices and may be used as a building block for generalized orthogonal matrices.

Planar $Ku$-Band 4$\,\times\,$4 Nolen Matrix in SIW Technology

In this paper, a 4 × 4 Nolen matrix beam-forming network for multibeam antenna applications is designed and demonstrated at 12.5-GHz center frequency. The structure is implemented using substrate integrated waveguide (SIW) technology for its attractive advantages including compact size, low loss, light weight, and planar form well suitable for high-density integration with other microwave and millimeter-wave planar integrated circuits. SIW cruciform couplers are used as fundamental building blocks for their wide range of coupling factors and their specific topology well adapted to the serial feeding topology of a Nolen matrix. The network performances are investigated over a 500-MHz frequency bandwidth ranging from 12.25 to 12.75 GHz. The matrix definition based on SIW cruciform couplers is similar to its microstrip counterpart in terms of coupling factors and phase delays. The whole network is fabricated. Measured results are in good agreement with the theoretical predictions, thus validating the proposed design concept. Using this matrix with a four radiating elements array antenna enables us to investigate the impact of the proposed matrix on the beam pointing angles versus frequency.

Printed S-Band 4 $\times$ 4 Nolen Matrix for Multiple Beam Antenna Applications

A Nolen matrix design method is proposed as an asymptotic singular case of a recent Blass matrix design algorithm. The procedure is illustrated by a 4 x 4 Nolen matrix, which design is centred at 2.2 GHz, with the amplitude and phase output excitation laws of a Butler matrix using 90deg hybrids. Simulation and measurement results are presented in this paper.