TABLE 2 Optimized Dimensions of the Six-Post Filter

To further illustrate this second point, the six-post problem was run ten times with different initial populations for both the CGA and the SGA. The SGA parameters were assumed to be the same as the parameters for the individual part of the CGA, except that the population size was taken as 3500}the total number of individuals in the CGA. The results are shown in Figure 8.

Note that the CGA, on average, converges to slightly better designs than the SGA. Furthermore, the deviation from the average result is lesser in the CGA, showing it to be a more robust algorithm. This is an especially encouraging result, as the run time of the CGA is about half that of the SGA due to its reuse of information. Moreover, although not shown explicitly in the Figures, the best result overall was obtained by the CGA.

There are several possible reasons for the superior performance of the CGA when compared to the SGA. Empirical GA research has shown that for many problems, several GA populations running in parallel with limited interaction between them can often improve convergence w11, 12x. This is often cited as a motivation for parallel GAs. Furthermore, the periodic mutative effect of the community part of the algorithm helps to prevent premature convergence.

Besides these ideas from GA research, however, there are sound electromagnetic engineering reasons why the CGA performs more optimally than the SGA. First, there is the obvious computational benefit of reusing information. More important, however, is the way the CGA uses data. Because the guide lengths between posts primarily set the resonances, the CGA spends most of its time optimizing these lengths. While the SGA population is more diverse than its CGA counterpart, the CGA has the same amount of diversity in the guide length parameters, which are of primary importance.

4. CONCLUSIONS

The community genetic algorithm was introduced and applied to the optimization of in-line, E-plane microwave filters. The analysis of such filters using an equivalent circuit technique was reviewed, and was shown to vastly accelerate the

calculation of the filter parameters. The community genetic algorithm was also shown to aid the convergence and robustness of the optimizations. The technique was demonstrated by application to the design of a four-post and a six-post filter. While this paper concentrated on just the CGA, this algorithm falls into the wider class of domain decomposition GAs, which the authors anticipate will become increasingly important as the need to apply GAs to problems involving computationally intensive objective function evaluations grows.

REFERENCES

1.K. Aygun,¨ D.S. Weile, and E. Michielssen, Design of multilayered strip gratings by genetic algorithms, Microwave Opt Technol Lett 42 1997..

2.R.L. Haupt, An introduction to genetic algorithms for electromagnetics, IEEE Antennas Propagat Mag 37 1995..

3.D.S. Weile and E. Michielssen, Genetic algorithm optimization applied to electromagnetics: A review, IEEE Trans Antennas Propagat 45 1997., 343]353.

4.T. Rozzi, F. Moglie, A. Morini, W. Gulloch, and M. Politi, Accurate full-band equivalent circuits of inductive posts in rectangular waveguide, IEEE Trans Microwave Theory Tech 401992., 1000]1009.

5.Y.-C. Shih, Design of waveguide E-plane filters with all metal inserts, IEEE Trans Microwave Theory Tech MTT-32 1984., 695]704.

6.Y. Konishi and K. Uenakada, The design of a bandpass filter with inductive strip-planar circuit mounted in waveguide, IEEE Trans Microwave Theory Tech MTT-22 1974., 869]873.

7.D.E. Goldberg, Genetic algorithms in search, optimization and machine learning, Addison-Wesley, Reading, MA, 1989.

8.R.E. Collin, Foundations for microwave engineering, McGrawHill, New York, 1992, 2nd ed.

9.D.S. Weile, E. Michielssen, and D.E. Goldberg, Genetic algorithm design of Pareto optimal broad band microwave absorbers, IEEE Trans Electromag Compat 38 1996., 518]524.

10.D.S. Weile and E. Michielssen, Integer coded Pareto genetic algorithm design of antenna arrays, Electron Lett 32 1996., 1744]1745.

11.J.P. Cohoon, S.U. Hedge, W.N. Martin, and D. Richards, Punctuated equilibria: A parallel genetic algorithm, Genetic Algorithms and Their Applications: Proc 2nd Int Conf Genetic Algorithms, 1987.

12.R. Tanese, Distributed genetic algorithms, Proc 3rd Int Conf Genetic Algorithms, 1989.

Q 1999 John Wiley & Sons, Inc.

CCC 0895-2477r99

FDTD INVESTIGATION OF END EFFECT AND MULTISLOT EFFECT ON THE CIRCUMFERENTIALLY SLOTTED COAXIAL ANTENNA

Y. F. Han,1 E. K. N. Yung,1 R. S. Chen,1 and Z. M. Xie1

1 Department of Electronic Engineering City University of Hong Kong Kowloon, Hong Kong

Recei¨ed 10 September 1998

ABSTRACT: The finite-difference time-domain method (FDTD) is first applied to in¨estigate the reflection and radiation properties of a finitely long coaxial antenna with circumferential slots on its outer surface. The end effect and multislot effect intractable for the moment method and

mode-matching method are analyzed efficiently and demonstrated in detail. According to the accurate analysis, the circumferential slots ha¨e a strong influence on the characteristics of the antenna. This effect can be used to effecti¨ely adjust the impedance matching and radiation pattern of the antenna. The ¨erification of the method is also presented by reference to the experiment and the literature. Q 1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 21: 35]39, 1999.

Key words: FDTD method; coaxial antenna; slotted antenna

INTRODUCTION

Due to the flexibility and conformability of the coaxial line, the radiator concerned with the coaxial line has been the focus of interest for several decades. The field radiation and feeding effect of the coaxial antenna have been widely investigated w1]7x. But the majority of these efforts has focused on the thin-form model of the slots and the antenna. The feeding slot is approximated as a delta source or a magnetic current ring, and the solution of radiation is based on the reduced kernel of the integration. These assumptions and approximations are limited to modeling thin wires and narrow slots up to about 0.01l. Beyond this, upon which these techniques are based, they begin to break down. So the strict method is very important to obtain the exact solution for a general coaxial slotted antenna.

Recently, the rigorous analysis of radiation from a circumferential slot on a coaxial line has received much attention. Park and Eom w8x studied the cylindrical edge-slot antenna. Cho et al. w9x approximately calculated and measured the leakage radiation from a circumferentially slotted cylinder. Kiang w10x analyzed the radiation properties of circumferential slots on an infinite coaxial cable with the Galerkin’s as well as mode-matching method. These analyses have broken through the restriction of thin slots or a thin coaxial antenna. But some limitations and problems also exist. First, Hankel functions were commonly used to calculate the outer fields of the cylinder antenna. Although it is convenient to calculate the exterior fields for an infinitely long cylinder, the benefit cannot be easily extended to a finitely long antenna. Second, the analysis assumed a uniform electric field on the slot. The assumption may simplify the analysis, but may bring deviations, especially for a wide slot. Last, but not least, only one slot was considered in a rigorous manner. No rigorous analysis has been presented for multislots on the coaxial antenna. Kiang w11x combined the moment method and transmission line theory to analyze the coaxial antenna with multislots. But he applied the equivalent radiation admittance of a slot on a finite coaxial cable to the case of multislots. The effect of slot coupling cannot be considered in the analysis. Furthermore, slot coupling will be too strong to be ignored, especially in the case of a short coaxial antenna with multislots. Due to the drastic discontinuities in the slots and near the end, conventional methods using a function approximation such as the moment method and mode-matching method become inefficient. In order to circumvent the difficulties, the finitedifference time-domain FDTD. method is applied to analyze the slotted coaxial antenna.

The FDTD method treats Maxwell’s equations directly w12x. The inherent simplicity and adaptability to the complex boundary result in the flexibility to adjust the dimensional parameters. In this paper, the advantage of the FDTD method is exploited to analyze the slotted coaxial antenna. With this method, the interior field of the coaxial line and the exterior field of the coaxial antenna can be treated in a generalized