**3. Feeding structures**

### **3.1 Hybrid couplers**

Hybrid couplers are the main building blocks of the beam switching network, which is used to divide the power equally with 90o phase shift and high isolation between the ports [47]. The design and analysis of several PRGW hybrid couplers configurations have been proposed in the literature, where two featured designs will be discussed in this section as are mainly deployed in beam switching antenna systems [45, 48–50].

The first design is shown in **Figure 5**, where four identical PRGW lines are connected through a rectangular coupling section with dimensions (*L W*). These dimensions mainly control the coupling in the desired operating bandwidth, where the initial dimensions are calculated through applying the even/odd mode analysis [49]. Since the impedance of the four PRGW ports is different from the impedance of the coupling section, a taper matching transformer is introduced to achieve a deep matching level over the operating frequency band, where the final dimensions of the

#### **Figure 4.**

*The design of coaxial to PRGW transition. (a) transition section with detailed dimensions. (b) fabricated layers. (c) simulated and measured results of the scattering parameters.*


#### **Table 3.**

*Dimensions of the coaxial to PRGW transition in Figure 4.*

coupler are listed also in **Table 4**. The performance of the coupler is evaluated through simulation, where 15 dB matching level and isolation over a relative bandwidth of 26.5% at 30GHz are achieved as shown in **Figure 5b**. In addition, 90°5° phase shift is achieved between the output ports over the whole operating bandwidth [49]. However, one major drawback of this coupler is the amplitude imbalance (3.5 dB 1.5) is large, where high performance beam switching systems require both precise amplitude and phase balance over the operating frequency band.

Therefore, an alternative model targeting the same frequency band is presented in **Figure 6a**, where a circular coupling section is used rather than the rectangular junction in the former design [51]. The circular junction consists of two rings with different radii representing the widths of the equivalent branched line directional coupler. A bowtie shape slot is introduced in the center of the rings with specific

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

**Figure 5.**

*Quadrature 3 dB hybrid coupler: (a) design details and dimensions. (b) S-parameters simulation results. (c) phase difference of output ports.*


#### **Table 4.**

*Dimensions of the coupling section illustrated in Figure 5a.*

orientation to adjust the coupler performance [51]. Furthermore, a step matching section is added to each transmission line to adapt the impedances over the operating band. The design depends on the suitable adjustment of each ring width, the bowtie slot, and the dimensions of the matching section. These parameters are given in **Table 5**, while the simulation results are illustrated in **Figure 6b** and **c** proving efficient operation over the frequency range of 26.4–33.75 GHz. As an assessment of the advantage of PRGW technology over other new technologies, **Table 6** summarizes a comparison among the performance of the rectangular hybrid coupler in **Figure 5** and other designs in the literature.

#### **3.2 Crossover**

Beam switching networks impose the usage of crossover connections when two PRGW lines cross each other at a point while at the same time must be totally isolated [55, 56]. Two main techniques can be used to implement crossovers, and two featured designs will be presented in this section [51, 57].

The first design is based on the traditional technique of cascading 3 dB directional couplers to implement the crossover. However, three quarter wavelength sections are used to widen the bandwidth more than that of the traditional designs which use two sections only [51]. Using three cascaded sections introduces more design variables and more degrees of freedom to optimize the performance. The analysis of the structure is

#### **Figure 6.**

*Design and performance of the ring coupler. (a) design details and dimensions (b) full S-parameters for a single port. (c) phase difference between output ports.*


#### **Table 5.**

*Dimensions of the design in Figure 6a.*

done by even\odd mode analysis, and the design parameters are optimized for minimum isolation and reflection [58]. The design is shown in **Figure 7a** and **b**, while the parameters are given in **Table 7**. As seen by the results in **Figure 7c**, the device achieves a relative bandwidth of 23% at 30 GHz with more than 15 dB isolation.

A disadvantage of the traditional technique of using cascaded couplers is the large size of the crossover. Aiming to avoid that common shortage, another model is presented in **Figure 8a**. This design is based on achieving 0 dB coupling in a directional coupler by designing even and odd impedances with 5% difference between each other over the frequency band of interest [57]. The design has the structure of four PRGW lines connected through a rectangular coupling section in the middle. By suitable choice of the dimensions of the coupling section, full isolation can be ensured between a single port and two of the four ports, yielding 0 dB coupling with the remaining port [57]. Multiple steps are added in the coupling section as tuning parameters to enhance the operating bandwidth [57]. The final dimensions of these steps and the coupling section are given in **Table 8**, for which the device produces the S-parameters illustrated by **Figure 8c** and obtained through CST simulation. These results indicate acceptable operation over the frequency range of 28.5–32.5 GHz in terms of isolation and coupling. The device achieves relative bandwidth of about 13.3%, which is typically higher than usual single layer crossover designs of the same size. Moreover, comparison with designs from other technologies is listed in **Table 9**, featuring the advantages of both the compact size and high relative bandwidth obtained by PRGW technology.


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

> **Table 6.**

*Comparison of PRGW hybrid coupler design with other technologies.*

#### **Figure 7.**

*Crossover design by cascaded couplers. (a)3D view of the PRGW crossover. (b) details and dimensions of the cascaded couplers. (c) simulated S-parameter response of the crossover along isolation and coupling directions.*


#### **Table 7.**

*Parameters of the crossover illustrated by Figure 7b.*
