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Analysis and design of microstrip to balanced stripline transitions
RUZHDI SEFA1, ARIANIT MARAJ
2
1Faculty of Electrical and Computer Engineering, University of Prishtina - Prishtina
2 Faculty of Software Design, Public University of Prizren - Prizren
1&2REPUBLIC OF KOSOVA
[email protected], [email protected] Abstract - A design method for microstrip to balanced stripline transition is presented. The transition is
suitable for application in feeding arrays of double-side printed antennas. The transition is a Chebyshev
taper impedance transformer and the conversion from unbalanced to balanced line relied on a gradual
change of the cross-section of the line. The transmission parameters of an asymmetric line are derived
with a method based on the quasi-TEM wave approximation. Also, in this paper are presented calculated
results for 50 microstrip to 100 balanced stripline and 100 microstrip to 50 balanced stripline
transitions.
Keywords- Microstrip, Balanced stripline, Transformer, TEM mode
1 Introduction Printed dipole radiators have been popular
candidates for phased-array antennas that
contain many elements because of their
suitability for integration with microwave
integrated circuit modules [1]–[3]. Arrays of
double-sided printed strip dipoles fed with
corporate networks of parallel striplines and
backed by conductor planes were developed for
radar and various military applications [4].
Various antenna structures of double-sided
printed strip dipoles connected through balanced
striplines having dual-band and broadband
properties have been reported [5]. These
structures are suitable for low-cost base station
antennas, because they have simple
configuration and can be easily manufactured.
To feed a double-sided printed strip antenna
from a conventional coaxial connector, however,
a transition from unbalanced line to a balanced
line must be used to keep the antenna in a
balanced state. The transition performs
conversion of electromagnetic fields and can be
used as impedance transformer. Moreover, the
transition must be capable of operating over a
large frequency range to be compatible with the
antenna performance.
Impedance transformation and matching are
required in general microwave networks and
antenna arrays to obtain maximum power
transfer between the source and load. In
addition, power often has to be divided between
different network elements. At high
frequencies, these common functions are usually
performed with distributed elements consisting
of sections of transmission lines. The most
commonly used quarter-wave impedance
transformer is shown in Fig. 1. A resistive load
of impedance LZ can to be matched to a network
with input impedance inZ by using a quarter-
wave section of transmission line with
impedance Linc ZZZ . The impedance is
perfectly matched only at the frequency at which
the electrical length of the matching section is
.4/L
Figure 1. Quarter wave transformer
The bandwidth provided by a quarter-wave
transformer may be adequate in many
applications, but there are also situations in
which a much greater bandwidth must be
provided. The bandwidth can be increased by
using cascaded quarter wave transformers [6] as
shown in Fig. 2. Each quarter wave section has
the same electrical length, and by a proper
choice of their characteristic impedances a
variety of pass-band characteristics can be
obtained [7]. The most commonly used multi-
Recent Researches in Telecommunications, Informatics, Electronics and Signal Processing
ISBN: 978-1-61804-005-3 137
section transformers are those with maximally
flat (binominal transformer) and equal-ripple
(Chebyshev transformer) reflection coefficient
characteristics. A typical plot of reflection
coefficient of a two-section quarter-wave
Chebyshev transformer as a function of is
shown in Fig. 2(b).
(a)
(b)
Figure 2(a) Multi-section quarter wave
transformer and (b) Input reflection coefficient
of a two-section quarter wave Chebyshev
transformer
Cascaded quarter-wave impedance
transformers of more than two sections are not
practical due to length constrains. Instead, a
transmission line which has the characteristic
impedance that varies continuously along its
length can be used as a broadband impedance
transformer. The broadband impedance
matching properties of the transformer are
obtained by utilizing a continuous transmission
line taper as shown in Fig. 3(a) with its
characteristic impedance changing smoothly
from LZ to inZ . If the variation of characteristic
impedance along the taper )(xZ is known, the
reflection coefficient can be easily calculated by
considering the taper to be made of a number of
short transmission line sections. Exponential
taper and taper with triangular distribution are
two examples of practical designs [7]. A more
important problem is to determine )(xZ to give
an input reflection coefficient with desired
frequency characteristics. An example of
practical importance is a taper that has its
characteristic impedance tapered along its
length. So that the input reflection coefficient
follows a Chebyshev response in the pass band.
The taper has equal-ripple minor lobes and is an
optimum design as it has the shortest length for a
given minor lobe amplitude.
Figure 3 Tapered transmission line
This paper presents a methodology to design
microstrip to balanced stripline (printed twin-
line) tapered transitions, and use them to
construct feed networks for arrays of double-
sided strip dipoles. The transition is
accomplished by narrowing the width of the
ground plane of microstrip line in tapered
fashion. The cross-section of the microstrip
conductor is then varied to obtain the required
impedance across the taper length. A quasi-TEM
method is used to calculate the transmission
characteristics of an asymmetric and in-
homogenous line. Conductor widths of various
printed microstrip to balanced stripline transition
are calculated and their characteristic impedance
and effective dielectric constant across the
length are presented.
2 Microstrip to balanced stripline
transition A microstrip to balanced stripline transition is
shown in Fig. 4. The transition is performed by
gradually changing the cross-section of the line
from microstrip (unbalance) at the input to the
strips of equal width (balanced) at the output. A
smooth change in cross-section of the line, such
as tapered line, is required so that the net
reflection at the input is arbitrary small [8]. The
transition itself together with the conversion of
electromagnetic field may be used to perform
the transformation of impedance. We use this
important advantage to design practically
convenient double-sided feed networks. These
networks consist of tapered line transitions and
cooperate feed network of balanced striplines.
Recent Researches in Telecommunications, Informatics, Electronics and Signal Processing
ISBN: 978-1-61804-005-3 138
Figure 4. Configuration of a microstrip to
balanced stripline transition.
We design tapered lines such that the input
reflection coefficient follows a Chebyshev
response in the pass band. To synthesize the
impedance taper, the parameters of an
asymmetric transmission line are derived by
using the rectangular boundary division method
[9]. The appropriate dimensions of cross-section
at each position along the taper are found by
assuming that the required taper impedance is
equal to the balanced mode characteristic
impedance of a uniform asymmetric line of that
particular cross-section.
3 Characterization Method A microstrip to balanced stripline transition is
designed as an impedance matching section,
which requires a synthesis procedure to
determine the line profile from the given
impedance profile. The tapered impedance
profile is selected so that the input reflection
coefficient follows a Chebyshev response in the
pass band. However, the tapered line shown in
Fig. 4 is an in-homogeneous line which supports
a non-TEM mode with the propagation constant
varying along its length. This makes the design
procedure very involved. As an approximation,
we start with the impedance profile of a TEM
Chebyshev taper, which can be obtained by
using the standard procedure [6], for given mZ ,
bZ , and desired ripple level. Such an impedance
profile will produce the same reflection
coefficient expressed in terms of electrical
length for any line structures. After the taper
profile is determined, the propagation constant
along the taper profile can be found and be
included in the calculation of the reflection
coefficient. The reflection coefficient obtained
in this way will be an approximation but close to
the starting reflection coefficient. The length of
the taper is determined by the lowest operating
frequency and the maximum reflection
coefficient which is to occur in the pass band.
The shape ratio, hw /1 and , at any position
x along the taper is determined by assuming
that the characteristic impedance of the taper at
that cross-section is equal to the characteristic
impedance of a uniform asymmetric line shown
in Fig. 5. The transmission characteristics of the
asymmetrical line are determined under the
quasi-TEM wave approximation, where the
problem is attributed to the calculation of the
line capacitance. The line capacitance for a
given structure is calculated by utilizing the
rectangular boundary division method [9]. The
structure to be analyzed is placed in a metallic
enclosure for the convenience of analysis, but
the dimensions of the enclosure are chosen large
enough such as the propagation characteristics
of the line are not significantly affected. The
presence of the metallic enclosure enables the
propagation of two fundamental modes (out-of-
phase and in-phase modes). The computation of
a taper performance based on the mode analysis,
however, showed that that spikes on the
reflection coefficient due to the excitation of in-
phase mode appear. In the case of an open
structure, the in-phase mode cannot be defined.
So, a different definition for the propagating
mode based on the balanced condition is used in
calculation.
For a two conductor system of fig. 5, a linear
system of equations can be written as:
2121111 VCVCQ (1a)
2221212 VCVCQ (1b)
where 1Q , 2Q denote the line charge per unit
length and 1V , 2V the line potential of each strip
conductor. The balanced condition is defined as
Recent Researches in Telecommunications, Informatics, Electronics and Signal Processing
ISBN: 978-1-61804-005-3 139
21 QQQ and 21 VVV (2)
Figure 5. Cross-section view of an asymmetrical
transmission line
Substituting Eq. (2) into Eq. (1) and rearranging,
the balanced mode capacitance is obtained as
122211
2122211
2CCC
CCC
V
QCb
(3)
The capacitance values 11C , 22C , and 12C are
obtained from three stationary values of
electrostatic energy corresponding to three
combinations of potentials on conductors and
the energy-capacitance relation give by
j
i j
iij VVCU
2
1
2
12
1 (4)
The balanced characteristic impedance and
effective permittivity are given as
00
1
bb
cCCv
Z (5)
0b
beff
C
C (6)
Where 0bC denotes the balanced mode
capacitance in y=the case where the dielectric
substrate in the structure is replaced by vacuum
and 0v denotes the phase velocity in vacuum.
Two parameters have to be determined from the
knowledge of the characteristic impedance at a
particular cross-section. This leads to a non-
unique solution. However, a profile that
changes smoothly along the taper must be
selected as to gradually perform the conversion
of the electromagnetic field. This is essentially
achieved by a tapered bottom conductor, the
parameters of which may be calculated knowing
the desired impedances of the microstrip and
balanced ends, namely mw2 and bw2 . Here, we
adopt a profile for the bottom conductor,
)/(2 Lxw , which can be expressed as
b
mu
mw
w
L
xwLxw
2
222 lnexp)/( (7)
The profile of the top conductor is then chosen
to achieve the Chebyshev impedance taper
between two impedances. The parameter u in
Eq. (7) is selected such that the obtained top
conductor profile changes smoothly along the
taper. Calculation experience showed that a
value between 2 and 3 will give satisfactory
results.
4 Calculated results The described characterization method was used
to find conductor width profiles of microstrip to
balanced stripline tapered transitions printed on
a substrate of height mmh 8.0 , relative
dielectric constant 2.2r , and conductor
thickness mmt 035.0 . The goal was to design
50 to 100 tapered transitions with reflection
coefficients lower than dB40 over the UMTS
frequency band of .17.2~71.1 GHzGHz Assuming
that the transition would have an average
effective dielectric constant of 2 along the taper
and the lowest operation frequency is GHz6.1 ,
the length of transition was found to be
mmL 90 . For calculation purposes, the
transition was considered as a number of short
transmission lines with uniform cross-sections.
First, the conductor profiles along a 50
microstrip to 100 tapered transition were
determined. For the given substrate, the
conductor widths on the microstrip and balanced
stripline ends were found as mmw 4.21 ,
mmw 0.242 and mmww 2.121 , respectively.
The lower conductor tapered profile was
determined by using equation (7). The width of
upper conductor was then determined such as
the characteristic impedance along transition is
similar to that of Chebyshev impedance taper.
The calculated conductor widths along this
Recent Researches in Telecommunications, Informatics, Electronics and Signal Processing
ISBN: 978-1-61804-005-3 140
transition are shown in Fig. 6(a). Variations of
characteristic impedance and effective dielectric
constant along the transition are shown in Fig.
6(b). Although this is an in-homogenous
transition with variable effective dielectric
constant, the response of input reflection
coefficient is similar to that of a typical
Chebyshev filter as shown in Fig 6(c).
(a)
(b)
(c)
Figure 6 (a) Profile of a 50 microstrip to
100 balanced stripline transition, (b)
Calculated characteristic impedance and
effective permittivity along the taper, (c)
Calculated input reflection coefficient
Next, the conductor profiles along a 100
microstrip to 50 tapered transition were
determined. For the given substrate, the
conductor widths on the microstrip and balanced
stripline ends were found as mmw 66.01 ,
mmw 0.202 and mmww 08.321 ,
respectively. The conductor widths of this
transition were calculated following the same
procedure and are shown in Fig. 7(a).
Variations of characteristic impedance and
effective dielectric constant along the transition
are shown in Fig. 7(b), and the input reflection
coefficient in Fig. 7(c). Again, the calculated
input reflection coefficient resembles that of a
Chebyshev taper.
(a)
(b)
(c)
Figure 7 (a) Profile of 100 microstrip to 50
balanced stripline transition. (b) Calculated
characteristic impedance and effective
permittivity along the taper. (c) Calculated input
reflection coefficient.
5 Conclusion A method to design microstrip to balanced
stripline tapered transitions was presented. Such
transitions are required when feeding balanced
antennas from unbalanced coaxial cables. The
Recent Researches in Telecommunications, Informatics, Electronics and Signal Processing
ISBN: 978-1-61804-005-3 141
transitions were also used as impedance
transformers to design feed networks that can be
used in arrays of double-sided printed strip
dipoles. The geometry of transition was selected
to provide a Chebyshev taper response as this
taper is characterized with smooth variations of
characteristic impedance along the taper that is
suitable for electromagnetic field conversion and
nearly perfect impedance matching over wide
frequency bandwidths. The transition was
accomplished by narrowing the width of the
ground plane of microstrip line in tapered
fashion.
A quasi-TEM method was used to
characterize asymmetric and in-homogenous
transmission lines encountered in design of
microstrip to balanced stripline transitions.
Calculated results for 50 microstrip to 100
balanced stripline and 100 microstrip to 50
balanced stripline tapered transition were
presented and their input reflection coefficients
shown to be similar to that of a TEM Chebyshev
taper.
References:
[1] A. J. Parfitt, D.W. Griffin, and P. H. Cole,
“Analysis of infinite arrays of substrate-
supported metal strip antennas,” IEEE Trans.
Antennas Propagat., vol. 41, pp. 191–199, Feb.
1993.
[2] J. R. Bayard, M. E. Cooley, and D. H.
Schaubert, “Analysis of infinite arrays of printed
dipoles on dielectric sheet perpendicular to a
ground plane,” IEEE Trans. Antennas
Propagat., vol. 39, pp. 1722–1732, Dec. 1991.
[3] B. Edward and D. Rees, “A broad-band
printed dipole with integrated balun,”
Microwave J., pp. 339–344, May 1987.
[4] W. C. Wilkinson, “A class of printed circuit
antennas,” in IEEE AP-S
[5] F. Tefiku and C. Grimes, “Design of broad-
band and dual-band antennas comprised of
series-fed printed-strip dipole pairs,” IEEE
Trans. Antennas Propagat., vol. 48, pp. 895–
900, Jun. 2000.
[6] Ruzhdi Sefa, Alida Shatri Maraj, Arianit
Maraj, “Analysis of transmission lines matching
using quarter-wave transformer, WSEAS
conference, ID: 649-290, 2011
[7] R. E. Collin, Foundation for Microwave
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[8] J. W. Duncan and V. P. Minerva, “100:1
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[9] E Yamashita, M. Nakajima, and K. Atsuki,
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Recent Researches in Telecommunications, Informatics, Electronics and Signal Processing
ISBN: 978-1-61804-005-3 142