Several innovative concepts and schemes to enrich the features of Butler matrices (BMs) to enhance their suitability over the conventional schemes are discussed, demonstrated, and analyzed. Mobile communication and radar systems require compact and versatile multibeam-forming networks (MBFNs). Therefore, the study is aimed to provide feasible and practical solutions with more flexible beam numbers of BMs, more concise configurations of the two-dimensional (2-D) beamforming, and broadband characteristics while maintaining the intrinsic merits of conventional BMs (such as theoretically lossless, spatially orthogonal beams, and relatively simple structure). In addition, the study implements some of the concepts to millimeter-wave (mm-wave) frequencies applications. 
Concretely, the effects of some components, such as T-junctions and crossovers, on the bandwidth of parallel-feeding networks and MBFNs, are investigated and analyzed. The corresponding solutions to broaden the bandwidth are suggested and verified by the measurements. Further, for the 2-D beamforming based on BMs, a generalized scheme to build 2-D MBFN with any 2M+N beams based on traditional 2M× 2M- and 2N× 2N BMs is elaborated and experimentally verified. Especially as the key component of 2-D BMs, an innovative eight-port coupler with a very compact structure is proposed. The applications of the coupler for 2-D monopulse arrays, dual-polarized monopulse arrays, and mm-wave 2-D beamforming are also demonstrated. Besides, two solutions to extend the numbers of beams of BMs from traditional 2N × 2N to almost arbitrary number, such as 2M×3N or M × 2N, are introduced by using a three-way coupler and electrically switchable coupler, respectively (M and N are arbitrary integers greater than 0). 
Though the majority of ideas and examples presented is exemplified by planar circuits and transverse-electro-magnetic (TEM) transmission lines, they can also be transferred to and applied on other circuit forms, such as ridge-gap waveguide (RGW), printed RGW (PRGW), substrate-integrated waveguide (SIW), and packaged microstrip line (PMSL) for mm-wave applications.
Keywords: Butler matrices, two-dimensional Butler matrices, directional couplers, reconfigurable couplers, phase shifters, crossovers, eight-port couplers, packaged microstrip line.