Design and Analysis of Parallel-Coupled Line Bandpass Filter Talib Mahmood Ali Asst. Lecturer, Electrical Engineering Department, University of Mustansiriyah, Baghdad, Iraq Abstract A compact microwave parallel coupled line resonator seventh order bandpass filter (BPF) is presented in this paper, consist a 8-parallel coupled line pairs designed for a maximally flat response or Butterworth response at a center frequency of 2.44175 GHz and with a fractional bandwidth, = 0.035. The filter was implemented in a microstrip platform with a permittivity of the substrate E r =4.4 and a substrate height h=1.5mm. The physical parameters of the parallel coupled line filter sections were optimized using the Microwave Office software to provide the closest values of the bandpass filter prototype values and electrical lengths for a given set of filter specifications. The simulation of direct calculation, show the attenuation S 11 response was observed at 2.44175 GHz with a value of -25 db and the corresponding Insertion Loss S 21 is - 1.8dB while the optimized design S 11 response at the centre frequency with a value of -113 db and the corresponding Insertion Loss S 21 is -2.2dB. Keywords Parallel Coupled line Microstrip, Butterworth, microwave BPF. 1. Introduction Microwave filters are two-port networks used in an electronic system capable of allowing transmission of signals over the pass-band and rejecting unwanted harmonics over the stop-band. Different kinds of approximations, like Butterworth, Chebyshev and Elliptic function [1] have been proposed and widely used as models for microwave-filter synthesis [2]. Butterworth Filters have the flattest possible pass-band magnitude response. That means all the derivatives of the amplitude with frequency are zero at DC [3]. The Butterworth response is a good compromise between attenuation characteristic and group delay. The group delay of Butterworth filters is reasonably flat but has a rise near the cut off frequency. The step response of these filters exhibits some ringing, which degrades its use for data communications. Parallel-coupled microstrip bandpass filters have been extensively adopted in the RF front end of microwave and wireless communication systems for decades. Two shortcomings limit the range of practical applications of coupled-line filters [4],[5]. The parallel coupled lines filter based on the odd and even wave coupling of transmission lines through a common ground plane, which results in odd and even characteristic line impedances. This sets the stage to an understanding of the coupling between two strip lines and their input/output impedances as part of a two port chain matrix representation. Cascading these elements gives rise to bandpass filter structures A simple modelling approach of coupled microstrip line interaction is established when considering the geometry depicted in Fig. 1. The parallelcoupled microstrip transmission lines can be used to construct many types of filters. The general conventional BPF structure of the parallel-coupled-line filter is based on the half-wavelength resonators [6],[7]. Figure 1. The parallel coupled lines microstrip geometry and structure. 2. Design procedure of the BPF The design parameters of the proposed maximally flat BPF are; filter type: Butterworth, mean frequency f o = 2.44175 GHz, lower limiting frequency f min =2.4 GHz upper limiting frequency f max =2.4835 GHz, degree of filtration N = 7 and system impedance Z o = 50 Ω. The degree of filtration, N, should always be selected to be odd (i.e.,3, 5, 7...), because the source resistance and the load resistance is identical under these conditions. The number of coupled line pairs is always 1 more than the selected degree of filtration. For N=7, there must thus be eight line pairs. Step 1: The Prototype elements of 7 th order Butterworth LPF was determined below g 1 =0.4450 g 7 =0.4450 ISSN : 0975-5462 Vol. 5 No.09 Sep 2013 1700
g 2 =1.2470 g 6 =1.2470 g 3 =1.8019 g 5 =1.8019 g 4 =2.000 Step 2 Calculating the fractional bandwidth of pass band: 2.4835 2.4 2.44175 0.0341967 Step 3 The proposed filter involved eight line pairs admittance inverter constants for the eight line pairs, the admittance inverter constants was computed for all line pairs; 1. Determining the admittance inverter constants for 1 st line pair: 2 0.347434 2. Determining the admittance inverter constants for 2 nd line pair: 3. Determining the admittance inverter constants for 3 th line pair: 4. Determining the admittance inverter constants for 4 th line pair: 5. Determining the admittance inverter constants for 5 th line pair: 6. Determining the admittance inverter constants for 6 th line pair: 7. Determining the admittance inverter constants for 7 th line pair: 8. Determining the admittance inverter constants for 8 th line pair: 0.072109494 0.035834 0.2829598 0.0282959845 0.035834932 0.0721094069 0.34743420 2 Step 4: The EVEN and ODD impedances of line pairs was determined by following formulae 50Ω 1 For 1 st line pairs: For 2 nd line pairs: 50Ω 1 50Ω 1 0.347434 0.347434 73.407236Ω 50Ω 1 0.347434 0.347434 26.5927638Ω 50Ω 1 0.0721095 0.0721095 53.86546Ω 50Ω 1 0.0721095 0.0721095 46.1345363Ω For 3 rd line pairs: Z EVEN =51.855490377Ω Z ODD =48.144096222 Ω For 4 th line pairs: Z EVEN =68.15130242 Ω Z ODD =31.84869575 Ω ISSN : 0975-5462 Vol. 5 No.09 Sep 2013 1701
For 5 th line pairs: Z EVEN =51.454832362 Ω Z ODD =48.5451676 Ω For 6 th line pairs: Z EVEN =51.55953717 Ω Z ODD =48.144046 Ω For 7 th line pairs: Z EVEN =53.86545867 Ω Z ODD =46.13454132 Ω For 8 th line pairs: Z EVEN =73.407236 Ω Z ODD =26.5727 Ω Step 5: Calculating Microstrip Widths, Lengths and Spacing: W 1 =2.7550260 mm l 1 =8.425656 mm S [1,2] =2.845856 mm W 2 =2.755026 mm l 2 =8.418619 mm S [2,3] =4.643744 mm W 3 =2.755026 mm l 3 =8.410632 mm S [3,4]= 5.384845 mm W 4= 2.755026mm l 4 =8.409676mm S [4,5] =5.384845 mm W 5 =2.755026mm l 5 =8.410632mm S [5,6] =4.643744 W 6 =2.755026 mm l 6= 8.418619 mm S [6,7] =2.845856 mm W [7] =2.755026 l [7] =8.425656 Wt 1 =2.739197 lt 1 =2.408472 Wt 7 =2.739197 lt 7 =2.408472 Figure (2) The parallel coupled lines microstrip BPF. Line Pair ZEVEN (Ω) ZODD (Ω) 1 73.407236 26.5927638 2 53.86546 46.1345363 3 51.855490 48.144096222 4 68.151302 31.84869575 5 51.454832 48.5451676 6 51.559537 48.144046 7 53.865458 46.13454132 8 73.407236 26.5727 Table 1. The Even and Odd Impedance for the proposed BPF. The parallel-coupled microstrip transmission lines can be used to construct many types of filters [8]. The general conventional BPF structure of the parallel-coupled-line filter is based on the half-wavelength resonators. The ISSN : 0975-5462 Vol. 5 No.09 Sep 2013 1702
proposed filter structure is constructed on the FR4, PCB board with dielectric constant E r = 4:4, and substrate thickness h = 1:6 mm. 3. Filter Simulation and Results The AWR Microwave Office was used to simulate the BPF design. Figure 4 detailed the dimensional data of the proposed BPF. A step element (offset)was inserted at the junction between the transmission line sections to make the simulated result more accurate. Figure (1) shows the simulated S 11, S 12, S 21 and S 22 while figure (5) illustrate the simulated S 11, S 12, S 21 after optimized the proposed design. Figure (3) The S-parameters Chebyshev, 0.01 ripple LPF. Figure (4) Response of filter designed by direct calculation, simulated by AWR software. Center frequency is 2.44175GHz. Bandwidth is 0.0835GHz. Figure (5) Response of filter designed by direct calculation, simulated by AWR software. Center frequency is 2.44175GHz. Bandwidth is 0.0835GHz. ISSN : 0975-5462 Vol. 5 No.09 Sep 2013 1703
4. Conclusion A coupled line bandpass filter was successfully designed by direct conventional calculation and simulated by using a CAD design tool. The proposed BPF was optimized by using Microwave Office optimizer. Both designs were slightly different due to numerical approximation of direct conventional calculation the attenuation S 11 response was observed at 2.44175 GHz with a value of -25 db and the corresponding Insertion Loss S 21 is - 1.8dB while the optimized design S 11 response at the centre frequency with a value of -113 db and the corresponding Insertion Loss S 21 is -2.2dB. A greater degree of filtration brings about sharper edges in the filter stop band, but the attenuation in the pass band is also increased, due to the greater number of line piars and their losses.tuning capability would have been a helpful calibration capability to resolve direct conventional calculation. Based on the results that have been obtained from this project, it is proven that the proposed BPF provides better results in term of stopband attenuation and operating frequency. REFERENCES [1] R. Levy and J. D. Rhodes, A comb-line elliptic filter, IEEE Trans. Microwave Theory Tech. vol. 19, pp. 26-29, Jan. 1971. [2] M. L. Roy, et. Al., The continuously varying transmission-line tecnique-application to filter design, IEEE Trans. Microwave Theory Tech., vol. 47, pp. 1680-1687, Sept. 1999. [3] K. C. Lek and K. M. Lum, Stepped Impedance Key-shaped Resonator for Bandpass and Bandstop Filters Design, Progress In Electromagnetics Research Symposium Proceedings, KL Malaysia, March 27-30, 2012. [4] Ian Hunter, Theory and Design of Microwave Filters, The Institution of Engineering and Technology, London, United Kingdom, 2006. [5] George D. Vendelin, Anthony M. Pavio and Ulrich, Microwave Circuit Design Using Linear and Nonlinear Techniques, Second Edition, A John Wiley & Sons, Inc., Publication, 2005. [6] Jia-Sheng Hong, M. J. Lancaster, Microstrip Filters for RF/Microwave Applications, John Wiley & Sons, Inc, PP 109, 2001. [7] Kuo-Sheng Chin, Yi-Ping Chen, Ken-Min Lin, and Yi-Chyun Chiang, Compact Parallel Coupled Line Baned Pass Filter with Wide Bandwidth and Suppression of,microwave AND OPTICAL TECHNOLOGY LETTERS / Vol. 51, No. 8, August 2009. [8] Reshma R. Lokapu, Hassan, International Conference on Electronics and Communication Engineering, 28 th April-2013, Bengaluru. ISSN : 0975-5462 Vol. 5 No.09 Sep 2013 1704