New Micro Strip Filters

Design of Microstrip Filters Using Neural Network Vivek Singh Kushwah & G.S. Tomar; Member IEEE Amity School of Engineering & Technology, New Delhi-india Vikrant Institute of Technology & Management, Indore 452009 E-mail:[email protected], [email protected]

Abstract This paper presents the general design procedure for microstrip filters using artificial neural networks and this is demonstrated using Low pass filters. In this design procedure, synthesis is defined as the forward side and then analysis as the reverse side of the problem. in this work, the neural network is employed as a tool in design of microstrip filters. MATLAB programming language GUI (Graphical User Interface ) tools are used for implementing results. Neural network Training algorithms are used for trained the samples so that error can be minimized. Therefore , one can obtain the geometric dimensions with high accuracy. Introduction: The design of low pass filters involves two main steps. The first one is to select an appropriate low pass prototype. The choice of the type of response, including Pass band ripple and the number of reactive elements will depend on the required specifications. The element values of the low pass prototype filters, which are usually normalized to make a source impedance go = 1 and a cutoff frequency Ωc = 1.0, are then transformed to the L-C elements 1.

for the desired cutoff frequency and the desired source impedance, which is normally 50 ohms for microstrip filters. The next main step in the design of microstrip low pass filters [9] is to find an appropriate microstrip realization that approximates the lumped element filter. The element values for the low pass prototype with Chebyshev response at pass band ripple m normalized values gi i.e. g1, g2, g3, g4......, gn. The filter is assumed to be fabricated on a substrate of dielectric constant εr and of thickness t mm. for Angular (normalized) cutoff frequency Ωc, characteristic impedance source/load, Zo = 50 ohms, are taken , whose physical lengths are smaller than a quarter of guided wavelength (λg/4) at which they operate, are the most common components for approximate microwave realization of lumped elements in microstrip filter structures.

Figure 1: Lumped-Element Lowpass Prototype Filter The simplest form of low pass filter may just consist of series inductors, which is

often found in applications for direct current or dc block. In design and realization of microstrip filters, short section of transmission line or stub, whose length is much smaller than a quarter of guided wavelength, are the most common components . As a small open circuited loss less microstrip line stub is equivalent to shunt capacitor and similarly small short-circuited line is equivalent to shunt inductor. For a more selective low pass filter, more of such elements are required [1]. The quasi lumped elements discussed for this design have their size smaller then the quarter of the guided wavelength at the cutoff frequency 0.75 GHz. This type of low pass filter may be designed based on a lumped-element lowpass prototype filter, using normalized elements values gi and by terminating into impedance ZO, as shown in figure 1. 2. Design for Microstrip Filters In order to design a three-pole open stub low pass filter while considering the normalized elements values; the values of series inductors L1 , L3 and capacitor C2 (as shown in figure 2) are obtained by using design equations (1) and (2). The components L1, L3 & C2 are realized by high and low impedance microstrip open circuited stub respectively. The values of various inductance Li and capacitance Ci are obtained from the equations, as Li = (Zo/go) (Ωc/2πfc) g1 (1) Ci = (go/Zo) (Ωc/2πfc) g2 (2) Physical length (in mm) of the high and low impedance lines (inductance and capacitance respectively) is found out by the formulae given below, IL = λgl /2π Sin-1 (ωc Li / ZOL) (3) IC = λgc /2π Sin-1 (ωc Ci Zoc) (4)

Figure 2: Lumped-Element Low Pass Filter 2.1 Design Parameters and Analysis For the proposed design shown in figure 1, which is consisting of short-circuited stub (grounded line) on a commercial substrate; the following parameters are considered: g1 = g3 = 1.0316 g2 = 1.1474 Cut-off frequency, fc = 0.75 GHz. Relative Dielectric Constant, єr = 4.7 Height of substrate, h = 1.6 mm Characteristic Impedance, ZO = 50 Ω Corresponding width of the microstrip, Wc = 2.91mm ZOC = 20 Ω ZOL = 100 Ω The step impedance open circuited step microstrip low pass filter has been design using the above equations and parameters .the conventional microstrip low pass filter is shown in figure 3.

Figure 3: Design

Microstrip Low Pass Filter

3. Implementation & Results Suppose that we have to design the microstrip low pass filter at 0.7 Ghz

resonant frequency using the following parameters. Dielectric constant = 4.7 Substrate thickness = 1.6 mm Now we can calculate the length and width of capacitive element of filters using general relations. Length and width of capacitive element of the filters for 0.7 Ghz frequency is calculated , given by In mm. εr =4.7, h=1.6, W=7.684, L=15.14, f=0.7Ghz

Figure 4: Microstrip Low Pass Filter Design When IE3D electromagnetic simulation is performed and changes the dimensions of filters then we obtain the different resultant graphs between return loss and frequency:

Figure 6: Response of microstrip low pass filter for 0.5 Ghz Now trained the neural network by using training algorithms and transfer function.Figure 7 shows the neural network training graph results for the Synthesis of microstrip Low pass Filter. it is clear from this figure ,training performs in 76 epochs . We pass the full set of input samples through the neural network to compute the least squared error function we will use in the back propagation of the errors step. Each such pass is called an epoch. From this figure it is clear that error minimizes from103 to nearly 100.

Figure 5: Response of microstrip low pass filter for 0.7Ghz If εr =4.7, h=1.6 , W=11.484, L=15.14

layer that produces the network output is called an output layer.

Conclusion

1 Figure 7 training graph results for microstrip low pass filter

In this work, the neural network is employed as a tool in design of the microstrip filters[11] . In this design procedure, synthesis is defined as the forward side and then analysis as the reverse side of the problem. Therefore, one can obtain the geometric dimensions with high accuracy, which are the length and the width of the filters in our geometry, at the output of the synthesis network by inputting resonant frequency, height and dielectric constant.

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Figure 8 Neural network architecture for microstrip low pass filters As shown in the above neural network architecture, it consists of three layers. The three-layer network has one output layer (layer 3), one hidden layer (layer 2) and one input layer (layer 1 ). Input and output layer consists of two neurons .inputs f1 and f2 are applied at the input neurons while outputs W & L are obtained from output neurons. A constant input 1 is fed to the biases for each neuron. Note that the outputs of each intermediate layer are the inputs to the following layer. A

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