# Design of True Time Delay Millimeter Wave Beamformers for 5G Multibeam Phased Arrays
## 1 Introduction
More recently, a Nolen matrix with slightly wider bandwidth of 1.4:1, amplitude imbalance less than 0.75 dB, phase variation 6\({}^{\circ}\), and return loss better than 16 dB was proposed by [PERSON] et al. [43]. The Blass matrix is the ordinary case of the Nolen matrix. In addition, the Blass matrix can provide non-uniform amplitudes (thereby overcoming Nolen matrix limitations for uniform amplitudes) but exhibits higher losses due to the use of matched loads. Moreover, the Blass matrix can be designed as a true time-delay network, thereby resolving (at least in theory) the bandwidth limitations of both Butler and Nolen matrices. A true time-delay Blass matrix with an instantaneous bandwidth of 5:1 was first reported by [PERSON] et al. [44]. However, this was an active network design that used amplifiers as directional couplers. Finally, Rotman lenses are passive topologies that have been used to implement true time-delay beamforming networks. The main advantage of Rotman lenses is that they require low number of switching elements, compared to Blass matrices. Rotman lenses have been extensively used with relatively wideband performance, such as 3.4:1 by [PERSON] et al. [45] and 10:1 by [PERSON] et al. [46]. However, Rotman lenses suffer from relatively low efficiency (e.g., 20-50% efficiency was reported by [PERSON] [46]). In this work, three novel analog beamforming networks are proposed as 5G mm-wave candidates. Each network separately tackles and solves specific limitations and drawbacks of its prior counterparts. First, a multilayer Blass matrix design is presented. To our knowledge, this is the first multilayer, circular Blass topology. Typical Blass networks are big in size and suffer from excessive losses. Aiming towards compact and highly efficient mm-Wave beamforming networks, we first transform the classical Blass matrix topology [28] into a circular design [47], and then implement it in a two-layer topology. The challenge of this attempt is the appropriate design of the couplers. Typical approaches use bondwires and bridges [48], two factors that decrease the efficiency of beamformers and increase the design complexity. In this work, to minimize the losses and significantly reduce the design complexity, a dual-layer directional coupler is designed and used. As a proof of concept, a 3 \(\times\) 4 Blass matrix is designed, which shows excellent performance. Compared to the typical single-layer Blass matrix the proposed dual-layer network achieves 60% size reduction. The second topology, which is presented here, is a modified Rotman lens topology. Rotman lenses, similar to the Blass matrix topologies have large footprints, while their efficiency is limited due to the existence of dummy ports. Aiming towards a compact, low cost and highly efficient design, we minimize the number of dummy ports by using field absorbers. Specifically, by imitating perfect matched layers (PMLs), we engineer the substrate by doping it with conductive material. This key modification essentially increases the loss tangent about ten times, yielding an almost perfect absorber and thereby eliminating the undesired reflections. As a proof of concept, a simple 3 \(\times\) 3 structure, which shows very good results, is presented here. Our last topology is a tree topology inspired by microwave photonics. Specifically, this implementation provides ultra-wideband operation; eliminates the problems of crossovers faced by Butler, Nolen, and Blass matrices; and is capable of providing significantly higher efficiencies than ordinary Rotman lenses. The primary novelty of this topology is the minimal number of delay lines. By hierarchically repeating the same feature, using successive power divisions (equal and un-equal) and by doubling the delay as we move diagonally from the first antenna port to its last port and towards the network input, we achieve the desired amplitude and phase difference. As a proof of concept, a three-layer 1 \(\times\) 4 network, which shows excellent results, is designed.