New Design Method of UWB Microstrip Filters Using Adaptive Genetic Algorithms with Defected Ground Structures

The effects of adaptive genetic algorithms (AGAs) and defected ground structures (DGSs) on performance optimization of tapered microstrip filter are investigated. The proposed structure achieves an ultra wide stopband with high attenuation within a small surface area, as well as 45% smaller size, in comparison with conventional filters. The parameters of the filter are optimized using in-home AGA code. In the proposed AGA algorithm, the crossover and mutation probabilities are adaptively changed according to the value of individual fitness. Then by utilizing the proposed DGS, a compact S-band low-pass filter with ultra-wide spurious free window is obtained. The proposed filter achieves an insertion loss of 0.8 dB from DC up to 4 GHz and 21 dB rejection in the stopband from 4.3 up to 60 GHz. The fabricated and measured results exhibit good agreement with the simulated results. They demonstrate that combining AGA and DGS yield best possible response for this group of filters.


I. INTRODUCTION
In practice, high-performance microwave filters with minimized size and weight are playing an important role for design and fabrication of high-efficiency miniaturized microwave systems. Recently, due to high demand for broad band services, design of such miniaturized wide and ultrawide stopband filters for interference cancellation (by means of out of-band signal suppression) is gaining more and more attention [1][2][3][4]. Non-uniform transmission lines (NUTLs) play an important role in microwave circuits.
Applications include impedance transformation & matching, filters and directional couples. The non-uniform line is traditionally analyzed in the frequency domain [5][6][7].
Genetic algorithms are widely employed in various fields such as optimal engineering designs. They have been successfully applied to finding the global optimum in a variety of unimodal domains. Parameter control methods are classified as deterministic and adaptive. Deterministic systems employ fixed, predefined parameters for GA. On the other hand, adaptive control uses feedback from the search process to find out how the parameter values change [8][9].
Many researchers have proposed and demonstrated electromagnetic bandgap (EBG) microstrip structures to achieve compact and wide frequency stopband [10][11][12]. Also recently, DGSs have become one of the most interesting areas of research in modern communication systems [13][14][15][16]. The DGS was first proposed by Kim et al. [17]. The An approximation theory, based on small reflections is used to predict the reflection coefficient response as a function of impedance taper Z(z) as follows (see [18]).  Fig. 1. The structure can be simulated more precisely using tapered sections. Therefore, the tapered sections are used for filter modeling [19][20].

III. ADAPTIVE GENETIC ALGORITHMS
In this section the optimization of the filter specifications using adaptive genetic algorithms [21][22][23] is introduced. The behavior of genetic algorithms is strongly influenced by the balance between exploration and exploitation. The GA control parameter settings, such as mutation and crossover probabilities (denoted m P and c P , respectively) and the 3 population size, are key factors in the determination of the exploitation versus exploration tradeoff. If poor settings are used, the exploration/exploitation balance may not be reached in a profitable way; the GA performance is severely affected due to the possibility of premature convergence.
Finding robust control parameters is not a trivial task since their interaction with GA performance is a complex relationship and the optimal ones are problem dependent.
where 11 S and 21 S are the worst points in the stopband and passband regions, respectively.
As the signal's frequency applied to millimeter-wave integrated circuit is steadily increased, some characteristic frequency may be reached at which undesirable effects occur. The same is true for monolithic integrated circuits.   Table I     In another optimized structure, we present a more compact design of the ultra-wide stopband lowpass filter. Fig. 8 illustrates the dimensions and frequency response of the optimized compact filter. According to its specifications, a conventional 10th order Chebyshev stepped-impedance lowpass microstrip filter is designed and optimized by Agilent ADS 2008 to highlight the performance of the optimized filter. The conventional Chebyshev filter has 32mm length while the optimized filter's length is less than a half-wavelength (i.e., 17mm). The optimized compact filter has sharper band edge and deeper and wider stopband. In this case, the stopband peak is less than -21 dB from 4.3 up to 60 GHz. As mentioned earlier, a compact deep attenuation and spurious-free filter is achieved by this method. The dimensions of the new DGS configuration are demonstrated in Fig. 8 (a) and Table I. One of the interesting results of using such structures is the ability to set up the cutoff frequency of these filters up to hundreds of MHz only by displacing a few millimeters of the DGSs with respect to their current positions as shown in