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EFFICIENCY COMPARISON OF THE OPTIMIZATION METHODS THAT ARE USED TO DESIGN MICROWAVE FILTERS

Автор Доклада: 
V. Tyurnev
Награда: 
EFFICIENCY COMPARISON OF THE OPTIMIZATION METHODS THAT ARE USED TO DESIGN MICROWAVE FILTERS

UDC 621.372.543.2

EFFICIENCY COMPARISON OF THE OPTIMIZATION METHODS THAT ARE USED TO DESIGN MICROWAVE FILTERS

Tyurnev Vladimir, DSc, Prof.
Kirensky Institute of Physics


Efficiency and accuracy of optimization methods are tested by the example of two bandpass filters of the sixth order. One of the filters comprises three dual-mode resonators. Testing shows that the intelligence optimization method is the most fast and accurate method. Its employment in bandpass filter design does the stage of direct parameter synthesis to be unnecessary.
Keywords: Computational efficiency, design, microwave filters, optimization methods.

1. INTRODUCTION
Design of microwave filters is usually fulfilled in two main stages. The first stage is a direct parameter synthesis and the second stage is optimization.
A direct parameter synthesis of a filter is usually based on any proper equivalent filter circuit, coupling coefficients or coupling matrix. The synthesis method may greatly vary depending on the filter structure. Most synthesis methods need in preliminary laborious manual studies of a pair of the coupled resonators. All synthesis methods are approximate especially when the passband width is not rather narrow. Therefore, optimization is an inherent stage of filter design.
Usually microwave simulation software products are used for optimization of microwave filters. Most of software products contain a few utilities using different standard optimization methods. These methods are universal. They may be applied both to filters and to other devices. However, efficiency and accuracy of those methods in filter design may vary considerably.
There are special optimization methods that are used only for microwave filter design [1–4]. One of them is the intelligence optimization method using a priori knowledge. It is exploited in the expert system Filtex32, intended for automated design of strip line and microstrip bandpass filters [5].
In this paper, efficiencies of various optimization methods that are exploited in microwave software products for bandpass filter design are compared.
2. OPTIMIZATION TESTS
We choose two different symmetrical constructions of microstrip bandpass filters of the sixth order to compare efficiency of optimization methods.
The construction of the first microstrip filter contains six parallel-coupled regular resonators. Its terminal resonators have input and output tappings. A layout of the first construction is illustrated in Figure 1.

Layout of the first microstrip filter and its adjustable parameters


Figure 1. Layout of the first microstrip filter and its adjustable parameters

Goal of optimization for the first construction is to synthesize a bandpass filter with the fractional bandwidth of 11 % and the midband frequency of 4 GHz. All five maximums of reflected power in the pass band are to be at the level of ?14 dB. Thus, the goal is specified with seven requirements.
Before each optimization start, the first construction has the same structure parameters, corresponding to the pass band with the fractional bandwidth of 10 %, the midband frequency of 4 GHz, and reflection maximums at the level of ?14 dB. Seven adjustable geometrical parameters are denoted in Figure 1. They are constrained during optimization. Boundaries cover both initial and optimal values of adjustable parameters. Upper boundaries are twice as lower boundaries. Every optimization session is repeated ten times.
The optimization results for the first construction are presented in Table 1. Here is a mean error of the optimization. It is equal to maximum deflection of reflection maximums from the specified level of ?14 dB. The standard deviation of x from is denoted as ?. Nonzero value of ? says that the optimization process varies from one session to another session. The dash in the table means that the optimization fails. Empty cell means that the optimization session has terminated ahead of schedule. The number of iterations means the number of frequency response computations.
Results in Table 1 say that the special intelligence optimization method is the most fast and accurate method. On the contrary, all standard universal optimization methods need in extremely large amount of frequency response computations for usual filters. At those, the error of universal optimization slow decays with increase of iteration number.

Optimization Results for the firts filter construction

The construction of the second microstrip filter contains three hairpin dual-mode stepped-impedance resonators [6]. One wide internal end of the folded terminal resonators and both ends of the twice-folded middle resonator are grounded. The terminal resonators have input and output tappings. A layout of the second construction is illustrated in Figure 2.

Layout of the second microstrip filter and its adjustable parameters


Figure 2. Layout of the second microstrip filter and its adjustable parameters

Dual-mode behavior of the resonators in the filter is achieved with folding and width stepping of their strip conductors. Properties of such the filter have been described in [7]. Here the intelligence optimization method has been proposed too.
Goal of optimization for the second construction is to synthesize a bandpass filter with the fractional bandwidth of 70 % and the midband frequency of 0.5 GHz. As before, all five maximums of reflected power in the pass band are to be at the level of ?14 dB. Thus, the goal for the three-resonator construction is specified with seven requirements too.
Initial values of the geometrical parameters are chosen to be equal to parameter values of the synthesized filter, which has the fractional bandwidth of 80 %, the midband frequency of 0.5 GHz, and reflection maximums at the level of ?14 dB. Notation of adjustable geometrical parameters are shown in Figure 2. There are nine of them, i.e. they are two more than goal requirements. Therefore, the chosen adjustable parameters have two extra degrees of freedom, which can be enabled to avoid disproportionate optimization solutions [7].
The optimization results for the second construction are presented in Table 2. Here are used the same notations as in Table 1.

Optimization results for the second filter construction

Results in Table 2 say that the special intelligence optimization method for the dual-mode filters remains the fastest and most accurate method. All standard universal optimization methods are too inaccurate and too slow to be used for optimization of dual-mode filters.
3. CONCLUSION
All standard universal optimization methods are rather slow and not quite accurate methods for microwave filter design. They are unsuited for design of complicated dual-mode filters.
The special intelligence optimization method is the most suitable optimization method for microwave filter design. It combines fast optimization convergence with high optimization accuracy.
Application of the intelligence optimization method in design of bandpass microwave filters, due to its fast convergence, allows excluding the laborious stage of direct parameter synthesis [5].

References:
1. Belyaev, B. A., M. I. Nikitina, V. V. Tyurnev, “Effective method of microwave filter optimization,” (in Russian), Proc. 1997 IEEE – Russia Conf.: MIA-ME’97, Novosibirsk, 1997, pp. 104–109.
2. Belyaev, B. A., V. V. Tyurnev, “Correction method for structure parameters in microstrip filter design,” (in Russian), Izvestiya vuz. Fizika, vol. 49, no. 9, Supplement, pp. 164–167, Sept. 2006.
3. Belyaev, B. A., V. V. Tyurnev, “The method for microstrip filters parametric synthesis,” Proc. 16th Int. Crimean Conf. Microwave and Telecommunication Technology: CriMiCo'06, Sevastopol, 2006, vol. 2, pp. 517-519.
4. Amari, S. C., LeDrew, and W. Menzel, “Space-mapping optimization of planar coupled-resonator microwave filters,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 5, pp. 2153–2159, May 2006.
5. Belyaev, B. A., S. V. Butakov, N. V. Laletin, А. А. Leksikov, V. V. Tyurnev, “Expert system FILTEX32 for computer-aided design of bandpass microstrip filters,” Proc. 15th Int. Crimean Conf. Microwave and Telecommunication Technology: CriMiCo'05, Sevastopol, 2005, vol. 2, pp. 504-505.
6. Dovbysh, I. A., V. V. Tyurnev, “Microstrip broad-bandpass filter,” RU Patent 2401490, Oct. 10, 2010.
7. Dovbysh, I. A., V. V. Tyurnev, “Synthesis and investigation of three-section microstrip filter on folded dual-mode stepped-impedance reso­nators,” Progress In Electromagnetics Research M, vol. 12, pp. 17–28, 2010.

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Рассматриваемые в статье

Рассматриваемые в статье методы оптимизации ,используемые для проектирования СВЧ фильтров и предложенный выбор методов оптимизации по критериям быстроты и точности, безусловно представляют научный и практический интерес.Применение предложенных методов оптимизации позволит решать актуальную проблему уменьшения трудозатрат при проектировании полосовых СВЧ фильтров.
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