Compact Parallel-Coupled Line Bandpass Filter for
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 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 Er=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 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 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 stopband. 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 parallel-coupled 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 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 = 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 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 2 Calculating the fractional bandwidth of
pass band:
𝑓𝑚𝑎𝑥 − 𝑓𝑚𝑖𝑛 2.4835 − 2.4
∆=
=
𝑓𝑜
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;
5. Determining the admittance inverter constants
for 5th line pair:
𝑍𝑜 × 𝐽5 =
𝜋×∆
2 × √𝑔4 × 𝑔5
= 0.0282959845
6. Determining the admittance inverter constants
for 6th line pair:
𝑍𝑜 × 𝐽6 =
𝜋×∆
2 × √𝑔5 × 𝑔6
= 0.035834932
7. Determining the admittance inverter constants
for 7th line pair:
𝑍𝑜 × 𝐽7 =
𝜋×∆
2×√𝑔6 × 𝑔7
= 0.0721094069
8. Determining the admittance inverter constants
for 8th line pair:
𝜋×∆
𝑍𝑜 × 𝐽8 = √
= 0.34743420
2 × 𝑔7 × 𝑔8
Step 4: The EVEN and ODD impedances of
line pairs was determined by following formulae
𝑍𝐸𝑉𝐸𝑁 = 50Ω × [1 + 𝑍𝑜 × 𝐽𝑛 + (𝑍𝑜 + 𝐽𝑛 )2 ]
𝑍𝑂𝐷𝐷 = 50Ω × [1 − 𝑍𝑜 × 𝐽𝑛 + (𝑍𝑜 + 𝐽𝑛 )2 ]
For 1st line pairs:
𝑍𝐸𝑉𝐸𝑁 = 50Ω × [1 + 0.347434 + (0.347434)2 ]
= 73.407236Ω
𝑍𝑂𝐷𝐷 = 50Ω × [1 − 0.347434 + (0.347434)2 ]
= 26.5927638Ω
For 2nd line pairs:
1. Determining the admittance inverter constants
for 1st line pair:
𝜋×∆
𝑍𝑜 × 𝐽1 = √
= 0.347434
2 × 𝑔1
2. Determining the admittance inverter constants
for 2nd line pair:
𝑍𝑜 × 𝐽2 =
𝜋×∆
2 × √𝑔1 × 𝑔2
For 3rd line pairs:
ZEVEN=51.855490377Ω
𝜋×∆
2 × √𝑔2 × 𝑔3
= 0.035834
4. Determining the admittance inverter constants
for 4th line pair:
𝑍𝑜 × 𝐽4 =
𝑍𝑂𝐷𝐷 = 50Ω × [1 − 0.0721095 + (0.0721095)2 ]
= 46.1345363Ω
= 0.072109494
3. Determining the admittance inverter constants
for 3th line pair:
𝑍𝑜 × 𝐽3 =
𝑍𝐸𝑉𝐸𝑁 = 50Ω × [1 + 0.0721095 + (0.0721095)2 ]
= 53.86546Ω
𝜋×∆
2 × √𝑔3 × 𝑔4
ZODD=48.144096222 Ω
For 4th line pairs:
ZEVEN=68.15130242 Ω
ZODD=31.84869575 Ω
= 0.2829598
For 5th line pairs:
ZEVEN=51.454832362 Ω
Wt1=2.739197
lt1=2.408472
ZODD=48.5451676 Ω
Wt7=2.739197
lt7=2.408472
For 6th line pairs:
Line Pair
ZEVEN (Ω)
ZEVEN=51.55953717 Ω
1
73.407236 26.5927638
ZODD=48.144046 Ω
2
53.86546
For 7th line pairs:
3
51.855490 48.144096222
ZEVEN=53.86545867 Ω
4
68.151302 31.84869575
ZODD=46.13454132 Ω
5
51.454832 48.5451676
For 8th line pairs:
6
51.559537 48.144046
ZEVEN=73.407236 Ω
7
53.865458 46.13454132
8
73.407236 26.5727
ZODD=26.5727 Ω
Step 5: Calculating Microstrip Widths, Lengths
and Spacing:
W1=2.7550260 mm
S[1,2]=2.845856 mm
l1=8.425656 mm
W2=2.755026 mm
S[2,3]=4.643744 mm
l2=8.418619 mm
W3=2.755026 mm
S[3,4]=5.384845 mm
l3=8.410632 mm
W4=2.755026mm
S[4,5]=5.384845 mm
l4=8.409676mm
W5=2.755026mm
S[5,6]=4.643744
l5=8.410632mm
W6=2.755026 mm
S[6,7]=2.845856 mm
l6=8.418619 mm
W[7]=2.755026 l[7]=8.425656
Figure (2) The parallel coupled lines microstrip BPF.
ZODD (Ω)
46.1345363
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
proposed filter structure is constructed on 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, S21 after
optimized the proposed design.
5. Conclusion
Figure (3) The S-parameters Chebyshev, 0.01 ripple LPF.
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
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.
REFERENCES
[1]
Figure (4) Response of filter designed by direct calculation,
simulated by AWR software. Center frequency is
2.44175GHz. Bandwidth is 0.0835GHz.
[2]
[3]
[4]
[5]
[6]
Figure (5) Response of filter designed by direct calculation,
simulated by AWR software. Center frequency is
2.44175GHz. Bandwidth is 0.0835GHz.
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