Compact Parallel-Coupled Line Bandpass Filterfor WLAN and ISM Bands
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 responseat a center frequency of 2.44175 GHzand with afractional bandwidth, ∆= 0.035. The filter was implemented in a microstrip platform with a permittivity of the substrate Er=4.4 and asubstrate height h=1.5mm. The physical parameters of the parallel coupled linefilter sections were optimized using the Microwave Office software toprovide the closest values of the bandpass filter prototype values and electrical lengths for a given set of filter specifications.The simulation of direct calculation, showthe attenuation S11 response was observed at 2.44175 GHz with a value of -25 dB and the corresponding Insertion Loss S21 is -1.8dB whilethe optimized design S11 response at the centre frequency with a value of -113 dB and the corresponding Insertion Loss S21 is -2.2dB.
Keywords ParallelCoupled 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 havethe 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 microstripbandpass filters have been extensivelyadopted in the RF front end of microwave and wireless communicationsystems for decades. Two shortcomings limit the range ofpractical applications of coupled-line filters [4],[5].The parallel coupled lines filter based on the odd and even wave couplingof transmission lines through a common groundplane, which results in odd and even characteristicline impedances. This sets the stage to anunderstanding of the coupling between two strip linesand their input/output impedances as part of a twoportchain matrix representation. Cascading theseelements gives rise to bandpass filter structures A simple modelling approach ofcoupled microstrip line interaction is establishedwhen considering the geometry depicted in Fig. 1.The parallel-coupled microstrip transmission lines can be used toconstruct many types of filters. The general conventional BPFstructure of the parallel-coupled-line filter is based on the half-wavelength resonators [6],[7].
Figure 1. The parallel coupled lines microstripgeometry and structure.
2. Design procedure of the BPF
The design parameters of the proposed maximally flat BPF are:
Filter type: Butterworth, mean frequency fo = 2.44175 GHz, lower limiting frequency fmin=2.4 GHz upper limiting frequency fmax=2.4835 GHz,degree of filtration N = 7 and system impedance Zo = 50Ω.
The degree of filtration, N, should always be selected to be odd (i.e.,3, 5, 7...), because thesource resistance and the load resistance is identical under these conditions. The number of coupled line pairs is always 1 more than the selected degree offiltration. For N=7, there must thus be eight line pairs.
Step 1:The Prototype elements of 7th order Butterworth LPF was determined below
g1=0.4450 g7=0.4450
g2=1.2470 g6=1.2470
g3=1.8019 g5=1.8019
g4=2.000
Step 2Calculating the fractional bandwidth of pass band:
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 1st line pair:
2. Determining the admittance inverter constants for 2nd line pair:
3. Determining the admittance inverter constants for 3th line pair:
4. Determining the admittance inverter constants for 4th line pair:
5. Determining the admittance inverter constants for 5th line pair:
6. Determining the admittance inverter constants for 6th line pair:
7. Determining the admittance inverter constants for 7th line pair:
069
8. Determining the admittance inverter constants for 8th line pair:
Step 4: The EVEN and ODD impedances of line pairs was determined byfollowing formulae
For 1st line pairs:
For 2nd line pairs:
For 3rd line pairs:
ZEVEN=51.855490377Ω
ZODD=48.144096222Ω
For 4th line pairs:
ZEVEN=68.15130242Ω
ZODD=31.84869575Ω
For 5th line pairs:
ZEVEN=51.454832362Ω
ZODD=48.5451676Ω
For 6th line pairs:
ZEVEN=51.55953717Ω
ZODD=48.144046Ω
For 7th line pairs:
ZEVEN=53.86545867Ω
ZODD=46.13454132Ω
For 8th line pairs:
ZEVEN=73.407236Ω
ZODD=26.5727Ω
Step 5: Calculating Microstrip Widths, Lengths and Spacing:
W1=2.7550260 mm l1=8.425656mm S[1,2]=2.845856 mm
W2=2.755026mm l2=8.418619 mm S[2,3]=4.643744mm
W3=2.755026mm l3=8.410632mm S[3,4]=5.384845mm
W4=2.755026mm l4=8.409676mm S[4,5]=5.384845mm
W5=2.755026mm l5=8.410632mm S[5,6]=4.643744
W6=2.755026 mm l6=8.418619 mm S[6,7]=2.845856 mm
W[7]=2.755026 l[7]=8.425656
Figure (2) The parallel coupled lines microstripBPF.
Wt1=2.739197 lt1=2.408472
Wt7=2.739197 lt7=2.408472
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 toconstruct many types of filters [8]. The general conventional BPFstructure of the parallel-coupled-line filter is based on the half-wavelength resonators. The proposed filter structure is constructedon the FR4, PCB board with dielectric constant Er= 4:4, and substrate thickness h = 1:6 mm.
Step 5. 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 S11, S12,S21 and S22 while figure (5) illustrate the simulated S11, S12,S21after optimized the proposed design.
Figure (3) TheS-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.
5. 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 calculationthe attenuation S11 response was observed at 2.44175 GHz with a value of -25 dB and the corresponding Insertion Loss S21 is -1.8dB while the optimized design S11 response at the centre frequency with a value of -113 dB and the corresponding Insertion Loss S21 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.
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