Α Uniform Design of Microstrip Hairpin Line Filter at 7.2 GHz

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1 Α Uniform Design of Microstrip Hairpin Line Filter at 7.2 GHz HARALAMBOS P. KOKKALELLIS (1) and EVANGELIA A. KARAGIANNI (2) (1) Department of Informatics and Telecommunications University of Athens, Panepistimiopolis, Ilissia GREECE (2) Hellenic Naval Academy, Sector of Electronics and Telecomunications Hadjikyriakou Avenue, Piraeus GREECE Abstract: - Recently, the design and development of microwave filters have remarkably improved, in order to correspond to the requirements of technology. In this paper, we present the microstrip resonant coupling structures and the characteristics of them. Based on a mathematical algorithm, we designed a microstrip Chebyshev Hairpin Line filter at 7.2 GHz, 2 db rejection at 6.7 GHz and.1 db ripple in the passband and we discuss about the initial conditions and the acceptances of the problem as well as the simulation s results. Afterwards, a new uniform design of the filter is presented, making a comparison with the previous design. Two of the materials that can be used for the fabrication of these circuits, are suggested. Finally, after fabricating, we will examine the possibility of developing this structure, as extended work, using a combination of transmission lines and split ring resonators as a defected ground plane. Key-Words: - Chebyshev, Coupling, DGPs, Hairpin-Line, Microstrip, Slot Split Ring, Uniform filter design. 1 Introduction Today, in contemporary telecommunications systems, the requirements of circuits as for the safety and the correctness of transmission data are quite high. Concretely, in civil and military telecommunications, the use of microwave filters is necessary. It is well known, that the basic role of a filter is, to separate or to combine frequencies, according to the special purposes of current application. In this paper, we focus on microstrip coupling resonant filters and particularly, on hairpin line filters, because it has been observed that, these filters have special and interesting properties such as low cost of design, smaller structure size than the classic type of filters, great frequency accuracy, etc. Basic purpose of this paper is the presentation of a microstrip Chebyshev hairpin line filter, which has center frequency at 7.2 GHz, 2 db rejection at 6.7 GHz and.1 db ripple in the pass-band. 2 The resonant coupling structures One simple structure of microstrip resonant coupling circuit with parallel lines is presented in Fig.1 [1] Fig.1 Resonant Coupling Structure of 5 Microstrips 2.1 Description of the structure These circuits consist of transmission lines with electrical length λ/4.the basic elements are opencircuits at the one edge which is possible to convert into short-circuits and vice versa. At the same time, high junctions are created because of the small distance of elements and the influence of the electromagnetic field. In addition, the first and the last line are matching networks into the characteristic impedance of the lines Ζo, as it is often called. Also, it is important to note that basic property of this kind of structure is the high quality factor Q, that is achieved. However, the dielectric loss of the substrate, the restricted conductivity of ISSN: ISBN:

2 microstrip and the loss of radiation of microstrip limit the quality factor of these circuits. 2.2 Estimating critical Parameters The structure can be modeled and described by a group of mathematical parameters which are shown in Fig.1. Firstly, the characteristic impedance of the transmission line is usually 5Ωhm. Also the distance between the coupled lines s i as it refers to i line of the structure and it is shown in Fig.1., must be greater than 6mils, in order to be possible to be fabricated. In addition to this parameter, the width of coupled lines w i plays the most important role to the good performance of the circuit. One another parameter is the effective dielectric constant and it is related with the substrate. It depends from the base material of structure and it is discussed in paragraph 3.6. Finally, there are two other frequency parameters, the bandwidth BW, which is the band of frequency that the bandpass filter is desired to operate and the fractional bandwidth, which is an additional mathematical parameter of frequencies [1]. If f u and f l are respectively, the upper and low frequency of band, the expression of these last two parameters is given by equations 1 and 2 [4]. BW = fu - fl 1 BW Δf =, f = fu fl 2 f 3 Design of the filter at 7.2GHz The center frequency of the filter is 7.2GHz and the desired fractional bandwidth is Δf = w =.1. We assume also, that 2dB attenuation is required at 6.7 GHz. For the design, a group of Chebyshev coefficients is necessary. These can be found from the Table 1. Table 1 : Chebyshev Coefficients for n=1(1) dB ripple Constraints and Approximations The real center frequency of the filter is 7.182, as it is computed from the equation (2). It is considered that it is near to 7.2 GHz. In addition, the real fractional bandwidth is.138, but it is considered.1, without fault generally. The design optimization based on the following constraints : Max(S 11 ) = -2dB & Min(S 21 )=-1 for GHz, Max(S 21 )= -6 for GHz So, the results have calculated with these approximations. 3.2 Calculation of parameters Initially, based on the algorithm which is described step by step [1], we calculate the line length of resonators, using equation (3). λ c l= = 3 4 4f ε r As it is calculated the length is equal to mm or mils. But, practically, we suppose that the whole length of every resonator is mils. 1 2 * 4 = w By using the equation (4), the frequency ratio is and help us to choose the number of resonators as we need, using also the appropriate graphs [1]. So, the number of resonators is equal to 6. In addition, using the seven Chebyshev coefficients from the table 1, we can calculate the characteristic impedance of every microstrip at the even and at the odd mode. Then, with the help of appropriate nomogramms, we calculate the widths of coupled lines w i and the distance between them s i. The resulted values are shown in Table 2. Table 2 : Dimensions Extraction of Microstrips I Zeven Zodd w s ISSN: ISBN:

3 For the first and the last transmission line, w=46.88mils, because of the characteristic impedance of the line, that is equal to 5Ωhm. 3.4 Design and results The simulation results have extracted with the help of a commercial software. The schematic diagram of the circuit is shown in Fig.2: 3.3 Algorithm of Design Firstly, the line length resonator is computed from the equation 3. Afterwards, a frequency space will be chosen, in intention to approximate a desired center frequency of the circuit that will be given from the following equation: 1 2 = 5 where 1 and 2 are the lower and upper frequency of the space. A fractional bandwidth contribute to the computation of the frequency ratio, as it is 1 shown from the equation 4. So, using the appropriate graph [1], corresponding with the type of filter and the given constraints, the number of the required resonators n is extracted. The basic operation of the algorithm consists of three steps. At first, using a group of coefficients for a specific Z mathematical type of filter, a useful ratio can K j,j+1 be computed for j = (1)n. As a second step, this ratio is used for the estimation of the impendence in odd and even mode respectively, Z o and Z e,, based on the iteration schemes that are shown in equation 6 and 7. Ze j+1 Z Z = Z K j, j+1 K j, j Zo j+1 Z Z = Z K j, j+1 K j, j+1 Finally, using the appropriate nomogramms [1], the width of coupled lines and the distance between them can be extracted. So, the resulted data can be used from the software and the simulation results can confirm if the theoretical values are good enough for the operation of filter. However, it is important to notice that the same algorithm can be used for a stripline structure, with the appropriate adaptation techniques. Fig.2 Microstrip Hairpin Line Filter at 7.2GHz As it is obvious in Fig.2, there are 5 resonators in Π configuration, so we are able to improve the occupied area of the filter, designing a smaller and useful structure. According to the acceptances and requirements, that described, we extract the following results, after a number of optimizations, based on the value of w i, s i and lengths of the transmission lines. Table 3: Dimensions of the Microstrips after optimization I Zeven Zodd w s As we can observe from the Table 3, values for the parameter s i, is extracted more than 6 mils, which is very important for the design and fabrication process. At the same time, the widths of coupled lines have almost the same size. This property prevents the structure from unwanted electromagnetic phenomena, because of the high junctions of the transmission lines. ISSN: ISBN:

4 The dependence of S parameters, S 11 and S 21 as a function of frequency is presented in Fig.3. db(s(2,1)) db(s(1,1)) m1 freq= 7.2GHz db(s(2,1))=-.413 m1 m2 m2 freq= 7.21GHz db(s(1,1))= freq, GHz Fig.3 : Simulation results of hairpin line filter As it is shown, the resonant frequency is given at 7.25GHz, where S 11 = db. This result has better approximation to 7.2 GHz than the theoretical value, as it is computed from the equation (2). Other resonant frequencies are also given at 7, 7.4, 7.6 and 7.7GHz. Additionally, the ripple of S 21 remains at the desired limits. Afterwards, the generation of layout for this schematic gives the pattern of Fig.4: so it causes no problems to the layout design and fabrication of the circuit. Additionally, it must be noticed that the distances s between coupled lines are now closed enough, in comparison with the previous results of Table 3. The final layout of the circuit is presented in Fig.5. Table 4: Dimensions Extractions of Uniform Design I Zeven Zodd w s Fig.4: Layout of Hairpin Line Filter at 7.2 GHz 3.5 Uniform design of the filter Let us suppose that all the widths of the coupled lines remain constant except from the first and the last transmission line. This uniformity of the design restrict undesirable phenomena in a high degree, like weak electromagnetic couplings, manufacturing problems, difficulties of waveguiding etc. So, for the schematic diagram that is shown in Fig.2, such a uniform design could be made, using the same variable for all the widths of coupled lines except from these at the edges of the circuit. In addition, if the values of these two variables are so closed, then the whole design can be characterized as ideal. The new array of values for w and s, using a number of optimization steps are given in Table 4. As it is obvious, the deviation of two variables is 5.67mils. This quantity can be considered so small, Fig.5: Layout of the Uniform Hairpin Line Filter at 7.2 GHz 3.6 Substrate and fabrication Today, there are several types of laminates, that can be used to fabrication of hairpin line filters. Rogers is one of the most popular companies for this purpose. So, RO443 and RO435 are two good choices. RO443 and RO435 laminates can be used in layers where operating frequency, dielectric constant control or high speed signal requirements dictate the need for superior materials [2]. RO443 prepreg is a new bonding material,which featuring a dielectric constant of 3.2, at 1GHz and at temperature of 23 ο C [5]. ISSN: ISBN:

5 The filter fabrication was made on RO43 dielectric substrate of the Rogers Microwave Corporation, with width of h=.5mm, dielectric constant of Ηr=3.38, and tand=.27. The depth of the metallic conductor is T=35um, and the material is copper with specific conductivity Siemens/m. The filter is contained in a hollowed aluminum box which has calculated dimensions for suppressing the electromagnetic modes of upper frequencies, so the filter is isolated at the maximum. The input and output of the box is containing SMA connectors of 5 Ohms. Measurement results are shown in Fig. 6 and they are in accordance with the simulating results. same, this new structure is presented below with an array of 2 SSRRs : Port 2 Port 3 Port 1 Port 4 Fig.7: Combination of transmission lines and SSRR Fig.6: Measurement results of hairpin line filter 3.7 Future work During the last few years, several studies have shown that the coupling between two parallel microstrip lines can be enhanced by using Slot Split Ring Resonators(SSRR) defected ground plane(dgp) [3]. DGPs are periodically patterned by Electromagnetic/Photonic Band Gap(EBG/PBG) structures. This technique has remarkably contributed for the size reduction of microwave circuits. As a result, the fabrication process is more flexible and simpler. Firstly, it is supposed that, we examine the initial shape of two parallel transmission lines, combined with a perfect electrical conductor(pec), as a ground plane [3]. In addition, the dimensions of the resonators are adjusted to the desired resonant frequency of this initial circuit and of the SSRR designed for the next step. Afterwards, the use of an array of SSRRs as a ground plane in the middle of the λ/4 lines can give the ability to route the signal from port 1 to other ports with respect to frequency. Considering that in fig.7, the distance between the coupled lines is the So, for example, the main desired signal can travel from port 1 to port 3 and other parasitic signals can be collected to other ports. So as it is obvious, the most important advantage of this combination is that the device can separate the main and the parasitic signals on two different accesses. So such a device can be made to operate at any frequency, acting as a router of signals into different ports. Several simulated and measured results have shown that a band-stop phenomenon is observed, when a microstrip line is placed on a SSRRs defected ground plane [3]. Today, may autonomous systems can use these techniques of filtering with great results. 3.8 Problems The extracted theoretical values of parameters of lines are often inappropriate to use them for the fabrication of filter. So, it is necessary to adjust them to real practical values of lines. In addition, because of the shape of resonators, many electromagnetic influences may be noticed between the lines, in such degree, so it causes alterations to the operation of filter. For this reason, the shape of each resonator can be appropriately modified. Finally, the choice of the base material can be influenced in important degree the operation of the filter. So, it is important to notice the characteristics of the materials and examine the combination of them, in intention to extract the ideal structure for the purposes, that it serves. ISSN: ISBN:

6 4 Conclusion In this paper, it is clear why microstrip hairpin line filters are widely used in the civil and military applications wireless or not, where the requirements of circuits as for the safety and the correctness of transmission data are quite high and the accuracy of the results is very important. We designed a new uniform microstrip Chebyshev Hairpin Line filter at 7.2 GHz, 2 db rejection at 6.7 GHz and.1 db ripple making comparisons with similar more bulky designs. Especially, a combination of a transmission line with an array of SSRRs gives the opportunity to the future scientists to work more in this section and examine several geometric schemes of transmission lines. So, future work is the possibility of developing this structure, using a combination of transmission lines and split ring resonators as a defected ground plane. References: [1] G.L. Matthaei, L. Young, Microwave Filters, Impedance Matching and Coupling Structures, E.M.T Jones, Artech House, 198. [2] Preliminary RO443 Prepreg Data Sheet, Rogers Corporation Microwave Materials Division, [3] Shah Nawaz Burokur, Mohamed Latrach, Serge Toutain, Coupling Enhancement of Parallel Transmission Lines Using a Slot Split Ring Resonators Defected Ground Plane. [4] Evangelia A. Karagianni, Yorgos E. Stratakos, Christos N. Vazouras and Michael E. Fafalios, Design and Fabrication of a Microstrip Hairpin Line Filter by Appropriate Adaptation of Stripline Techniques, 11 th International Symposium on Microwave and Optical Technology (ISMOT), Italy, 27 - Dec.17-21, pp [5] RO43, RO435 High Frequency Laminates Woven Glass Reinforced Ceramic Filled Thermoset Materials, [6] Anurag Bhargava, Kamaljeet Singh and Surendra Pal, Symmetric and asymmetric coupled lines band-stop filters at Ku/Ka bands, RF Design, March 26 [7] F. Martın, J. Bonache, F. Falcone, M. Sorolla, R. Marque s, Split ring resonator-based lefthanded coplanar waveguide, Applied Physics Letters, Vol. 83, No 22, 1 December 23 ISSN: ISBN: