International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 8, August 2014)

Bandwidth Analysis of Slotted Hairpin BandPass Filter Using Neural Network Sudhir Singh1, Vandana Vikas Thakare2 Department of Electronics, Madhav Institute of Technology and Science Gwalior, India An ANN model based Feedback propagation algorithms are used to train the network and three training function TRAINLM, TRAINSCG, TRAINGDA are used to compare mean square error (MSE) and to compute the bandwidth to varying the slot length of the finger of the filter. This paper gives the effect of slot value on bandwidth of the filter for the same physical design parameters.

Abstract- Hairpin bandpass filter are compact structures they may theoretically be obtained by folding the resonator of parallel-coupled half wave length resonator which reduces the coupling between resonators. This type of U shape resonator is so called hair pin resonator. In the present paper a novel technique has been proposed for the estimation of bandwidth for variation of slot length on the bandpass characteristics of the filter has been presented using artificial neural networks (ANN). The different variants of training algorithms of MLPFFBP-ANN (Multilayer Perceptron feed forward back propagation Artificial Neural Network) have been used to implement the neural network model and compare with Radial basis fewer (RBF) network and concluded that RBF network is more accurate than MLPFFBP and performance comparison of the EM simulated result with ANN is evaluated in terms of maximum estimated error (MSE)

II.

DESIGN O F T HE F ILTER

The structure for hairpin bandpass filter and its equivalent circuit is shown in fig.1

Keyword- Artificial neural network (ANN), Hairpin band pass filter (HPF), Mean square error (MSE), Multilayer feed forward network, Radial basis fewer (RBF,)Computer simulation technology (CST).

I.

INTRODUCTION

In microwave communication systems, high performance and small size bandpass filters are basically required to enhance the system performance and to reduce the fabrication cost. The length of parallel coupled filter is too long and it further increases with the order of filter. To solve this problem, hairpin line filter using folded λ/2 resonator structures were developed [1]. In addition to small size, high selectivity and narrow bandwidth, good Return Loss (RL) and low cost are desirable features of narrowband bandpass microstrip filters. Artificial neural networks (ANNs) [2] are information processing systems with their design encouraged by the studies of the ability of the human brain to learn from observations and to generalize by concept. A neural network model for microwave circuit can be developed from simulated microwave data, through a process called training. Once the ANN model is fully trained, the calculation time is usually negligible and thus eliminates the complex and time consuming mathematical procedures [7].

a) Hairpin bandpass filter

b) Equivalent circuit Figure-1: a) Taped Hairpin Bandpass Filter b) equivalent circuit.

The advantage of hairpin filter over end coupled and parallel coupled Microstrip realizations are the optimal space utilization. In the present paper uses a taped line input five-pole hairpin bandpass filter that are commonly used in filter realization and are in shown fig-2 respectively

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International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 8, August 2014)

Figure-2: Taped line input 5-pole Hairpin filter

A microstrip hairpin bandpass filter is designed to have a fractional bandwidth of 55% or FBW = 0.55 at a midband frequency f0 = 3.045 GHz. A five-pole (n = 5) Chebyshev lowpass prototype with a pass band ripple of 0.1 dB is chosen. The lowpass prototype parameters, given for a normalized lowpass cut off frequency Ωc = 1, are g0 = g6 = 1.0, g1 = g5 = 1.1468, g2 = g4 = 1.3712, and g3 = 1.9750, having obtained the lowpass parameters and design parameters [8] can be calculated as

Figure-3: Proposed Hairpin bandpass filter.

There are various slots that can be used for the design of microstrip filter and their dielectric substrate are usually FR4 (Lossy) is used with dielectric constant (r) = 4.3.The software used to model and simulate the proposed microstrip filter is CST. As an example a microstrip filter of length L=30 mm and width W=13.237 mm is simulated using CST Simulator which is resonating at 3.045 GHz frequency. The dielectric substrate FR4 (Lossy) is used with dielectric constant (εr)  4.3, and substrate thickness (h) =1.6 mm on a ground plane. Fig 4 shows the return loss (S11), insertion loss (S21) vs. Frequency curve for the proposed filter. Return loss of the filter is -21db.

Where Mi,i+1 is the mutual coupling coefficient between two resonator and Qe1,Qen are the quality factor at the input and output. The arm length L of hairpin filter can be calculated by [1]

(4) Where is the wavelength of the filter with frequency f0 in vaccum. Hairpin bandpass filter with N=5 pole was design to work for frequency of 3GHz. The arm length L of hairpin resonator is 30mm,arm width W is 13.237mm and thickness of each resonator is 2mm, the gap between resonator is 0.4mm & 0 .6mm which gives M1,2=M4,5=0.1594 and M2,3=M3,4=0.1215. The insertion loss and return loss for entire simulation results remain less than -1db and -21db respectively which shows the enhanced performance of Band pass filter. The layout of the final filter design with all the determined dimensions is illustrated in Figure 3.

Figure-4: S-parameter in dB versus resonating frequency of the filter.

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This network can be used as a general function approximator. It can approximate any function with a finite number of discontinuities, randomly well given sufficient neurons in the hidden layer. The transfer function preferred is tansig and purelin in the network with error goal 0.001and learning rate 0.1.

ANN MODEL FOR ANALYSIS OF B ANDPASS F ILTER

The artificial neural network model has been developed for microstrip filter as shown in Figure 5. The feed forward network has been utilized to analyze the bandwidth and to calculate the center frequency of the filter for the given value of length of the filter L (mm), Width W (mm) and slot X (mm), as the input to network and centre frequency and bandwidth as the output of the network without doing complex calculations using empirical formulas W

Table 1 Comparison of results obtained using CST and MLPFFBP-ANN using Levenberg-Marquardt Algorithm for the analysis of Bandwidth of Slotted Microstrip Filter.

Slot length

Bandwidth CST

Bandwidth LM

Absolute Error

MSE

Fc X

ANN

0.4 0.8

MODEL h

1.2

BW

1.8 2.2

Figure-5 Analysis ANN Model.

2.6

In order to evaluate the performance of proposed MLPFFBP-ANN based models for the design of microstrip filter, simulation results are obtained using CST Software[9] and generated 50 input-output training patterns and 15 inputs-output test patterns to validate the model. IV.

3.2 4.2 5.2 5.4

MULTILAYER P ERCEPTRON FEED FORWARD B ACK P ROPOGATION (M LPFFBP) N EURAL NETWORK

6.8

Multilayer perceptron networks are feed forward networks trained with the standard back propagation algorithms to achieve the required degree of accuracy. They are supervised networks, and also they required a desired response to be trained. With one or two hidden layers they can estimated virtually any input output map. The weights of the networks are usually computed by training the network using the back propagation algorithms [3, 6]. For the present work the multilayer perceptron feed forward back propagation neural network (MLPFFBP) [4, 5] is used with 3 different training algorithms.

7.4 8

0.68397

0.68448

-0.0005

2.601E-07

0.68495

0.68496

-1E-05

1E-10

0.68177

0.68482

-0.0030

9.302E-06

0.68368

0.68493

-0.0012

1.563E-06

0.68278

0.685

-0.0022

4.928E-06

0.68345

0.68507

-0.0016

2.624E-06

0.67965

0.68519

-0.0055

3.069E-05

0.6857

0.68538

0.00032

1.024E-07

0.6811

0.68557

-0.0044

1.998E-05

0.68182

0.68585

-0.0040

1.624E-05

0.69521

0.67937

0.01584

0.000250

0.68686

0.68603

0.00083

6.889E-07

0.67197

0.68077

-0.0088

7.744E-05

In the Table 2 Mean Square Error of the different algorithms are shown. Accuracy of Levenberg-Marquardt Training Algorithm is 97.85%, Scaled Conjugate Gradient is 97.80% and Gradient descent algorithm is 97.60% respectively. It is also observed from Table II that the Mean Square Error (MSE) is minimum in Levenberg-Marquardt training Algorithm amongst all.

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International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 8, August 2014) Table 2 Comparison of different variants of Back Propagation Training Algorithms for the Analysis of Bandwidth of slotted hairpin bandpass filter.

slot length

TrainLM

0.4 0.8 1.2 1.8 2.2 2.6 3.2 4.2 5.2 5.4 6.8 7.4 8

TrainSCG

2.6E-07 1E-10 9.3E-06 1.56E-06 4.93E-06 2.62E-06 3.07E-05 1.02E-07 2E-05 1.62E-05 0.000251 6.89E-07 7.74E-05

1.76E-07 1.19E-06 4.67E-06 2.3E-07 2.37E-06 1.08E-06 2.61E-05 2.21E-07 2.15E-05 1.72E-05 0.000225 2.56E-08 0.000124

The hidden layer neuron represents a series of centres in the input data space. Each of these centres has an activation function, typically Gaussian.[6] In the RBF network, the spread value was chosen as 0.04, which gives the best accuracy. The network was trained with 50 samples and tested with 15 samples. RBF networks are more fast and effective as compared to MLPFFBP for proposed Filter design. The RBF network automatically adjusts the number of processing elements in the hidden layer till the defined accuracy is reached. The training algorithm is unsupervised k-means clustering algorithm. Figure 4 shows the training performance of the neural network model is trained in 25 epochs with MSE = 3.146E-05

TrainGDA

2.22E-05 3.24E-05 6.3E-06 1.95E-05 1.24E-05 1.76E-05 1.52E-07 4.15E-05 3.39E-06 6.55E-06 0.000189 5.78E-05 5.31E-05

Table 3 Comparison of results obtained using CST and RBF-ANN Algorithm for the analysis of bandwidth of hairpin bandpass filter

Slot lengt h

0.4 0.8 1.2

Average MSE vs Traning Algorithm

1.8 2.2

Average MSE

0.000036 0.000035

2.6

0.000034

3.2

0.000033

4.2

0.000032

5.2

0.000031 0.00003

lm

scg

5.4

gda

6.8

Series1 3.19E-05 3.26E-05 3.55E-05

7.4

Figure-6 Graph Showing Variation of MSE on test data set for various back propagation algorithms.

8 V.

RBF NETWORK

Radial basis function is feed forward neural network with single hidden layer that uses radial basis activation function for hidden neurons. It consists of three layers of neurons - Input, hidden and output.

BW CST

BW RBF

Absolute Error

MSE

0.6839

0.68461

-0.00064 4.096E-07

0.6849

0.68461

0.00034 1.156E-07

0.6817

0.68461

-0.00284 8.066E-06

0.6836

0.68461

-0.00093 8.649E-07

0.6827

0.68664

-0.00386 1.49E-05

0.6834

0.68664

-0.00319 1.018E-05

0.6796

0.68461

-0.00496 2.46E-05

0.6857

0.68461

0.00109 1.188E-06

0.6811

0.68461

-0.00351 1.232E-05

0.6818

0.68461

-0.00279 7.784E-06

0.6952

0.68461

0.0106 0.000112

0.6868

0.68461

0.00225 5.062E-06

0.6719

0.68461

-0.01264 0.000159

Figure7 shows the training performance of the developed neural network using RBF network.

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International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 8, August 2014)

Average MSE vs Training Algorithm Average MSE

0.000032 0.0000318 0.0000316 0.0000314 0.0000312 Series1

lm

rbf

3.19022E-05

3.14636E-05

Figure 8 Average MSE vs. Training algorithm.

Figure 7: Number of epochs to achieve minimum error level in RBF Network

VI.

Table 4 Result obtained using CST, Levenberg-Marquatdt, and RBF Algorithm.

mean square

r

BW (GHz) CST A

0.4

0.6839

0.8

BW (GHz) ANNRBF C

MSE A-B

MSE A-C

0.6844

0.6846

2.601E-07

4.096E-07

0.6849

0.6849

0.6846

1E-10

1.156E-07

1.2

0.6817

0.6848

0.6846

9.302E-06

8.066E-06

1.8

0.6836

0.6849

0.6846

1.563E-06

8.649E-07

2.2

0.6827

0.685

0.6892

4.928E-06

4.238E-05

2.6

0.6834

0.6850

0.6892

2.624E-06

3.411E-05

3.2

0.6796

0.6851

0.6846

3.069E-05

2.46E-05

4.2

0.6857

0.6853

0.6846

1.024E-07

1.188E-06

5.2

0.6811

0.6855

0.6846

1.998E-05

1.232E-05

5.4

0.6818

0.6858

0.6846

1.624E-05

7.784E-06

6.8

0.6952

0.6793

0.6846

0.000250

0.000112

7.4

0.6868

0.6860

0.6846

6.889E-07

5.062E-06

8

0.6719

0.6807

0.6846

7.744E-05

0.000159

RESULTS

It has been established from Table 1 that the Levenberg-Marquardt algorithm is the optimal model to achieve desirable values of speed of convergence. It has been observed that 144 epochs are needed to reduce MSE level to a low value 3.19e-05 for two layers MLPFFBP with Levenberg-Marquaradt (LM) training algorithm and purelin as a transfer function. Achievement of such a low value of performance goal (MSE) indicates that trained ANN model is an accurate model for designing the microstrip filter. It is observed that purelin is most suitable transfer function for the present work. The MLP neural network is trained using learning Algorithms namely Levenberg-Marquaradt (LM), Scale Conjugate Gradient Back propagation (SCGBP), Gradient descent algorithm (GDA). Minimum MSE is calculated after training the network and indicated [10] in Table 1. It is concluded that Levenberg-Marquardt is most suitable learning method for the proposed neural model of microstrip filter. A Radial Basis Function (RBF) neural network has an input layer, a hidden layer and an output layer. The neurons in the hidden layer contain Gaussian transfer functions whose outputs are inversely proportional to the distance from the centre of the neuron. It is established from Table 2 that RBF is giving results not only more accurate but fast also, the presented RBF network has performed training in less epochs than in MLPFFBP. So it is concluded that RBF architecture is better from MLPFFBP and its accuracy is up to 98.14%. Simulated results for trainLM and RBF network are compared in Table 3 and Figure 8 showing the best algorithm to use in the following training purpose.

489

BW (GHz) ANNLM B

International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 8, August 2014) VII.

[4 ] [5 ]

CONCLUSION

In the present paper, microstrip hairpin bandpass filter using MLPFFBP and RBF-ANN has been modelled. The results obtained with the present technique are closer to the experimental results generated by simulating a large no of microstrip filter using CST software on the different substrate. The paper concludes that results obtained using present ANN techniques are quite reasonable and followed the experimental leaning and also that RBF is giving the best approximation to the design as compared to MLPFFBP.

[6 ]

[7 ]

[8 ]

REFERENCES

[9 ]

[1 ] J. Lakshmi Narayana, Dr. K. Sri Rama Krishna, Dr. L.Pratap Reddy, High Dimensional Modeling of Microstrip Hairpin Bandpass Filter Using Artificial Neural Networks. [2 ] Hui-Sheng Wang and Xiu-Ping Li, Asymmetrical Two 2J2 Resonators Bandpass Filter Design by Artificial Neural Network Modelling. [3 ] Abhishek Tripathi, P. K. Singhal, Vandana Vikas Thakare, Analysis of Triangular Microstrip Patch Antenna Using Artificial Neural Network.

[10 ] [11 ]

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Haykin, S., Neural Networks, 2nd edition, pHI, 2003. Hassoun, M. H., Fundamentals of Artificial Neural Networks, Chapter 8, New Delhi, Prentice Hall of India, 1999 Vandana Vikas Thakare Pramod Singhal.Artificial Intelligence in the Estimation of Patch Dimensions of Rectangular Microstrip Antennas”. Circuits and Systems, 2011, 2, 330-337 .Vandana Vikas Thakare and Pramod singhal, “Neural network based CAD model for the design of rectangular patch antennas”, Journal of Engineering and Technology Research Vol.2 (7), pp. 126-129, July 2010. [10] Vandana Vikas Thakare, Pramod Singhal, “Bandwidth Analysis By Introducing Slots In Microstrip Antenna Designs Using Ann”. Progress In Electromagnetic Research M, Vol. 9, 107{122, 2009 Pozar DM, Microwave Engineering, 2nd edition, Wiley, New York, (1998). CST (Computer Simulation Technology) Microwave Studio Suit Software 2010 MATLAB Software, version 7.10