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ISSN ONLINE(2320-9801) PRINT (2320-9798)

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HALF-WAVELENGTH PARALLEL EDGE COUPLED FILTER SIMULATION USING MATLAB

Girraj Sharma1, Patel Shreyas Navin2, Yogesh Bhati3, Yash Walia4
  1. M.Tech Scholar, Dept. of ECE, Jaipur National University, Jaipur, India
  2. M. Tech Scholar, Dept. of ECE, Sri Balaji College of Engg. and Tech., Jaipur, India
  3. B.Tech scholar Dept. of ECE, Arya institute of Engg. & Technology, Jaipur, India
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International Journal of Innovative Research in Computer and Communication Engineering

Abstract

This paper presents a practical design procedure for edge coupled bandpass resonator filters using Matlab. The design process starts with the theoretical design of the filter.. Finally, the results of the implementation of the design are presented. the MATLAB code gave a center frequency of 2.45 GHz. Spurious modes which do appear due to inhomogeneities of the microstrip are not shown here.



 

INTRODUCTION
Stripline filters play an important role in many RF applications. As technologies advances, more stringent requirements of filters are required. One of the requirements is the compactness of filters . At very high frequencies, the practical inductors and capacitors loses their intrinsic characteristics. Also a limited range of component values are available from the manufacturer. Therefore for microwave frequencies (>3GHz), passive filter is usually realized using distributed circuit elements such as transmission line sections. Many works have been reported that use waveguides for transmission line filter. However, waveguides systems are bulky and expensive. Low-power and cheaper alternatives are stripline and microstrip. These transmission lines are compact. Edge-coupled stripline is used instead of microstrip line as stripline does not suffer from dispersion and its propagation mode is pure TEM mode. Hence it is the preferred structured for coupled-line filters. Therefore, a third order chebyshev edge-coupled stripline filter is designed in the research.

BASIC THEORY

PARALLEL-COUPLED,HALF-WAVELENGTH RESONATORS FILTERS
Figure 2.1 illustrates a general structure of parallel-coupled (or edge-coupled); microstrip bandpass filters that use halfwavelength line resonators. They are positioned so that adjacent resonators are parallel to each other along half of their length. This parallel arrangement gives relatively large coupling for a given spacing between resonators, and thus, this filter structure is particularly convenient for constructing filters having a wider bandwidth as compared to the structure for the end-coupled microstrip filters.
The design equations for this type of filter are given by
image
image
where g0, g1… gn are the element of a ladder-type low-pass prototype with a Normalized cutoff Ωc = 1, and FBW is the fractional bandwidth of band-pass filter. J j, j+1 are the characteristic admittances of J-inverters and Y0 is the characteristic admittance of the terminating lines. The equation above will be use in end-coupled line filter because the both types of filter can have the same low-pass network representation. However, the implementation will be different.
To realize the J-inverters obtaine
image

DESIGN METHODOLOGY
Given a center frequency of 2.45 GHz, bandwidth of 10% and equal ripple in the pass-band of 0.5dB and 30dB design a band-pass filter for the ISM band with 3rd order Coupled Line configuration for the given specification. Use FR4 and Roger Ro4003c substrate of dielectric constant 4.2 with thickness of 1.58mm and 3.38 and 3.38mm respectively. Refer to the filter tables given in D.M Pozar [2] to find the following coefficients for 0.5dB and 30dB ripple third order Chebyshev filter.
g0 = 1.0000 and 1.0000 g1 = 1.5963 and 3.3487 g2 = 1.0967 and 0.7117 g3 = 1.5963 and 3.3487 g4 = 1.0000 and 1.0000
These values are for low-pass prototype design with source and load impedance equal to unity. A ladder circuit that begins with a series element is chosen, g1and g3 are inductors and g2 is a capacitor.
Using (1) and (2) design equations yield the design parameters, half of which are listed in Table I because of symmetry of the filter, where the even- and odd-mode impedances are calculated for Y=1/Z and Z=50 ohms.
The next step of the filter design is to find the dimensions of coupled microstrip lines that exhibit the desired even- and odd-mode impedances. Firstly, determine equivalent single microstrip shape ratios (w/d) s. Then it can relate coupled line ratios to single line ratios. For a single microstrip line
image
Use single line equations to find (w/h)se and (w/h)so from Zose and Zoso. With the given r ? =4.2, find that for Zo=50, w/h is approximately 1.95. Therefore, W/h? 2 has been chosen for this case. 2 h W F
image
At that point, it’s able to find (w/h)se and (w/h)so by applying Zose and Zoso (as Zc) to the single line microstrip equations. Now it comes to a point where it reach the w/h and s/h for the desired coupled microstrip line using a family of approximate equations as following
image
image
The microstrip transmission line by an overall dielectric constant in order to assume TEM propagation. There are a number of formulas, listed for the calculation of eff ? . The most basic formula is given by Pozar as follows: [2]
image
Once the effective dielectric constant of a microstrip is determined, the guided wavelength of the quasi-TEM mode of microstrip is given by
image
Thus the required resonator, image
Using the design equations for coupled microstrip lines given (3a) and (3b), the width and spacing for each pair of quarterwavelength coupled sections are found, and listed in Table II
The final filter layout with all the determined dimensions is illustrated in Figure 3.2
For section 1 and 4,
s/h=0.0288? s=0.046 mm and w/h=1.6106 ? w=2.54mm
For section 2 and 3,
s/h=0.2728? s=0.431 mm and w/h=2.2368 ? w=3.53mm

RESULTS AND ANALYSES
All the formulas were coded in MATLAB . The MATLAB response is shown in Figure 3.5. As shown in figure, the MATLAB code gave a center frequency of 2.45 GHz. Spurious modes which do appear due to in-homogeneities of the microstrip [7, 8] are not shown here.

CONCLUSION
The Edge coupled filter for different center frequency and for different substrates are simulated and we find that for compact design rogerR04003 c substrate is suitable for 2.45GHz frequency .The coupled line filter is a band-pass filter used for narrow bandwidth. Wider bandwidth filters require very tightly coupled lines which are difficult to fabricate. One advantage of this type over the capacitively coupled is the smaller size; it uses quarter wave instead of half wave resonators.

FUTURE WORK
Physical development and measurement of RF filters design for more accurate design. Use additional software such as ADS simulations to compare the results with MATLAB to accurately determine the final design.

Tables at a glance
Table icon Table icon
Table 1 Table 2

Figures at a glance
Figure 1 Figure 2 Figure 3
Figure 1 Figure 2 Figure 3
Figure 1 Figure 2 Figure 3
Figure 1 Figure 2 Figure 3

References