**5. Beamforming techniques**

Beamforming is performed by means of a beam switching network (BSN) or a butler matrix which controls the signal feeding to\from the antennas in the array. The essential components constituting BSNs are the phase shifters, hybrid couplers, power dividers and crossovers discussed in the former sections. Upon introducing these components, we present two designs of butler matrices in this section and the deployment of these matrices to design beam scanning antenna arrays.

**Figure 17a** shows a 4 � 4 butler matrix realized by four directional couplers to distribute the signals, with the desired phase relations, between the four feeding ports and the four array elements [71]. Various designs of hybrid couplers are presented in Section 3.1, which cover the whole desired band of 27–33 GHz. This 4 � 4 butler matrix achieves two-dimensional beam scanning in the horizontal plane. The obtainable beam directions are *<sup>θ</sup>*<sup>0</sup> <sup>¼</sup> 450 and *<sup>ϕ</sup>*<sup>0</sup> ¼ �450, 450, 1350 and �135<sup>0</sup> for excitations from Ports 1, 2, 3 and 4 respectively. The performance of this matrix is first evaluated in terms of ports' matching and isolation. Simulated and measured scattering parameters of Port 1 are shown in **Figure 17b** where more than 10 dB return loss and isolation is obtained over the band. These levels are then expected for all other ports due to the design symmetry. To test the scanning abilities, the matrix is used to feed an array of four MEdipole antennas and the radiation pattern is simulated and measured [71]. The array shows a measured realized gain of 9.7 �0*:*4 dBi where the reduction from the simulated results is mainly caused by feeding network losses. The simulated and measured radiation patterns in *<sup>ϕ</sup>* ¼ �450 and *<sup>ϕ</sup>* <sup>¼</sup> 1350 planes are given for Port 1 and Port 3

#### **Figure 16.**

*Magneto-electric dipole antenna performance. (a) simulated and measured S-parameters. (b) simulated and measured gain over the band. (c) simulated and measured radiation patterns at 30 GHz for horizontal polarization in E- and H-planes. (d) simulated and measured radiation patterns at 30 GHz for vertical polarization in E- and H-planes respectively.*

excitations. The beam is nearly identical, emphasizing efficient scanning, with low cross-polarization level of less than 20 dB at the main direction [71].

An alternative 4 4 butler matrix is shown in **Figure 18a**, where the ring power divider, cascaded crossover and the Schiffman phase shifter described in the previous sections are all integrated in one network [51]. The four input ports to the matrix are all coaxial ports where coaxial to PRGW transition are used. The matrix is feeding four *Ridge Gap Waveguide Beamforming Components and Antennas for Millimeter-Wave Applications DOI: http://dx.doi.org/10.5772/intechopen.105653*

#### **Figure 17.**

*4* � *4 butler matrix, realized by four directional couplers, and achieves 2D beam scanning. (a) detailed 3D view of the matrix and the fed antennas. (b) simulated and measured reflection coefficient and isolation of the first port. (c) simulated and measured gain and efficiency over the band. (d) simulated and measured radiation pattern at <sup>ϕ</sup>* ¼ �450 *with Port 1 excited (left) and at <sup>ϕ</sup>* <sup>¼</sup> 1350 *with Port 3 excited (right).*

wideband semi-log periodic dipole antennas to test the array performance [72]. Since the radiating elements are all printed antennas with microstrip feeding input, MSPL to PRGW transition is used at each matrix output. Two secondary antennas are added to enhance the symmetry of the radiation pattern.

The array performance is illustrated by **Figure 18b–d**. The simulated and measured scattering parameters indicate isolation and return loss levels of more than 10 dB over the frequency range of 26–34 GHz. The array achieves radiation efficiency of 78% with gain value ranging from 10 dBi to 11.35 dBi over the whole frequency band (for excitation from port 1). The obtainable angles of the beam are 13, 36, 36, and 13° for excitation from ports 1, 2, 3, and 4 respectively [51]. The simulated and measured gain patterns in **Figure 18d** are obtained at 30 GHz and emphasize the scanning ability of the array.

#### **Figure 18.**

*Design and performance of the second* 4 4 *butler matrix for beam switching network. (a) design details. (b) simulated and measured reflection and isolation for Port 1. (c) simulated and measured realized gain for Port 1. (d) simulated and measured radiation pattern for the excitation from the four ports.*

*Ridge Gap Waveguide Beamforming Components and Antennas for Millimeter-Wave Applications DOI: http://dx.doi.org/10.5772/intechopen.105653*
