# Design of True Time Delay Millimeter Wave Beamformers for 5G Multibeam Phased Arrays
## 2 Beamforming Networks Design
### Rotman Lens Architecture  
In our second approach, a novel true time delay Rotman lens is used. Rotman lenses, similar to classical Blass topologies, are known for two main limitations: their large footprint and their limited efficiencies (typically 50-60%) due to the dummy ports. Aiming at high efficiency, we propose a novel dummy-ports-free Rotman lens utilizing the idea of field absorbers. Specifically, imitating perfect matching 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 eliminating the undesired reflections. As is well known, the original Rotman lens is a metallic plate waveguide, loaded with dielectric for miniaturization purposes, where its input ports lie upon the beam contour and the output ports lie upon the array contour. As its grounded substrate is extended beyond the waveguide boundaries for practical purposes, it resembles a printed microstrip structure, although the area between the two metallic planes remains a parallel plate waveguide operating at its TEM mode. As shown in Figure 9, the Rotman lens is considered as a \(M\times N\) beamforming network. Its functionality is: when an input port is excited, the input signal is divided into \(N\) output ports with different amplitudes and phase sequences, which create a radiated beam with its maximum directed along a specific direction. When the same input signal is fed to another input port, a beam oriented to a different scanning angle is created. The energy fed to each input port emerges as rays directed towards all possible directions inside the parallel plate region. Some of them collimate, feeding the antennas through the output ports. However, there are also rays that propagate towards the top and bottom sides of the waveguide (in Figure 9, the top and bottom sides are considered the sides where the dummy ports are placed). These rays may be reflected to arrive at the output ports (even at the input ports) interfering with the directed rays at arbitrary phase, thus \"contaminating\" the desired signals (or causing mismatching at the inputs). Hence, the energy of these side-propagating rays must be absorbed and dissipated when they arrive at the side edges of the lens. To reduce the reflections in the parallel plate region, the dummy ports are used, as shown in Figure 9. Essentially, the dummy ports serve as absorbers for the spillovers of the lens, reducing the multiple reflections and standing waves, which undermine the lens performance [52]. Figure 9: Principle Rotman lens architecture. Rottman Lens Design Methodology  
In this work we follow the classical Rotman lens design approach, as depicted in Figure 10 given by [52]. Aiming at a compact, low cost, and highly efficient design, our goal is to minimize the number of dummy ports. However, when a small number of dummy ports is used, the Rotman lens performance degrades radically, as the inputs are no longer well matched, and the outputs' phase response fluctuates leading to a non-constant group delay. This is a well-recognized problem and numerous attempts have been made by researchers to confront it. Indicatively, [PERSON] et al. [53] utilized field absorbers at the side edges built up on a metamaterial approach. Here, we take a different path, imitating the perfect matching layers (PML). For this purpose, we appropriately engineer the substrate by doping it with conductive material, (e.g., carbon), on the area directly beyond the sides of the upper metal. This is considered to retain about the same dielectric constant but increasing the loss tangent about ten times. Thus, we can efficiently absorb the incident waves and in turn attenuate the standing waves of the parallel plate region.