# 3D FEM and EM Simulations for DRFs

#### A high frequency structure simulator is used to compute the 3-D structure of a microwave dielectric resonator (DRF) in a rectangular metallic enclosure

Three-dimensional (3D) fullwave analysis of a microwave dielectric resonator filter (DRF) in a rectangular metallic enclosure is presented. By using a 3D finite-element method (FEM) to perform numerical simulations, parameters and predictions that are difficult to measure but actually affect the performance of a microwave DRF can be accurately determined. In the process, a significant phenomenon was uncovered. The numerical results are in agreement with the experimental measurements.

Due to its desirable properties such as small size, low cost and good temperature stability, a DR not only acts as a frequency determination element but also offers high stability.^{1,2} Analysis methods of the inner electromagnetic properties of applied DR devices such as the perfect magnetic conducting wall method,^{3} the moment method based on the surface integral techniques^{4,5} and general mode matching approaches^{6,7} have been studied. Although the E-field and H-field attributes inside a microwave DRF are hard to observe, an accurate analysis of the overall inhomogeneous structure is inevitably required for practical design and application considerations.

With the advancement of computer hardware and software, numerical techniques enable us to perform more rigorous and complicated analysis on 3D structures. Two- and three-dimensional finite-element methods applied for microwave DRF simulation have been previously reported.^{8,9} In those articles, DRFs coupled by coaxial probes were numerically simulated in the TM_{01*} mode with a cylindrical DR placed along the central axis. In addition, a 3D FEM simulation of a DR coupled to microstrip lines in a DRF was studied by Chuang, et al.^{10} for various dielectric constants.

This article deals with excitation in the TE_{01*} mode, the highest Q value among all resonant modes of a cylindrical DR coupled to microstrip lines. The Ansoft^{®} 3D FEM CAD tool of the high frequency structure simulator (HFSS) was used to compute the 3D structure of the DRF.

DRF DESIGN AND FABRICATION PROCEDURES

The coupling coefficient between DRs and the external coupling Q factor of a resonator to a microstrip line have been clearly described by Sun, et al. ^{2} The design and fabrication procedures of a DRF are briefly described as follows: First, the size of metal cavity and DRs are chosen from bandpass filter (BPF) specification requirements; next, the theoretical external Q and coupling coefficients of the desired BPF are determined, along with the external Q values and coupling coefficients (k_{j,j+1} ); finally, the DRF is assembled in the metallic cavity.

The top view of the DRF, shown in Figure 1, indicates two DRs coupled to two straight microstrip lines in a rectangular metallic enclosure. The parameters of the designed DRF are listed in Table 1. Element values of the designed DRF are g_{0 } = 1.0000, g_{1 } = 1.0378, g_{2 } = 0.6745 and g_{3 } = 1.5386 with coupling parameters of Q_{e in } = 58.38, k_{12 } = 0.02125 and Q_{e out } = 58.38,^{2} where Q_{e in} , Q_{e out} and k_{12 } are the external Q factors at the input and output ports and the coupling coefficient between two DRs, respectively.

DRF 3D FEM SIMULATIONS

Generally speaking, it is required to divide the structure into triangular two-dimensional (2D) or tetrahedron (3D) subdomains for EM analyses. FEM was applied to solve Maxwell's equations of the 3D-structured DRF. The FEM tool of Ansoft HFSS for 3D-structure computation was carried out on an HP-9000/735 with a PA-RISC7100 CPU and a 99 MHz clock rate. Figure 2 shows the FEM with 15292 meshes that models the DRF 3D structure. Figure 3 shows the E-field distribution parallel to the X-Y plane of the DRF with two straight microstrip couple lines. It is clear to see that the E-field distribution is not symmetrically centered on the circular plate of the DR dielectrics. Its simulated S_{11} and S_{21} results are shown in Figure 4, which indicates the broaden area of rejection slope on the sideband.

After altering its coupling configuration as shown in Figure 5, the filter's performance is greatly improved. Current distribution on the substrate surface of the DRF is shown in Figure 6, and Figure 7 illustrates the E-field distribution as being almost a symmetrical circle enclosed around the center of DR ceramics. This effective phenomena of the E-field and H-field distribution indicates that a coupled microstrip line with its arc-shaped open-end induces a better symmetrical E-field distribution than just a straight microstrip couple line. It improves the performance of the DRF by allowing most of the E-field energy to be symmetrically stored in the high Q dielectric resonator. Figure 8 shows the H-field vector distribution seen from a cutaway surface parallel to y-axis of the DRF. It obviously demonstrates that the magnetic field vector distribution is the H-field coupling of the TE_{01*} mode that operates like a magnetic dipole mode with magnetic coupling in between. Figure 9 shows the simulated data which is better than the previous performance and in agreement with the measured results.

CONCLUSION

This article has presented a 3D fullwave analysis of a microwave DRF in a rectangular metallic enclosure. By using 3D FEM for numerical simulations, the device's field and current distribution can be visualized in a physical structure to abet the design process. The EM analysis permits accurate parameters and predictions to be determined that are difficult to measure and important for a microwave DRF designer to understand. The article also investigated the 3D electromagnetic and current distributions of the designed DRF with different couple configurations. It was discovered that the performance of the DRF is improved by altering the microstrip coupling structure to an arc shape. The E-field distribution is mostly a symmetrical circle shape around the center of the DR. Obviously, most of the E-field energy is stored in the high Q dielectric resonator in this way. The numerical results of the microstrip DRF are in agreement with experimental performance. *

References

1. D. Kajfez and P. Guillon, Dielectric Resonators, Artech House, 1986.

2. J.S. Sun and Y.L. Huang, "Design and Implementation of an X-Band DR Bandpass Filter," Microwave Journal, Vol. 42, No. 11, September 1999, pp. 92103.

3. Okaya and Barash, "The Dielectric Microwave Resonator," Proceedings of the IRE, Vol. 50, October 1962, pp. 20812092.

4. A.W. Glisson, D. Kajfez and J. James, "Evaluation of Modes in Dielectric Resonators Using a Surface Integral Equation Formulation," IEEE Transactions on Microwave Theory and Techniques, Vol. 31, December 1983, pp. 10231029.

5. A.W. Glisson and D.R. Wilton, "Simple and Efficient Numerical Methods for Problems of Electromagnetic Radiation and Scattering from Surfaces," IEEE Trans. Antennas Propagat., Vol. 28, September 1980, pp. 593603.

6. J. Van Bladel, "On the Resonances of a Dielectric Resonator of Very High Permittivity," IEEE Transactions on Microwave Theory and Techniques, Vol. 23, February 1979, pp. 195208.

7. M. Verplanken and J. Van Bladel, "The Electric Dipole Resonances of Ring Resonances of Very High Permittivity," IEEE Transactions on Microwave Theory and Techniques, Vol. 24, February 1976, pp. 108112.

8. J. Cousty, S. Verdeyme, M. Aubourg and P. Guillon, "Finite Elements for Microwave Device Simulation: Application to Microwave Dielectric Resonator Filters," IEEE Transactions on Microwave Theory and Techniques, Vol. MTT-40, No. 5, May 1992, pp. 925932.

9. D. Baillargent, S. Verdeyme, M. Aubourga and P. Guillon, "CAD Applying the Finite-element Method for Dielectric Resonator Filters," IEEE Transactions on Microwave Theory and Techniques, Vol. MTT-46, No.1, January 1998, pp. 1017.

10. H.R. Chuang, J.W. Huang, C.C. Wei and J.C. Chang, "3D DEM Simulation and Experimental Measurements of Microstrip Dielectric Resonator Filters," Microwave and Optical Technology Letters, Vol. 8, No. 4, March 1995, pp. 196200.

Jwo-Shiun Sun received his BS degree in Electrical Engineering from National Cheng Kung University (NCKU) in 1983. After graduation, he served in the army as a communications officer for two years. He received the MS degree and PhD degree in EE from NCKU in 1988 and in 1992, respectively. Sun is currently a professor with the Dept. of Electronic Engineering in National Taipei University of Technology, Taipei, Taiwan. His research interests are in the fields of microwave devices and circuits, microwave dielectric materials, EM-wave and analyses, and satellite mobile communication.

Jier-Chih Hsieh was born in Taipei, Taiwan, R.O.C, in 1972. He received the BS and MS EECS degrees from National Chiao Tung University in 1994 and 1996, respectively. He was a circuit design engineer for Motorola, Taipei, in 1997. He is now a PhD program student in the Dept. of Engineering and System Science, National Tsing Hua University. His studies involve microwave circuit devices and their applications in telecommunication systems.