**3.3 Phase shifters**

Phase shifters are essential components in Butler matrices, implemented to provide the required phase difference between the antennas in the beam scanning arrays. For efficient beam control, the introduced phase shift must be stable over the operating bandwidth with low insertion loss, where several techniques have been investigated in the literature to achieve that property [47, 61]. One technique is based on using four port directional couplers with the isolated and through ports connected to each other. This produces the well-known Schiffman phase shifter for which the differential phase shift can be adjusted through careful selection of impedances of the coupled lines [62].

**Figure 9a** illustrates a Schiffman phase shifter based on PRGW technology, designed to achieve a 450 differential phase shift around 30 GHz [62]. Widths of the input and output lines, as well as those of the coupled section were all designed using *Ridge Gap Waveguide Beamforming Components and Antennas for Millimeter-Wave Applications DOI: http://dx.doi.org/10.5772/intechopen.105653*

#### **Figure 8.**

*Design of 0 dB coupler using rectangular coupling section to provide a crossover around 30 GHz. (a) 3D view of the crossover. (b) details of the coupling section. (c) simulated S-parameters assessing the isolation and coupling around 30 GHz.*


#### **Table 8.**

*Dimensions (in mm) of the coupling section and the matching steps in the crossover of Figure 8b.*


#### **Table 9.**

*Comparison of a proposed PRGW crossover with other technologies.*

even\odd mode analysis of directional couplers [58]. The length of the coupled section was optimized for increased operating bandwidth. Final dimensions are given in **Table 10**, while the simulated S-parameters response is given in **Figure 9b**. The

**Figure 9.**

*Design and performance of the Schiffman* 450 *phase shifter. (a) detailed design dimensions. (b) simulated S-parameters magnitude. (c) phase difference between the input and output ports.*


**Table 10.**

*Dimensions of the Schiffman phase shifter illustrated in Figure 9a.*

device achieves 21.7% relative bandwidth at 30 GHz with 450phase shift <sup>2</sup>*:*50 differential phase error and less than 0.4 dB insertion loss [62].

### **3.4 Differential feeding power dividers**

One of the main targets of mm-Wave beam switching arrays is to overcome the multipath fading in wireless communication channels by using space or polarization diversity techniques [9, 10]. These diversity techniques require the array to have highly stable radiation characteristic and low cross polarization level [61]. Such demands impose the usage of differential feeding for the array elements, which can be provided through out of phase power dividers. In this section, two designs for differential feeding power dividers are introduced.

The first design is shown in **Figure 10a**, where the power divider is implemented using two layers of PRGW structure coupled by I-shaped slot [63]. The first layer has the input feeding line connected to a matching stub optimized to achieve a deep matching level over a wide bandwidth, while the upper layer contains the two output PRGW lines, where the coupling through the I-shaped slot achieves the 180<sup>0</sup> phase difference [63]. The design dimensions are listed in **Table 11**, and the simulated S-parameters response shown in **Figure 10b** reveals a 20% relative bandwidth with more than 15 dB return loss and less than 0.3 dB insertion loss over the whole operating bandwidth. The phase difference between the output ports is stable around 180<sup>0</sup> ensuring differential output.

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

**Figure 10.** *Power divider design (a) detailed design dimensions for the feeding and divider layers. (b) Simulated S-parameters. (c) Phase difference between output ports.*


#### **Table 11.**

*Dimensions of the power divider in Figure 10a.*

An alternative design is shown in **Figure 11a** where a hybrid ring or rat-race directional coupler is used to satisfy the power divider function with 1800 in the output phase shift [64]. One advantage of rat-race couplers is that they can be used to produce in-phase or out-phase feeding according to the choice of the input port. The illustrated design has an introduced open circuited stub at the middle of the 3*λ=*4 part of the ring which controls the signal splitting ratio between the output ports. Furthermore, at each port of the coupler, a quarter wavelength transformer is added to enhance the relative bandwidth [64]. The design dimensions of the ring, the stub and the quarter transformers are given in **Table 12**. With these dimensions, the device achieves 27.69% bandwidth at 30 GHz with more than 15 dB isolation as shown by the S-parameters in **Figure 11b**. A brief comparison is listed in **Table 13** among the former rat race coupler and other designs based on SIW technology, revealing the promising performance of the PRGW design.

**Figure 11.**

*Rat-race coupler design. (a) design with details and dimensions. (b) simulated S-parameters. (c) Phase difference between output ports.*


**Table 12.**

*Values of the rat-race coupler dimensions illustrated by Figure 11a.*


**Table 13.**

*Comparison with other technologies design for power dividers.*
