диафрагмированные волноводные фильтры / bbcd2c19-e68c-4a1e-acb6-c22510756fa9

Applications of Arti¯cial Neural Network Techniques in Microwave Filter Modeling, Optimization and Design

H. Kabir1, Y. Wang2, M. Yu2, and Q. J. Zhang1

1Department of Electronics, Carleton University, Ottawa, Ontario, Canada

2COM DEV Ltd., Cambridge, Ontario, Canada

Abstract| This paper reviews state-of-the-art microwave ¯lter modeling, optimization and design methods using arti¯cial neural network (ANN) technique. Innovative methodologies of using ANN in microwave ¯lter analysis and synthesis are discussed. Various ANN structures including wavelet and radial basis function have been utilized for this purpose. ANN also ¯nds application in ¯lter yield prediction and optimization. The results from di®erent work demonstrate that ANN technique can reduce the cost of computation signi¯cantly and thus can produce fast and accurate result compared to the conventional electromagnetic (EM) methods.

DOI: 10.2529/PIERS060907172141

Microwave ¯lters are widely used in satellite and ground based communication systems. The full wave EM solvers have been utilized to design these kinds of ¯lters for a long time. Usually several simulations are required to meet the ¯lter speci¯cations which takes considerable amount of time. In order to achieve ¯rst pass success with only minor tuning and adjustment in the manufacturing process, precise electromagnetic modeling is an essential condition. The design procedure usually involves iterating the design parameters until the ¯nal ¯lter response is realized. The whole process needs to be repeated even with a slight change in any of the design speci¯cations. The modeling time increases as the ¯lter order increases. With the increasing complexity of wireless and satellite communication hardware, there is a need for faster method to design this kind of ¯lters. Arti¯cial neural network (ANN) or simply neural network (NN) has been proven to be a fast and e®ective means of modeling complex electromagnetic devices. It has been recognized as a powerful tool for predicting device behavior for which no mathematical model is available or the device has not been analyzed properly yet. ANN can be trained to capture arbitrary input-output relationship to any degree of accuracy. Once a model is developed it can be used over and over again. The trained model delivers the output parameters very quickly. This avoids any EM simulation where a simple change in the physical dimension requires a complete simulation. For these attractive qualities, ANN has been applied to di®erent areas of engineering and biomedical. While the present state of the art neural network modeling technique for EM modeling and optimization is available in detail in [1{3], it is beyond the scope of this paper. This paper reviews the ANN techniques dealing with microwave ¯lter.

Waveguide cavity ¯lters are very popular in microwave applications. Several results have been reported using neural network techniques to model cavity ¯lters including E-plane metal-insert ¯lter [4], rectangular waveguide H-plane iris bandpass ¯lter [5{8], dual mode pseudo elliptic ¯lter [9], cylindrical posts in waveguide ¯lter [10] and etc. The simplest form of modeling is the direct approach where the geometrical parameters are related to its frequency response. Response of a ¯lter is sampled at di®erent frequency points to generate the training data. Result shows that ANN can provide accurate design parameters and after learning phase the computational cost is lower than the one associated with full wave model analysis [4]. In a similar work the performance of ¯lter obtained from the ANN was much better than obtained from parametric curve and faster than ¯nite element method (FEM) analysis [5].

Simpler structure or lower order ¯lter is feasible to realize the whole model in a single NN model. For higher order ¯lter several assumptions and simpli¯cations are required to lower the number of NN inputs. Filter can be modeled by segmentation ¯nite element (SFE) method and using ANN [6]. Filter structure was segmented into small regions connected by arbitrary cross section and then the smaller sections were analyzed separately. The generalized scattering matrix (GSM) was computed by FEM and the response of the complete circuit was obtained by connecting the smaller sections in proper order. In general the optimization of microwave circuits is time consuming. To attain a circuit response by analytical method is too slow. Therefore, ANN based analytical models were used. The method was applied to a three-cavity ¯lter. The response of the ¯lter rigorously found

from SFE was compared with the same response obtained from the GSMs of the irises computed from ANN and excellent agreement was observed. In similar approach smooth piecewise linear (SPWL) neural network model can be utilized for design and optimization of microwave ¯lter [7]. SPWL has the advantage of smooth transitions between linear regions through the use of logarithm of hyperbolic cosine function. This feature suits well for the inductive iris modeling. A rectangular waveguide inductive iris band pass ¯lter was modeled using SPWL neural network model. Several multi section Chebyshev band pass ¯lters in di®erent bands have been tested and each showed very good agreement with full 3D electromagnetic solution. Again using the NN speeds up the design process signi¯cantly.

Waveguide dual-mode pseudo-elliptic ¯lters are often used in satellite applications due to its high Q, compact size and sharp selectivity [11]. Recently NN modeling technique has been applied to design wave-guide dual-mode pseudo-elliptic ¯lter [9]. The coupling mechanism for dual mode ¯lters is complex in nature and the numbers of variables are quite high. This makes the data generation and NN training an overwhelmingly time-consuming job. Therefore, ¯lter structures were decomposed into di®erent modules each representing di®erent coupling mechanism. This ensures faster data generation, NN training and better accuracy. This model may be applied to ¯lter with any number of poles as long as the ¯lter structure remains the same. Due to the coupling between orthogonal models, GSM of the discontinuity junctions in the ¯lter is necessary to characterize most of the modules. Equivalent circuit parameters such as coupling values and insertion phase lengths were extracted from EM data ¯rst. Neural network models were then developed for the circuit parameters instead of EM parameters. The method was applied to a four pole ¯lter with 2 transmission zeros. The ¯lter was decomposed into three modules: inputoutput coupling iris, internal coupling iris and tuning screw. NN models were developed for each module and irises and tuning screw dimensions were calculated using the trained NN models. The dimensions found from the NN models are within 1% of the ideal ones.

The other popular type of microwave ¯lters is built in planar con¯guration such as microstrip and strip line. Numerous works have been published modeling microwave ¯lters using ANN including low pass microstrip step ¯lter [12], coupled microstrip band pass ¯lter [13{22], microstrip band rejection ¯lter [23], coplanar waveguide low pass ¯lter [24] etc. The trained neural networks become fast ¯lter model so that a designer can get the parameters quickly by avoiding long EM simulations. Wide bandwidth band pass ¯lters were designed using microstrip line coupling at the end [14]. Coupling gaps are critical for designing these kinds of ¯lters and the optimization of gaps require signi¯cant amount of time. To speed up the optimization of coupling gaps ANN models were developed and these models were used to design a ¯lter. For a given ¯lter speci¯cations, physical parameters were obtained using ANN models. With these physical dimensions the ¯lter was analyzed using a circuit simulator. A signi¯cant improvement in terms of speed has been realized using ANN models. The method can be generalized for low-pass, high pass, band pass or band rejection ¯lters using planar con¯guration. A little modi¯cation is needed if the structure of the ¯lter is changed from microstrip to strip line, but the general process remains the same. ANN models can be developed to model the entire ¯lter if the number of variables is kept low. For larger dimensions some parameters are kept constant to keep the model simple.

Multi-layer asymmetric coupled microstrip line has been modeled using ANN [16]. The ANN replaces the time-consuming optimization routines to determine the physical geometry of multiconductor multi-layer coupled line sections. ANN models for both synthesis and analysis were developed. The methodology was applied to a two layer coupled line ¯lter and compared with segmentation and boundary element method (SBEM). Circuit elements were obtained much faster by ANN models than the optimization method. Circuit parameters can also be used as modeling parameters for this kind of ¯lter. For all these cases ANN models are capable of predicting the dimensions or circuit parameters accurately compared to that obtained from the analytical formulas.

Microstrip ¯lter on PBG structure were also designed using neural network models [17]. A new NN function called sample function neural network (SFNN) was employed for the modeling purpose. The PBG structures are periodic structures that are characterized by the prohibition of electromagnetic wave propagation at some microwave frequencies. A 2 dimensional square lattice consisting of circular holes were considered as the modeling problem. Radius of the circle of the periodic holes and frequency was input and s-parameters were considered as output of the neural network. Regular MLP was unable to converge to right solutions. RBF and wavelet functions improved the result but it was not accurate enough. Due to these reasons a new activation function called the sample activation function were used. The result shows that the SFNN can produce complex

input-output relationship and could model the PBG ¯lters on microstrip circuits accurately. Neural network has been combined with some other optimization process in order to achieve ¯lter

design parameters quickly. A design technique combining ¯nite-di®erence-time domain (FDTD) and neural network was proposed [19]. Two-stage time reduction was realized by utilizing an autoregressive moving-average (ARMA) signal estimation technique to reduce the computation time of each FDTD run and then the number of FDTD simulations was decreased using a neural network as a device model. The neural network maps geometrical parameters to ARMA coe±cients. The trained network was incorporated with an optimization procedure for a microstrip ¯lter design and signi¯cant time saving was achieved. Di®erent algorithms can be developed combining NN and optimization method for faster and accurate ¯lter solution. A Neuro-genetic algorithm was developed for microwave ¯lter [20]. NN models were combined with genetic algorithms to synthesize millimeter wave devices. The method has been used to synthesize low pass and band pass ¯lters in microstrip con¯guration. While the method worked well for low pass ¯lters it showed limited accuracy for band pass ¯lter. In order to overcome the problem some modi¯cation is required in the layout and design space.

Wavelet neural network (WNN) [22] and radial basis function (RBF) [12] can be advantageous for some special applications. Wavelet radical and the entire network construction have a reliable theory, which can avoid the fanaticism of network structure like back propagation (BP) NN. Also it can radically avoid the non-linear optimization issue such as local most optimized during the network training and have strong function study and extend ability. For these qualities WNN was chosen in [22]. Microstrip band pass ¯lter was optimized where the geometrical parameters were changed to obtain the desired output response. The result was compared with that obtained using ADS optimizer. Fast and accurate results were obtained. In a similar work, radial basis function neural networks (RBF-NN) were used to model microstrip ¯lter. Segmentation of the structure was employed for a 13 sections microwave step ¯lter. Using the RBF-NN shows much faster and better accurate result than full wave analysis.

NN also ¯nds applications in the design of microwave ¯lters consists of dielectric resonator [25]. A rigorous and accurate EM analysis of the device was performed with FEM and combined with a fast analytical model. The analytical model was derived using segmented EM analysis applying to neural network. The method was then applied to dielectric resonator (DR) ¯lters and good agreement between theoretical and experimental result has been achieved within a few iterations.

NN has been employed to obtain starting point for optimizer used for yield prediction algorithm [26]. The yield was computed as a ratio of the number of cases passing the speci¯cation to the total number of simulations performed. For e±cient calculation of yield, the choice of starting point is critical. It requires the knowledge of ¯nal solution, which is not available. Neural network was used to predict this solution and then the solution was used as the starting point of the optimization. Di®erent structures realizing the same response was used to calculate the yield. Result suggests that by using neural network models, computational e®ort can be reduced signi¯cantly.

In conclusion this paper has reviewed the role of ANN in microwave ¯lter modeling, optimization and design. The ANN method provides fast and accurate results and reduces the computational costs associated with a time consuming EM solver in the design of microwave ¯lters. These methods can be used in combination with standard ¯lter design methods to design complex microwave ¯lters. It helps to improve the speed and accuracy of ¯lter design for communication circuit and systems.

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