Circuits and Systems, 2011, 2, 121-126
doi:10.4236/cs.2011.23018 Published Online July 2011 (http://www.SciRP.org/journal/cs)
Copyright © 2011 SciRes. CS
Analyzing an UWB Bandpass Filter for High Power
Applications Using Rectangular Coaxial Cables with
Square Inner Conductors
Nasreddine Benahmed1, Nadia Benabdallah2, Salima Seghier3, Fethi Tarik Bendimerad1,
Boumedienne Benyoucef1
1University Abou Bekr Belkaid-Tlemcen, Tlemcen, Algeria
2Preparatory School of Sciences and Technology (EPST-Tlemcen), Tlemcen, Algeria
3University of Saida, Saida, Algeria
E-mail: N_Benahmed@yahoo.fr
Received February 5, 2011; revised April 6, 2011; accepted April 13, 2011
Abstract
Using the finite element method (FEM) in two dimensions and the CST MICROWAVE STUDIO® (CST
MWS) Transient Solver, the electromagnetic (EM) analysis and the design of a novel compact ultra wide-
band (UWB) bandpass filter using rectangular coaxial cables with square inner conductors, convenient for
high power applications, are presented. The design of the UWB BP filter is based on the use of impedance
steps and coupled-line sections. The center frequency around 6.85 GHz was selected, the bandwidth is be-
tween 3 - 10 GHz, the insertion-loss amounts to around 0.35 dB and the return loss is found higher than 10
dB in a large frequency range 4 - 9.5 GHz. The simulated results of stopband performances are better than 15
dB for a frequency range up to 11 GHz. For the selected center frequency and on a substrate with a dielectric
constant of 2.03, the rectangular coaxial cables BPF with square inner conductors is only 6.7 × 8.9 × 33.4
mm in size.
Keywords: Rectangular Coaxial Cables, Square Inner Conductors, Ultra Wideband Bandpass Filter, Compact
Filter, Electromagnetic Parameters, Analysis and Design, FEM Method, CST MWS Transient
Solver
1. Introduction
Since the Federal Communications Commission (FCC)
released the unlicensed use of ultra-wideband (UWB: 3.1
to 10.6 GHz) wireless systems in February 2002 [1],
many researchers have started exploring various UWB
components, devices, and systems [2,3]. As one of the
key circuit blocks in the whole system, the UWB band-
pass filter (BPF) has been studied through the use of the
matured filter theory [4] and other techniques [5,6].
On the basis of impedance steps and coupled-line sec-
tions as inverter circuits, several works were interested in
the design of planar broadband filters with low loss,
compact size, high suppression of spurious responses,
and improved stopband performances [7,8].
In this work, we propose a novel and a simple compact
ultra wideband (UWB) bandpass filter using rectangular
coaxial cables with square inner conductors, convenient
for high power applications. The filter can be easily de-
signed and fabricated using FeeFEM environment [9],
CST MICROWAVE STUDIO® (CST MWS) Transient
Solver [10] or other commercial EM software. The de-
sign of the UWB filter is based on the use of impedance
steps and coupled-line sections. The center frequency
around 6.85 GHz was selected, the bandwidth is between
3-10 GHz, the insertion-loss amounts to around 0.35 dB
and the return loss is found higher than 10 dB in a large
frequency range (4 - 9.5) GHz. The simulated results of
stopband performances are better than 15 dB for a fre-
quency range up to 11 GHz. For the selected center fre-
quency and on a substrate with a dielectric constant of
2.03, the rectangular coaxial cable BPF with square inner
conductors is only 6.7 × 8.9 × 33.4 mm in size. What
follows are the analysis and the design of this compact
UWB filter using both FEM method under FeeFEM en-
vironment and CST MWS Transient Solver.
122 N. BENAHMED ET AL.
2. Rectangular Coaxial Cables
Coupled rectangular coaxial cables can provide signal
coupling in a compact form for any characteristic im-
pedance systems. They were used previously in [11] to
build a directional coupler. This kind of coupler has ex-
cellent performance in terms of high directivity, low
VSWR, good isolation, excellent electromagnetic inter-
ference (EMI) shielding, high power handling capability,
and low cost due to the use of commercial semirigid rec-
tangular coaxial cables and elimination of a mechanical
housing.
Figure 1 shows the cross-section of a rectangular co-
axial coupled line with square inner conductors. The ca-
ble is assumed to be lossless with an inner squared con-
ductor of side (2a1) and an outer rectangular conductor of
height (2a2) and width (2(a2 + h)). Dielectric material
with dielectric constant (
r) fills the inside of the cable. A
portion of each cable is cut out and two of these cut ca-
bles are joined to form the coupled line. The cut depth is
represented by (h) on the cross section as shown in Fig-
ure 1.
3. Numerical Resolution
The electrical properties of the lossless and homogene-
ous symmetrical coupler presented in Figure 1 can be
described in terms of its primary parameters [L] and [C],
and its secondary parameters k, Z0e and Z0o [12,13].
where: ;

11 12
21 22
LL
LLL




11 12
21 22
CC
CCC



The inductance matrix [L] contains the self-induct-
ances on the diagonal (L11 = L22 are the proper induct-
ances) and the mutual inductances (L12 = L21) between
the two coupled lines.
Matrix [C] accounts for the capacitative effects be-
tween the two coupled lines, characterizing the electric
field energy storage in the coupler. (C11 = C22) are the
proper capacitances and (C12 = C21) is the coupling ca-
pacitance.
a
2
ε
γ
, μ
γ
= 1
a
1
h
Figure 1. Cross section of the rectangular coaxial coupled
line with square inner conductors.
12 12
11 11
LC
kLC
;
is the coupling coefficient and (Z0e, Z0o) are respectively
the even- and the odd-modes characteristic impedances
of the coupler.
On the other hand, the isolated line of Figure 2 is de-
scribed in terms of its inductance and capacitance per
unit length (L and C) and in term of its characteristic
impedance Z0.
In reference 14, we successfully realized a numerical
tool under FreeFEM environment, used to analyze elec-
tromagnetic (EM) parameters for rectangular coaxial
couplers with square inner conductors. This numerical
tool can be easily adapted to study any other TEM or
quasi-TEM structure [15]. Also, we proposed rigorous
analytical expressions for the primary parameters (in-
ductance [L] and capacitance [C] matrices) and the im-
pedances (Z0e, Z0o) of the even- and odd-modes for rec-
tangular coaxial couplers with square inner conductors
[14]. The analytical expressions are convenient for all
coupled rectangular coaxial couplers having square inner
conductors with a wide range of cut depths and an outer
to inner conductor ratio between 1.4 and 10. We pro-
posed others analytical expressions in order to calculate
the EM parameters of squared coaxial lines [16]. All our
analytical expressions were deduced from rigorous
analyses by the FEM and MoM methods under respect-
tively FreeFEM and LINPAR [17] environments. Using
these analytical expressions, an analysis can be readily
implemented in modern CAE software tools for the de-
sign of microwave and wireless components.
4. UWB Filter Using Rectangular Coaxial
Cables
Assuming 50- external feeding lines, Figures 3(a) and
3(b) show respectively the 3D schematic representation
and the longitudinal section of the proposed UWB BPF.
An isolated rectangular coaxial line with one square inner
conductor in the middle and a rectangular coaxial coupled
line with square inner conductors at the two ends [18].
a
2
ε
γ
, μ
γ
= 1
a
1
h
Figure 2. Cross section of the rectangular coaxial line with
one square inner conductor.
Copyright © 2011 SciRes. CS
N. BENAHMED ET AL.
123
To achieve the specified UWB bandpass, the three
sections of this filter are arranged with the lengths of
about one quarter-, one half-, and one quarter-wave-
length, i.e.,
/4,
/2 and
/4 [18], as marked in Figure
3(b).
5. EM Analyses and Design
As part of the study, we were interested in the design of
the 50 -UWB bandpass filter having an inner conductor
of side (2a1 = 2 mm), an outer conductor of side (2a2 =
6.7 mm) and a dielectric constant of 2.03, we have varied
the cut depth (h) from (a1) to (a2) in order to assure for
the rectangular coaxial coupler a coupling coefficient
less than 5 dB (Figure 4).
A coupling coefficient of 2.4 dB was obtained using
our previous works based on FEM for a cut depth (h) of
1.1 mm, yielding a characteristic impedance of approxi-
mately 00eo
Z
Z = 26.24 and the following pri-
mary EM parameters:

190.9 144.6
144.6 190.9
nH
Lm







278.7 211.4
211.4 278.7
pF
Cm






(a)
(b)
Figure 3. Longitudinal section of the proposed UWB BPF
using rectangular coaxial cables with square inner conduc-
tors.
For a length of one quarter-wavelength, i.e., l =
/4
and in order to verify if the designed coupler has a cou-
pling coefficient less than 5 dB in the frequency range
[3.1 - 10.6] GHz, we plotted the resulting coupling coef-
ficient of the rectangular coaxial coupler of Figure 4
versus frequency as shown in Figure 5, using MATPAR
software [19]. From this figure, it appears clearly that the
coupling coefficient (S12) and the isolation (S14) vary
respectively between 4 - 5.5 dB and 11.4 - 11.5 dB in the
frequency band [3.1 - 10.6] GHz. In the same frequency
band the minimum directivity of the coupler
14 12
SS
is approximately 6 dB.
For the middle line of the UWB BPF represented in
Figure 6, the outer conductor parameters, the cut depth
(h) and the dielectric constant were kept constants (i.e. a2
= 3.35 mm, h = 1.1 mm and
r = 2.03) and the inner
conductor side (2a1) was varied as needed in order to get
a characteristic impedance (Z0) of 19 for the middle
line. This value of (Z0) was obtained for (a1 = 2.1 mm),
yielding an inductance and a capacitance per unit length
respectively of 90.75 nH/m and 248.55 pF/m [14].
a
1
a
2
2(ha
1
)
Figure 4. Rectangular coaxial coupler with square inner
conductors.
S
11
S
12
S
13
S
14
Figure 5. Scattering parameters of the rectangular coaxial
coupler presented in Figure 4.
Copyright © 2011 SciRes. CS
N. BENAHMED ET AL.
Copyright © 2011 SciRes. CS
124
cables with square inner conductors, are in very reason-
able agreement with those using planar structures. The
plotted wideband also accorded the FCC-defined UWB
for high power applications.
V/m
V/
m
For the simulated UWB filter using CST, the inser-
tion-loss amounts to around 0.35 dB and the return loss
is found higher than 10 dB in a large frequency band (4 -
9.5) GHz. The simulated results of stopband perform-
ances are better than 15 dB for a frequency range up to
11 GHz.
For this type of UWB bandpass filter using rectangular
coaxial cables with square inner conductors, there are no
numerical or experimental results in the scientific litera-
ture. In order to check our results obtained by the CST
MWS Transient Solver we were obliged, for the same
geometrical and physical parameters of our filter, to
make simulations using our previous works and estimate
the resulting scattering parameters of the designed UWB
filter using MATPAR software. The results coefficients
(S11) and (S12) as functions of frequency for the proposed
UWB BP filter structure are provided in Figure 9. The
Figures 8 and 9 show that the responses obtained by the
two numerical models (CST and MATPAR) are in a
good agreement.
Figure 6. CST simulation of the middle line of the proposed
UWB BPF.
We applied the CST MWS Transient Solver in the aim
of checking the predicted electrical performance of our
proposed and designed UWB BPF using rectangular co-
axial cables of Figure 3. The designed filter is charac-
terized by the features marked in Figure 7.
In the frequency range [1 - 11] GHz, Figure 8 provides
plots of the resulting scattering parameters obtained of the
proposed and designed UWB BPF. It can be seen that the
simulated responses, obtained by the CST MWS Tran-
sient Solver, of the UWB filter using rectangular coaxial
Figure 7. Longitudinal section view of the designed UWB BPF.
S
12
S
22
S
12
S
22
Figure 8. Scattering parameters of the designed 50 -UWB BPF obtained by the CST MWS Transient Solver.
N. BENAHMED ET AL.
125
S
12
S
11
S
12
S
11
Figure 9. Scattering parameters of the designed 50 UWB BPF obtained by MATPAR software.
6. Conclusions
A novel and a simple compact ultra wideband bandpass
filter using rectangular coaxial cables with square inner
conductors, convenient for high power applications, is
presented, analyzed and designed. The design of the
UWB filter is based on the use of impedance steps and
coupled-line sections.
The designed rectangular coaxial cable bandpass filter
is only 6.7 × 8.9 × 33.4 mm in size and can be easily
designed and fabricated using CST MICROWAVE
STUDIO® Transient Solver or other commercial EM
software. The bandwidth of the designed filter is between
3 - 10 GHz, the insertion-loss amounts to around 0.35 dB
and the return loss is higher than 10 dB in a large fre-
quency range. The simulated results of stopband per-
formances are better than 15 dB for a frequency range up
to 11 GHz.
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