Analyzing an UWB Bandpass Filter for High Power Applications Using Rectangular Coaxial Cables with Square Inner Conductors

doi:10.4236/cs.2011.23018

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Circuits and Systems, 2011, 2, 121-126

doi:10.4236/cs.2011.23018 Published Online July 2011 (http://www.SciRP.org/journal/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: [email protected]

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

LLL









11 12

21 22

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.

, μ

= 1

Figure 1. Cross section of the rectangular coaxial coupled

line with square inner conductors.

12 12

11 11

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-Ω 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].

, μ

= 1

Figure 2. Cross section of the rectangular coaxial line with

one square inner conductor.

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 = 26.24 Ω and the following pri-

mary EM parameters:



190.9 144.6

144.6 190.9















278.7 211.4

211.4 278.7















(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 =



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].

2(h – a

)

Figure 4. Rectangular coaxial coupler with square inner

conductors.

Figure 5. Scattering parameters of the rectangular coaxial

coupler presented in Figure 4.

N. BENAHMED ET AL.

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

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.

Figure 8. Scattering parameters of the designed 50 Ω-UWB BPF obtained by the CST MWS Transient Solver.

N. BENAHMED ET AL.

125

Figure 9. Scattering parameters of the designed 50 Ω 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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