**2. Design of the circular waveguide TE01 mode transducer**

#### **2.1 Foundation of the mode transducer operation**

 The radial combiner in **Figure 1** is based on the TE01 circular waveguide mode, which is used in different fields of microwave and millimeter wave engineering. For instance, some oversized circular waveguides work with the TE01 mode because of its low attenuation constant, since its electric field is progressively smaller when approaching the circular boundary [18–19]. Metallic cavities made up of a cylinder with circular cross section provide resonant TE01p modes, used for microwave filters with very low insertion loss, and this type of cavities are also common in plasma systems, gyrotrons, masers, etc. [20–23].

 In all these applications, it is necessary to convert first the power coming from the generator in the fundamental mode of a suitable transmission system (typically a coaxial, or a rectangular waveguide for high frequency bands) into the TE01 circular waveguide mode, which is not the fundamental mode of the circular waveguide. The device performing this function is the circular waveguide TE01 mode transducer. Although there are many implementations of this device, there are two main methods for the generation of this mode from a TE10 rectangular waveguide mode.

 The first developed method was based on transforming the cross-section of the input rectangular waveguide progressively into the cross-section of the output circular waveguide, leading to a flared structure. This conversion is usually very long and involves many sections cascaded in-line following a symmetric pattern in order to prevent the generation of higher-order modes, which may degrade the overall performance [11]. Some examples are the Southworth-type converter [18, 24], the Marie-type [25, 26], and the sector converter [27]. At the beginning of these developments, the design of this type of converters was based on the expertise of the designers; nowadays, powerful tools for computer aided design (CAD) are also combined with the know-how of the designers. The main drawbacks of this kind of in-line configuration are their large length and the high level of the excited undesired modes [11].

The second method uses a sidewall coupling (by one or more several sides) between the rectangular and the circular waveguides [28]. The flower-petal transducer follows this configuration [29]. There are two main drawbacks for this

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

structure, its narrow bandwidth and its high insertion loss level. Ka-band transducers with four branches are presented in [12, 30], showing moderate return loss level. In these references, the sidewall coupling is a simple aperture with limited degrees of freedom. As shown in [31], better return loss and wider band can be obtained by improving the sidewall coupling. Hence, the designs presented in this chapter are based on improvement made to the sidewall coupling.

 The work in [31] forms the basis for the designs. **Figure 2** shows the operating principle of this type of transducer. In this figure, the converting section (dashed circle) is excited in its four sides by the TE10 rectangular mode, generating the TE01 mode at the circular waveguide. **Figure 2** also shows the feeding network routing the input to the four arms of the converting section.

 For the design of the transducer, the classical goal is to obtain a challenging return loss at the input with high purity conversion to the circular waveguide TE01 mode. Thus, it is essential to control the level of the non-desired modes in the circular waveguide, especially those that are propagating, with lower cutoff frequency than the TE01 mode. A higher level for these modes degrades the conversion efficiency, but it can also lead to spurious resonances in the power divider (not always treated in detail in the literature of these devices). Thus, the first consideration in the design is to identify how the different propagating modes of the circular waveguide can be controlled, since the TE01 mode is not its fundamental mode (i.e., it is not the mode with the lowest cutoff frequency).

 This study can be done by analyzing the modes with respect to the number of symmetry planes (1, 2 or 4) of the physical structure along with the symmetry of the excitation, as in **Table 1**. **Table 1** shows the modes associated to the cases of one, two or four symmetry planes and the normalized cut-off frequencies of the modes involved in the structure. The excitation in **Figure 2** will be done with the TE10 mode of the rectangular waveguide at the input, which has electric wall (EW) symmetry. The TE01 mode of the circular waveguide has EW symmetry at four symmetry planes of the circular waveguide, including the planes at the four sides for the excitation. In fact, this TE01 mode has EW symmetry for any radial plane.

The study leads to the following considerations:


#### **2.2 Converting section design**

The converting section has two symmetry planes with four rectangular ports at the excitation sides. This avoids the generation of the TE21c mode, according to the considerations in previous subsection. In addition, some kind of matching elements must be included for obtaining a challenging return loss level in broadband

#### **Figure 2.**

*Scheme of a sidewall coupling for a circular waveguide TE01 mode transducer, showing the electric field lines, the converting-section (dashed circle) excited in its four sides, and the input feeding network (with E-plane T-junctions and waveguide bends).* 

#### **Table 1.**

*Circular waveguide modes associated to the case of one, two, or four symmetry planes and their normalized cut-off frequencies.* 

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

 applications. This is done with a one-section stepped transformer shown in the insets of **Figure 3a** and **b**, connecting the circular waveguide with the rectangular waveguide ports. A circular metallic post has been also placed at the bottom of the cylinder for improving the return loss.

**Figure 3** shows the simulated response of the converting-section for both designs at Ku- and W-band, respectively, obtained with CST Microwave Studio [32]. The simulations have taken into account the four symmetry planes. In both designs, the return loss level for the TE01 mode is better than 30 dB. In the insets of **Figure 3**, a 3D CAD view of the final converting section is included.

 It is important to note that, in this structure, the only propagating mode at the circular waveguide is the TE01, according to the third column of **Table 1**, and, thus, the reflection coefficient in **Figure 3** fully characterizes the behavior of the converting section with the considered symmetries. Moreover, it is also emphasized that the manufacturing process has been taken into account in the full-wave optimization, imposing constraints and limitations in the dimensions of the matching elements for easing the fabrication. For instance, for the W-band design that will be implemented by micromachining, corners are rounded in the simulation with 0.2 mm radius. In addition, the transformer sections keep the width of the WR10 standard waveguide used for the ports.

#### **2.3 Feeding network design**

 The converting section is fed from the input rectangular port by means of the feeding network shown in **Figure 2**, which is composed of the following building blocks: two types of T-junctions and three types of waveguide bends, all in E-plane configuration (there is no width variation in the feeding network).

All these individual components (the building blocks), and their connection (leading to more complex building blocks), must preserve the bandwidth and the return loss level obtained previously in the converting section. Moreover, the footprint is minimized. A step-by-step process has been carried out in the design of all these individual components separately. The complete feeding network is obtained after a final optimization, varying only some connection lengths between its building blocks.

#### **Figure 3.**

*Simulated response of the reflection coefficient for circular waveguide TE01 mode in the converting-section, taking into account the four symmetry planes with electric wall boundary condition (EW). In the insets, a 3D CAD view of the full converting-sections is shown. (a) Ku-band response and (b) W-band response.* 

## **2.4 Final design of the transducer**

 The converting section and the feeding network, separately designed in the previous stages, are now connected. A final optimization is carried out in order to fulfill the specifications of the return loss level and high purity conversion from the rectangular waveguide TE10 mode to the circular waveguide TE01 mode. Only one-half of the converter is analyzed due to the single physical symmetry plane of the complete transducer, which has EW field symmetry. This reduces the time of the full-wave simulations. Nevertheless, since accurate results are needed in this stage, the high computational cost of the electromagnetic analyses makes crucial to minimize the number of optimization variables.

In addition, the cost function, which traditionally only involves the return loss and/or the insertion loss, must also include the level of the four higher propagating modes in the circular waveguide (TE11c, TE21c, TM11s, TE31c, according to the first column of **Table 1**), for controlling their required attenuation with respect to the desired TE01 mode. As it could be expected, the radius of the circular waveguide is a key optimization parameter, since it controls the cutoff frequency of the modes, and it is directly related to the challenging level of 30 dB required for the return loss.

The final structure of the transducer in Ku-band is presented in the inset of **Figure 4a**, where the electric field pattern under operation is also shown. **Figure 4a**  shows the simulated response achieving a return loss level higher than 30 dB, while **Figure 4b** shows the attenuation level, higher than 50 dB, for the four propagating modes in the design band from 11 to 13 GHz. A back-to-back measurement of two similar transducers manufactured in brass can be seen in [13], showing a very good agreement with respect to the theoretical simulation.

The final mode transducer for the W-band design is shown in the inset of **Figure 5a**, also with the electric field configuration. The simulated return loss, with a level better than the specified 30 dB, is shown in **Figure 5a**. The response for the attenuation is shown in **Figure 5b**, achieving levels higher than 55 dB for the four propagating modes in the design band from 88 to 100 GHz.

Both transducers have been designed in this chapter for integration with a radial divider. However, they can be also used as separated devices in diverse applications of high-energy particle accelerators or plasma heating. In all these cases, power rating is a key parameter. For the presented transducers, it has been calculated at the lowest frequency of operation in each band, i.e., 11 GHz in Ku-band and 88 GHz

#### **Figure 4.**

*(a) Simulated return loss of the Ku-band transducer, better than the 30 dB goal in 2 GHz centered at f = 12 GHz (16.7%). In the inset, the electric field configuration is shown. b) Level of the four propagating modes (transducer with one physical symmetry plane having EW) at the circular waveguide (transmission from TErec 10), higher than 50 dB in the 11–13 GHz band.* 

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

**Figure 5.** 

*(a) Simulated return loss of the W-band transducer, better than the 30 dB goal in 12 GHz centered at f = 94 GHz (12.8%). In the inset, the electric field configuration is shown. b) Level of the four propagating modes (transducer with one physical symmetry plane having EW) at the circular waveguide (transmission from TErec 10), higher than 55 dB in the 88–100 GHz band.* 

in W-band. Assuming a break down field of 30 kV/cm, and analyzing the critical dimension of each design, a 240 kW value has been obtained for the Ku-band transducer, while 9.6 kW for the W-band design.
