Research Article  Open Access
Guang Hua, Jiefu Zhang, Jiudong Wu, Wei Hong, "Design and Optimization of a Millimetre Wave Compact Folded MagicT", International Journal of Antennas and Propagation, vol. 2012, Article ID 838962, 6 pages, 2012. https://doi.org/10.1155/2012/838962
Design and Optimization of a Millimetre Wave Compact Folded MagicT
Abstract
A millimetre wavefolded magicT junction compensated with metal cone is designed using a particle swarm optimization (PSO) algorithm. An offcentred metallic frustum was used to enhance the bandwidth and a metallic post is used to compensate the mismatched Earm. The geometrical parameters of the frustum and the post are optimized by PSO. The optimized magicT for Wband application is designed and tested. The design features are simple in structure and easy to fabricate. The 2% bandwidth with centre frequency of 94 GHz and return loss less than −20 dB is achieved.
1. Introduction
In communication and radar systems, waveguide junction components, such as couplers, magicTs, and orthogonal mode transformers (OMTs) have been used widely. MagicT features good isolation and power dividing performance, thus plays a key role in monopulse radar systems [1]. There have been various analyses of waveguide Tjunctions using FDTD/matrix pencil method [2] and BCMM method [3]. FEM [4] and MoM [5] analysis of magicT and folded magicT compensated by offset metallic post of arbitrary height have also been reported. However, conventional methods require long computation time, and these magicTs demonstrate a narrow bandwidth at each port with return loss less than −20 dB. Recently, particle swarm optimization (PSO) was introduced in the optimization of electromagnetic problems [6]. Compared with conventional methods, PSO features fast convergence rate and the capability for multiple parameters. An Xband waveguide magicT compensated by a stepping conducting cone was reported recently [7]. However, due to the reduction in size, it is very difficult to fabricate the stepping cone at Wband.
This paper presents the design and optimization of a millimetre folded waveguide magicT junction compensated with an offcentred metallic frustum in the cavity region and a metallic post in the Earm. A threedimensional finite element method (FEM) is used to compute the scattering parameters of each port of the proposed magicT, and the calculated results were then sent to PSO code to evaluate the fitness. The PSO algorithm adjusts and updates the parameters accordingly until all parameters were optimized. The optimized folded magicT junction was simulated and tested at Wband applications and demonstrated an over 2% −20 dB reflection bandwidth. The design, optimization, and the measured performance of the proposed folded magicT are described in the following.
2. MagicT Design
The configuration of the proposed folded magicT is shown in Figures 1 and 2. Ports 1 and 4 are E and Harm waveguide portsrespectively, and ports 2 and 3 are two branch waveguide ports. The structure consists of four waveguide ports, a waveguidefolded T junction, a metallic frustum in the cavity region, and a metallic post in the Earm.
(a)
(b)
(a)
(b)
As magicT junction itself is inherently mismatched; it requires compensation units. Here, a metallic frustum was employed to achieve complete impedance matching in the Harm and halfimpedance matching in the Earm, while a metallic post is employed to provide complete impedance matching of the Earm.The frustum structure can effectively enhance the bandwidth performance of all the four ports. A detailed profile of the frustum and the post is shown in Figures 1(b) and 2(b). The optimization parameters of the E and Hplanefolded magicT are the bottom and top radiuses of the frustum, the offcentre distance, the height, the radius, and position of the post.
As for Eplanefolded magicT, the main waveguide is placed directly under the Eplane branch, and a 45 degree cutoff is used to match the impedance at the mitred corner, as shown in Figure 3. The length of the cutoff L is 0.9b [8], and the radius of inner corner is preoptimized as 0.5 mm. The frustum is placed in the cavity region of the main waveguide to provide impedance matching to both E and Hplane branch. As for Hplanefolded magicT, a waveguide taper is employed to ensure enough space for compensation units in the cavity region; also, as shown in Figure 3, the length of the taper l is optimized with the frustum. In both Eplane and Hplane magicT, the design consists of two steps: first, the Harm is fully compensated by the frustum and the Earm is partly compensated; second, the Earm is fully compensated by the offcentre metallic post. Capacitive posts reflect the electric field more effectively than inductive posts, but the latter is only half the length of the former and given the very small radius, which is easier to manufacture and more stable in performance thus is used in both the two folded magicTs.
3. Optimization
Wband standard waveguides with the size of mm and mm were used to implement the magicT. First, only the parameters of the frustum were optimized; as shown in Figure 1, there are four parameters: the radii of upper and lower section, the offset length, and the height. The modal is simulated by commercial software HFSS, and the results were fed into PSO MATLAB program with the optimization goal set to dB within the frequency range of 93 to 95 GHz. VB (Microsoft Visual Basic) script is employed to connect the MATLAB and HFSS simulations in such an iteration that the initial model parameters in the script are simulated in HFSS to get an Smatrix, which is sent to the MATLAB to evaluate the fitness function and update the model parameters, and finally the updated model parameters are fed back into HFSS to get a renewed Smatrix. This iteration will carry on until the Smatrix values meet the set goals.
According to PSO algorithm, the parameters were updated using the following rule: The constants and are 1.494, and the weighting term decreases from 0.729 to 0.6 with 50 iterations. After the Hplane waveguide branch was optimized, the post was added to the Earm without entering the cavity region of the main waveguide. The post radius and offset coordination in  and axes were optimized using the same equation. The total number of parameters optimized was seven. As for Hplanefolded magicT, the taper length was also optimized in the first step; there was one more parameter.
4. Results
The optimized parameters were obtained after 87 iterations for Eplanefolded magicT and 102 iterations for Hplanefolded magicT. The total simulation time on an Intel Core 2 2.1 GHz computer is 12.5 hours (frequency sweep step set to 0.1 GHz). However, a gradient method of the Quasi Newton optimizer is adopted in the HFSS; it suffers from the possible presence of local minima and numerical noise. It is nothing but dB with 44.25 computing hours. Table 1 shows the final results of all parameters after the PSO process.

Figure 4 shows the simulated reflection coefficients of the halfcompensated Eplanefolded magicT (only frustum and without post). It shows that the frustum alone has fully matched port 3 (Harm) in the frequency range of 92 GHz~96 GHz, and the Earm is only halfcompensated. Figure 5 shows the reflection coefficients after the post is added. The reflection coefficients of all ports are below −20 dB with 2.7% bandwidth. Figures 6 and 7 show the transmission and isolation coefficients, as well as the phase characteristics of EFMT. The power from E or Harms is divided equally into two ports of the main waveguide, and the phase difference is, respectively, 0 and 180 degrees. Similarly, Figures 8, 9, and 10 show the reflection, isolation, and transmission coefficients, as well as the measured return loss of the fully compensated sumdifference device with horn. The bandwidth with dB of the HFMT is 2.1% with the centre frequency of 94 GHz. The magnitude differences of the transmission coefficients of the two main waveguide ports within 0.1 dB, and measured ports return losses of the compensated sumdifference device with horn are less −15 dB, respectively.
An inverse Cassegrain antenna at millimeter waveband with the sumdifference network comprised of the proposed folded magicT were also fabricated and tested. Figure 11 shows the photo of sumdifference device with horn. Figures 12 and 13 show the tested sum and difference beam, compared to the gain of a standard horn antenna. The antenna shows good gain and beamwidth characters in the frequency band of 93 to 95 GHz, as well as an acceptable null depth (<−30 dB). However, due to the limitations of the fabrication precision, frequency shift is observed.
5. Conclusions
A HFSS (Ansoft) and PSO (Matlab) cooperating simulation was utilized to optimize waveguide magicT junctions. The simulation time has been reduced effectively due to the fast convergence feature of PSO. A novel Wbandfolded magicT compensated by a frustum and a metallic post was designed. The compensational units were simple in structure and easy to fabricate, and the operation bandwidth reaches more than 2.0% with the center frequency of 94 GHz. Compared with other 94 GHz magicT for monopulse radar applications, this design effectively enhanced the bandwidth and still maintains good performance ( dB) among all ports. The inversed Cassegrain antenna with sum and difference network comprised of the proposed folded magicT has been tested and has shown narrow beamwidth, high gain, and acceptable null depth of the difference beam, thus proved the proposed design to be feasible in millimeter monopulse applications.
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Copyright
Copyright © 2012 Guang Hua et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.