**3. Design of the 16-way and 5-way power dividers**

 The circular waveguide TE01 mode generated by the transducer has to excite the radial divider, whose symmetry guarantees that the *N* output ports in **Figure 1** will have the same signal in amplitude and phase. Under the assumption that the radial divider will have low return loss, the power carried by the circular waveguide TE01 mode is equally divided in magnitude and phase into the TE10 mode of the *N* rectangular waveguides at the output ports. The radial dividers have typically a metallic post (with one or more sections) at the bottom of the structure. However, since the number *N* of output ports for the Ku- and W-band designs is very different (16 versus 5, respectively), additional strategies have been followed in each design for obtaining the specified challenging return loss level.

#### **3.1 16-way radial divider**

In the case of a large number of ports, as in the 16-way power divider in the Ku-band, reduced height rectangular waveguides are typically connected to the base of the radial divider [11, 12]. Since the ports are implemented in standard waveguides, in this case *N* stepped transformers (normally only changing the height) would be required between the output ports and the circular cylinder of the divider. Therefore, the complexity, the size and the insertion losses would be increased. The design shown in **Figure 6a** avoids these transformers, with standard WR75 waveguides directly attached to the divider base. Therefore, even though 16 output waveguide ports are involved in the design, the radius of the base size is not enlarged. Since the height of the waveguide is not decreased, full power handling capability is maintained, and insertion losses are not degraded. In addition, 16 transformers are avoided, simplifying the manufacturing process and reducing the cost.

The radial symmetry with appropriate EW boundary conditions is also exploited in the simulations to reduce drastically the computation time. **Figure 6b** shows the

**Figure 6.** 

*(a) 3D CAD view of 16-way divider with the standard WR75 waveguides directly attached to the base without stepped transformers. (b) Simulated response of the reflection coefficient of the circular waveguide TEcir 01 mode, and the transmission to the TErec 10 rectangular ports (from the TEcir 01), in the 16-way divider (only one quarter of the structure); in the inset, a 3D CAD view includes the port numbering.* 

theoretical full-wave simulated response of one quarter of the divider. The return loss level is better than 30 dB in the 2 GHz bandwidth. In the same figure, it can be seen the transmission coefficients corresponding to the simulation of one quarter of the whole structure. Thus, insertion loss in ports P3, P4 and P5 is 6 dB, but in ports P2 and P6, with half-height, the level is 3 dB lower than in the other three, i.e., 9 dB (see the port numbering in the inset of **Figure 6b**). After this response is obtained, the 16-way power divider is ready to be connected to the transducer.

#### **3.2 5-way radial divider**

 The ideal S-parameter matrix of a 5-way power divider is shown in (Eq. (1)), following the notation used in [33] (**Figure 7**). The coefficients α and β represent the matching of the input and output ports, respectively. The coefficient γ is related to the input power division, while the coefficients η1 and η2 describe the coupling between pairs of different waveguide ports, two values in the case of *N* = 5. Assuming that the structure is lossless, the S-matrix is unitary and, consequently, it is possible to obtain the value of its elements, imposing perfect matching at the input port, i.e., α = 0. **Table 2** collects all the possible values for the other four elements (16 different matrices). It is interesting to note that in the case of *N* = 5, it is theoretically possible to match all the ports (α = β = 0).

**Figure 7.**  *Scheme of a 5-way radial power combiner with port numbering according to (Eq. (1)).* 


*Design of Radial Power Combiners Based on TE01 Circular Waveguide Mode DOI: http://dx.doi.org/10.5772/intechopen.82840* 

**Table 2.** 

*All possible solutions for the S-matrix coefficients in an ideal 5-way radial divider.* 

**Figure 8.** 

*(a) 3D CAD view of the 5-way divider. (b) Simulated response of the reflection coefficient for the circular waveguide TEcir 01 mode, and the transmission to the TErec 10 rectangular ports (from TEcir 01) (only half of the structure); in the inset, a 3D CAD view including the port numbering is shown.* 

 For our W-band design, the 5-way power divider implementation will follow the configuration shown in **Figure 8a**. In the full-wave simulations, the radial symmetry with appropriate EW boundary conditions is exploited to reduce the computation time. **Figure 8b** shows the theoretical full-wave simulated response of the divider. The return loss level is better than 30 dB in the 12 GHz bandwidth. Since the simulation has been done over one half of the structure, the insertion loss for ports P3, P4 is 4.77 dB. In port P2, with half-height, the level is 3 dB lower than in the others three, i.e., 7.77 dB (see the port numbering in the inset of **Figure 8b**).
