# Design of True Time Delay Millimeter Wave Beamformers for 5G Multibeam Phased Arrays
## 2 Beamforming Networks Design
### Tree Type Beamforming Network Architecture  
Our last design is focused on the development of a novel tree-based beamforming network, which mimics topologies that have been employed in microwave photonics [54]. We expect that this design will enable the development of new tunable three-dimensional (3D) beamformers for next-generation hybrid phased array systems providing game-changing capabilities compared to other beamformers. Specifically, the proposed implementation provides ultra-wideband operation, eliminates the problems of crossovers faced by Butler, Nolen, and Blass matrices, and is capable of exhibiting significantly higher efficiencies than Rotman lenses. Figure 12 shows our proposed tree topology. As can be seen, the building blocks of this topology are transmission lines and power dividers, making its topology relatively simple. The primary novelty of this topology is the minimal number of the involved delay lines. This idea stems from microwave photonics, and it is exploited in microwave and millimeter wave regimes. The key feature to observe refers to the hierarchical usage of delay lines with multiples of the basic delay \(\tau\) from the antenna ports level towards the transceiver port. The idea is to hierarchically repeat the same feature by doubling the delay while moving diagonally from the first antenna port towards its last port and towards the network input. Specifically, the signal entering the input port undergoes successive power divisions by reaching the output ports with both the desired amplitude and phase. Even though our proposed design looks similar to corporate-type beamforming networks [55], the time delays in the form of transmission line paths are introduced in the common branches and not before the output ports of the network. This modification is crucial as it offers two main advantages. First, in the tree topology, the total delay (or phase shift) is introduced through the common branch, instead of the multiple small branches used in the corporate network that introduce the desired time delays in parallel. This key modification makes the tree beamforming network significantly more compact compared to the corporate network. Secondly, and most importantly, the transmission lines playing the role of phase shifters are true time delay elements, which eliminates the beam squint phenomenon. As is expected, a tree-based network can introduce only a specific time  
Figure 11: Rotman lens architecture with three inputs (red), three outputs (green), and two absorbers in the side walls. The scale is 10:3.06 mm. delay, steering the beam towards only one specific angle. However, this limitation can be overcome using multi-layer topologies with a different tree network on each layer, where each layer is devoted to steer the beam towards a specific angle. Figure 13 shows in detail our proposed multilayer design. To connect the different layers a single pole multiple throw (SPNT) type switch is used at the input and at each antenna port to effectively activate the corresponding layer (tree-topology) and provide the desired radiated beam (thereby achieving beamsteering). The challenge here is to appropriately design the interconnecting lines so that they are compatible with the monolithic microwave integrated circuits (MMICs) of SPNT switches. To address this challenge, all the interconnecting lines are designed as striplines, an approach that has never been implemented before on these networks. This design approach not only provides the needed multilayer beamformers but also ensures low losses at mm-wave frequencies. As is expected, a critical component of the tree beamformer is the power divider. The power divider has to be appropriately designed to support the required bandwidth while it simultaneously introduces the desired amplitude distributions at the radiating elements of the network. At this stage of our research, we are only focused on the second aim, leaving the wideband behavior as a future task.