диафрагмированные волноводные фильтры / 5c6ed324-4fef-4627-bc3e-9a02603a6a5f

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J. of Electromagn. Waves and Appl., Vol. 20, No. 8, 1061–1069, 2006

DESIGN E-PLANE BANDPASS FILTER BASED ON EM-ANN MODEL

L. Jin, C.-L. Ruan, and L.-Y. Chun

College of Physical Electronics

University of Electronic Science and Technology of China Chengdu 610054, P. R. China

Abstract—A novel design method has been developed for E-plane bandpass filter synthesis based on an electromagnetic artificial neural network (EM-ANN) model. EM-software analysis is employed to characterize an E-plane strip. The EM-ANN model is then designed by exchanging the EM-software input/output. The filter is designed without finding the physical parameters by solving equation. A W- band E-plane bandpass filter is designed by this method, the insertion loss of which is less than 1.5 dB, and the center frequency is 94 GHz with a bandwidth of 4 GHz.

1. INTRODUCTION

E-plane waveguide filters has been widely used at millimeter-wave frequency because they have many favorable properties such as simple structure, low passband insertion loss, easy to mass production. Thereafter, except for all-metal insert [1, 2], it expanded to singleridge finline [3], double-ridge finline [3], large gap finline insert structures [4]. Accordingly, a kind of analysis and design techniques, such as variational technique [1] residue-calculus technique [2] , and mode-matching method [2], were developed. Among them, modematching method is the most e ective for simple structure E-plane filters [5]. However, it requires very sophisticated theoretical analysis and complicated programming for di erent structures and it is even impossible for some irregular structures.

At present, ANN models are widely used in EM modeling [6, 7]. They provide the same accuracy as the EM simulation and the same speed as the equivalent circuit computation means. In most EM-ANN models, frequency and physical dimensions of structure are adopted as input variables, and S-parameters/equivalent circuit

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parameters as output variable. But this scheme is not suitable for circuit synthesis because it requires the transformation from the needed network parameters to practical size. For the sake of facilitating the circuit synthesis design, physical dimensions of structure are adopted as output variables, and then the best filter size can be gotten directly.

2. EQUIVALENT CIRCUIT AND EM-ANN MODEL FOR E-PLANE STRIP

w1 L1 w2 L2 …

Figure 1. The structure of E-plane bandpass filter.

The structure of E-plane filter is shown in Fig. 1. It is comprised of a rectangular waveguide and some metal sheets or metal sheets with substrate support located at the E-plane (TE10 mode) of the waveguide. A single metal sheet is shown in Fig. 2a. Whether or not the substrate is present, the single metal sheet can be treated as a T-type equivalent inductor network in Fig. 2b. Assuming a TE10-type incident wave, the exited fields are composed of the TEn0-type waves [8]. All of higher modes are localized around the E-plane strips. They are evanescent modes so only dominant S-parameters are taken into consideration. The dominant mode scattering parameter elements are denoted S11, S12, S21, S22. According to two-port network theory, we can get

where Xs, Xp are both normalized by waveguide characteristic impedance. A shunt inductor with inductance far less than the

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Figure 2. Equivalent circuit for a E-plane strip.

transmission line characteristic impedance can be characterized by the equivalent impedance inverter with a pair of negative electrical length transmission line [3]. So the E-plane strip is transformed into the equivalent circuit in Fig. 2c. The parameters have relationships as follow:

The S-parameters of regular E-plane strips can be calculated by mode-matching method. Then the parameters of the equivalent circuit elements can obtain easily. When the structure of the E-plane strip is complicated, for example, the strips are embedded in the wall of the waveguide or when a few of medium substrate layers are involved, it is di cult to analyze by mode-matching method. But the complicated structure can be simulated easily by commercial 3D EM simulation software, such as CST Microwave Studio r . Although the software can not be used to synthesize the E-plane filter and is rather timeconsuming in optimizing computation, it can establish training samples for the EM-ANN model of the E-plane strip. The trained EM-ANN model is conveniently used for filter synthesis.

The parameters of E-plane strip equivalent circuit depend on many factors, such as work frequency, substrate permittivity and thickness, the localization and depth embedded in the waveguide wall, and its dimensions. Generally the operating frequency band determines the standard rectangle waveguide selection. It is supposed that only the width of the strip is unknown variable. Then K and θ are only determined by operating frequency and the width of strips. This relationship can be approximated by the EM-ANN model trained with some sample data. We specify an EM-ANN model mapping as follow:

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Usually, the EM-ANN model utilizes frequency and structure parameters as input variables, and the network or equivalent circuit parameters as output variables. However mapping (5) cannot be used to synthesize design filter directly. The K of the impedance inverter for filter synthesis can be found by a distributed stepped-impedance low-pass prototype. Then w can be found by solving equation (5). We can defined a new EM-ANN model mapping in order to facilitate filter synthesis without solving equation as below:

As a result, if K is given by filter prototype, the filter’s structure parameters can be obtained using formula (6) without solving equation.

At present, multilayer perception neural network (MLPNN) is one of the NN models that is in most common use. It generally consists of one input layer, one output layer and one or more hidden layer [9]. In this paper, the EM-ANN model is chosen as a MLPNN with two hidden layers. Once the EM-ANN model frame is determined, it must be trained with enough sample data.

In order to train the EM-ANN model as formula (6), the sample data should be (K, f) as input vector, (w, θ) as output vector in principle. But this will resulted in solving complicated equations. Many kinds of commercial EM simulation software can get S-parameters only if the EM component structure is known. Then the parameters of the equivalent circuit in Fig. 2 can be derived by the S-parameters. In order to get sample data conveniently, (w, f) acts as input variable, and the S parameters are simulated by EM software, and (K, θ) are obtained by equations (3), (4). Then exchanging w and K of the sample data, w is chosen as output variable, K as input variable. The processed sample data satisfy with equation (6). Obviously, this scheme avoids the trouble in figuring out w by solving equation (5).

The commercial EM software CST Microwave Studio r was used for EM simulation to get the strip S-parameters. The rectangular waveguide for the E-plane filter working in W-band is WR100 having width a = 2.54 mm, height b = 1.27 mm. The substrate material of finline is ROGERS RT/Duriod5880 with εr = 2.2, the thickness 0.127 mm and the thickness of metal strip 18 µm. The frequencies were chosen including all of the W-band in equal intervals at 31 points from 80 to 110 GHz. The width of the E-plane strip adopts 21 points from 0.01 mm to 1.9005 mm according to geometric proportion factor 1.3. This geometric progression growth of the strip’s width can represent the characteristic of the E-plane strip much better than the arithmetical progression one. The calculation results show that

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the adjacent sample points of the strip width in equal interval when the width is very small vary several times, and the EM-ANN cannot approach the characteristic of the E-plane strip. When the variable has a wider range, more accuracy can be obtained using much less sample points with geometric progression growth. In such a way the simulation points of the E-plane strip are 651 for training EM-ANN model. The neural network is MLPNN, which consists of two hidden layers. The first layer contains 10 neurons and the second layer contains 5 neurons. The input layer and output layer are two neurons for two dimension variable.

0.4f=100GHz

Strip width(mm)

Figure 3. Impedance inverter K of strip simulated by EM-ANN and CST.

The E-plane strip EM-ANN model was designed and trained with Mathworks Matlab neural networks toolbox [9]. Less time for training is needed because of the fewer input variables and sample points. The E-plane strip simulation results by CST and the designed EM-ANN model are shown in Fig. 3. K was chosen in equal intervals at 21 points as input variable for the EM-ANN model di erent than the points in training. The four curves in Fig. 3 are simulated at 80, 90, 100 and 110 GHz, respectively. The trained EM-ANN-model figures out w, which is the input variable of the simulation by CST because we cannot use K as the input variable of the EM software. In order to compare the results, K is the input variable of EM-ANN and is the output of CST. The results of the EM-ANN model in Fig. 3 are close to the CST ones. It should be noted that, in Fig. 3, the abscissa variable is the output of the EM-ANN model, but it is the input variable of EM software. The output variable θ of the EM-ANN model is only

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relative to K and frequency, and the one of the EM software is only relative to w and frequency. So the results of θ are not showed in figure for inconvenient comparison. The purpose of getting the value of θ is to determine the length of waveguide between two adjacent E-plane strips in the synthesis of the filter.

3. E-PLANE FILTER SYNTHESIS BASE ON EM-ANN MODEL

Base on the mapping of K to w, the E-plane filter can be synthesized by the prototype filter. As for Chebyshev bandpass filter, K is given in reference [3, 10]. We denote the passband ripple ε, the lower and upper frequencies fL and fH , and the out of band rejection L(dB). The midband guide wavelength λg0 is determined by the equation

where λgL andλgH are the guide wavelengths in the inhomogeneously filled waveguide at fL and fH , which can be determined by the method in the reference [11]. If the waveguide has irregular cross section, the guide wavelengths can be computed by the EM software. For a narrow band bandpass filter, the midband guide wavelength is as follow

where λg is the stopband wavelength at the stopband frequencyfs. Then the number of resonators is accomplished by finding the minimum integer N, for which the most severe constraints on the rejection L satisfies

where TN is the Chebyshev polynomial of degree N.

The impedance inverter K can be calculated by following

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wn can be obtained by the finline strip EM-ANN model. But the impedance inverter of finline strip has a pair of lengths, which can be obtained by the EM-ANN model of the strip too. To obtain these parameters we do not need to solve any equation but must have the guide wavelength. So the nth resonator length between the nth and the (n + 1)th strip is

Based on the above method, we designed a W-band E-plane bandpass filter, operating at center frequency 94 GHz with 4 GHz bandwidth. The strips widths of the filter are w1 = w7 = 0.153 mm, w2 = w6 = 0.808 mm, w3 = w5 = 1.041 mm, w5 = 1.077 mm, and the resonator waveguide lengths are l1 = l6 = 1.266 mm, l2 = l5 = 1.269 mm, l3 = l4 = 1.268 mm. The filter results by CST simulation and measurement are shown in Fig. 4. The simulation results of the filter in Fig. 4 are rather perfect, and in good agreement with the expectation. Its return loss is lower than 20 dB. But the measured

Frequency (GHz)

Figure 4. Measured and simulated results of the W-band E-plane filter.

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results are a little di erent from the simulation ones, namely the center frequency is lower and the bandwidth is larger. The measured loss is less than 1.5 dB from 92 GHz to 96 GHz. The di erence exist because the strips’ widths have been made with 10 µm error. The wavelength at W-band is 3 mm, so it requires strict mechanical machining. The error is about 6.5 per cent of the smallest w1. A little manufacturing error leads to varying the experimental results. The simulation results validate the filter synthesis method. We can obtain better experimental results by improving the manufacturing precision.

4. CONCLUSION

In this paper, the EM-ANN model has been developed for the E- plane strip whose input/output variables have been selected advisably. The EM-ANN model utilizes the impedance inverter K value as an input variable and corresponding physical dimension as output, which simplify traditional filter synthesize including getting physical dimension from K value by solving equations. The sample data of the EM-ANN model are obtained by CST Microwave Studio simulation, and then the model is trained using Matlab neural network toolbox. The E-plane bandpass filter can be synthesized e ectively and conveniently with the EM-ANN model. A W-band E-plane bandpass filter is designed by the method, and we show whose simulation and experiment results agree with the expectation.

REFERENCES

1.Konishi, Y. and K. Uenakada, “The design of a bandpass filter with inductive strip-planar circuit mounted in waveguide,” IEEE Trans. On MTT , Vol. 22, No. 10, 869–873, 1974.

2.Vahldieck, R., et al., “Optimized waveguide E-plane metal insert filters for millimeter-wave applications,” IEEE Trans. On MTT , Vol. 31, No. 1, 65–69, 1983.

3.Shib, Y. -C., T. Itoh, and I. Q. Bui, “Computer-aided design of millimeter-wave E-plane filters,” IEEE Trans. On MTT , Vol. 31, No. 2, 135–141, 1983.

4.Uher, J., J. Bornemann, and U. Rosenberg, Waveguide Components for Antenna Feed Systems: Theory and CAD, Artech House, Boston, 1993.

5.Vahldieck, R. and W. J. R. Hoefer, “Finline and metal insert filters with improved passband separation and increased stopband