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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 55, NO. 5, MAY 2007
Dual-Band Filter Design With Flexible Passband
Frequency and Bandwidth Selections
Hong-Ming Lee, Member, IEEE, and Chih-Ming Tsai, Member, IEEE
Abstract—In this paper, improved dual-band filter design is
studied. The dual-band resonators are composed of shunt openand short-circuited stubs. In order to fulfill the requirements
of dual-band inverters, a structure of stepped-impedance asymmetric coupled lines is proposed and its equivalent circuit is
also derived. The dual-band filter is then designed based on this
equivalent circuit. This type of filter can achieve relatively large
practical passband center frequency ratios (in theory infinite),
and it has more freedom of bandwidth ratio. The circuit size is
also reduced. Detailed design procedure is presented and, finally,
a filter example is given to validate the theoretical study.
Index Terms—Coupled transmission lines, distributed parameter filters, immittance inverters, transmission line resonators.
I. INTRODUCTION
R
ECENTLY, the fast growing wireless local area network
(LAN) and cellular phones have become the most popular
mobile communication technologies and the people’s demands
for them are still continuously increasing. Dual-band, even triband, systems are employed in these ubiquitous wireless communications to enhance the reliability. Therefore, multiband filters become key components in the front end of these portable
devices. The simplest way to construct a dual-band filter is combining two single-band filters at different passband frequencies
[1]–[3]. However, they have the double size and cost of a singleband filter. Alternatively, the dual-band filter can be achieved by
a bandpass filter and a bandstop filter in a cascade connection
[4]. The circuit size is still larger since two filter sections are
also needed. Elaborate procedures were also proposed for dual
passband filters by synthesizing a bandstop response between
two passbands [5], [6]. One of these methods has the limit that
the two passbands must have symmetric responses. Examples
based on these procedures for filters with two widely separated
passbands are not yet shown.
Dual-band filter design based on lumped elements was presented in [7]. However, in that study, the realized resonators
and inverters using distributed circuits do not have the same
properties as those of the lumped elements at both the passband
frequencies. Stepped-impedance resonators are suitable for the
dual-band filter designs because their harmonic frequencies are
tunable [8]–[10]. Most of the studies focused on the design of
two passbands with required central frequencies, but very little
Manuscript received June 28, 2006; revised August 30, 2006. This work was
supported in part by the National Science Council, Taiwan, R.O.C., under Grant
NSC 94-2213-E-006-043 and Grant NSC 95-2221-E-006-085.
The authors are with the Institute of Computer and Communication Engineering, Department of Electrical Engineering, National Cheng Kung University, Taiwan 70101, R.O.C. (e-mail: tsaic@mail.ncku.edu.tw).
Digital Object Identifier 10.1109/TMTT.2007.895410
Fig. 1. (a) Dual-band resonator with parallel open- and short-circuited stubs.
(b) Type-III filter after [10].
have been done with the control of bandwidth for each band. The
dual-band coupling structures were firstly proposed in [11] and
can be used for the tuning of the required coupling coefficients.
The dual-band filter synthesis following the classical filter design methods was proposed in [12], and two types of dual-band
filters, which were called type-I and type-II filters, were studied.
The dual-band resonators were composed of parallel and series open stubs for type-I and type-II filters, respectively. Four
parameters, two characteristic impedances, and two electrical
lengths were used to meet the requirements of the resonant frequencies and slope parameters for the resonators at the two passband frequencies. Therefore, the dual-band filters can be successfully synthesized with the specified passband frequencies
and bandwidths. However, these two types of filter have some
restrictions such as the limitations of the passband frequency
ratio and bandwidth ratio.
In this paper, an improved dual-band filter design, called a
type-III filter, is proposed. As shown in Fig. 1, the resonator of
the type-III filter consists of both the open- and short-circuited
stubs. This filter structure is similar to that in [13]. However, in
their study, the absolute bandwidths of the two passbands are restricted to be the same since the electrical lengths of the stubs are
forced to be 90 at the average frequency of the two passbands.
In this paper, the type-III filter does not have such a limitation because the lengths of stubs are also the design parameters.
The inverters between the resonators can be realized with coupled-line sections. Since a uniform coupled-line circuits could
not generally have both the properties of the dual-band inverters
and resonators, a new structure of stepped-impedance coupled
lines is firstly introduced. Its equivalent circuit is derived and
then the basic equivalent circuit of the type-III filter is modified. It was found that type-III filters have advantages such as the
reduced circuit size and more freedom of passband frequency
ratio and bandwidth ratio. Finally, a filter design example is
given, and its experimental results are well within the theoretical prediction.
0018-9480/$25.00 © 2007 IEEE
LEE AND TSAI: DUAL-BAND FILTER DESIGN WITH FLEXIBLE PASSBAND FREQUENCY AND BANDWIDTH SELECTIONS
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Fig. 2. Stepped-impedance coupled-line structure for type-III filter.
Fig. 3. Equivalent circuit of the stepped-impedance coupled-line structure.
II. STEPPED-IMPEDANCE ASYMMETRIC COUPLED LINES
AND ITS EQUIVALENT CIRCUIT
For the inverters and stubs realized with the coupled-line sections, it was found that stepped-impedance coupled lines are
inherently necessary to have the dual-band properties [12]. In
order to simplify the synthesis procedure, a suitable coupledline structure for the type-III filter is first studied. The proposed
stepped-impedance coupled-line structure is shown in Fig. 2,
which is composed of two identical asymmetric coupled-line
sections. These two coupled-line sections are connected skew
symmetrically, and the diagonal ports are grounded. The electrical length of a single coupled-line section is , which is defined at the fundamental passband frequency . The even- and
and
are defined
odd-mode characteristic admittances
with the assumption that the lines are driven by identical magnitude of voltages with equal and opposite phases, and the detailed calculation can be found in [14]. The complete matrix
of the stepped-impedance coupled-line structure is calculated as
Fig. 4. (a) Transmission line shunted by short-circuited stubs with the negative
characteristic admittances on its sides. (b) and (c) Its equivalent circuits.
Fig. 5. Equivalent circuit of the stepped-impedance coupled-line structure.
(4)
Besides, it can be proven that a transmission line, with characteristic admittance of
and electrical length of , shunted
at its ends by two short-circuited stubs, with characteristic adand electrical length of , can be equivalent
mittance of
to an admittance inverter of
(5)
(1)
From (1), the equivalent circuit of the stepped-impedance coupled-line structure is proposed as that shown in Fig. 3, where a
and a charactransmission line with an electrical length of
is shunted on its sides by open- and
teristic admittance of
short-circuited stubs with electrical lengths of and characteristic admittance of and , respectively. After comparing the
-matrices of the circuits in Figs. 2 and 3, the conditions for
this two circuits to be equivalent at all frequencies are found as
as shown in Fig. 4(a) and (b). Furthermore, it can also be shown
that the short-circuited stubs can be replaced by open- and shortcircuited stubs with half the electrical lengths and characteristic
admittances, as shown in Fig. 4(c).
This equivalent circuit of an inverter is very similar to that in
Fig. 3. It implies that an inverter is embedded in the steppedimpedance coupled-line structure and can be extracted from the
equivalent circuit in Fig. 3. This results in the circuit shown in
Fig. 5. The structure is represented by an admittance inverter
shunted by open- and short-circuited stubs on its sides, with the
characteristic admittances given as
(2)
(6)
(3)
(7)
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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 55, NO. 5, MAY 2007
where is the termination conductance, is the low-pass proand
are the relative bandwidths at
totype value, and
and , respectively.
Since (9)–(12) are too complicated for solving the circuit paand
rameters, they are further simplified by eliminating
as
Fig. 6. (a) Modified type-III dual-band resonator and (b) filter.
III. MODIFIED TYPE-III DUAL-BAND FILTER
AND ITS DESIGN EQUATIONS
(15)
The modified type-III dual-band resonator and filter is shown
in Fig. 6. The original short-circuited stubs with an electrical
length of at in Fig. 1 are now replaced by open- and shortcircuited stubs with electrical lengths of at . According to
the discussion in Section II, the stepped-impedance coupled-line
structure can be equivalent to an admittance inverter shunted by
open- and short-circuited stubs, and these stubs are now parts of
the dual-band resonators. As shown in [12], at least four variables are needed for a resonator to have adjustable dual-band
properties. Assume that is the central frequency of the second
passband, and is the ratio of to . The inverter is required
to be the same at the central frequencies of the fundamental and
, if the ressecond passbands, i.e.,
onators at each stage are selected identical for simplicity. Therefore, the electrical length has to be
(8)
The rest of the four parameters of the dual-band resonator, i.e.,
, , , and , are used to meet both the requirements of
resonant frequencies and slope parameters at the two passbands,
which can be written as follows four simultaneous equations:
(9)
(10)
(11)
(12)
where and are the susceptance slope parameters at and
, respectively [15]. From the classical filter synthesis method
[15], the slope parameters and admittance inverters are determined by
(13)
and
(14)
(16)
for yielding
and . These two parameters should be solved
numerically, and they are then substituted into (9) and (11) to
and . It should be noted that (9)–(12) have analytic
obtain
solutions when the two passbands have the same absolute band. Under this condition, it was found that
widths, i.e.,
(17)
(18)
and, thus, the filter is reduced to the basic circuit configuration
of the type-III filter shown in Fig. 1.
The design curves of
for modified type-III filters
are plotted in Fig. 7(a) with the absolute bandwidth ratio
and
. The normalized impedances
of the open- and short-circuited stubs for a third-order
are given
Chebyshev filter with 0.1-dB ripple and
in Fig. 7(b) and (c). It was found that there is no limitation
of the passband frequency ratio for the modified type-III
filter, whereas the frequency ratios of type-I and type-II filters
have an upper limit of three [12]. However, the impedance
ratios between the stubs would be larger as the frequency ratio
goes higher, which might lead to an impracticable circuit, and
thus, only the design curves with the typical frequency ratios
smaller than five are plotted in Fig. 7. From (8) and the
design curves in Fig. 7(a), it is clear that the electrical lengths
and
are smaller than
, therefore, the total length of
the resonator could be shorter than . Each resonator of type-I
filters has two stubs. Typically, the lengths are approximately
and
, respectively. The total length of
. This is the same with type-II
the resonator is
filters. However, the length of dual-band resonators in type-III
, as indicated in (8) and (17).
is only approximately
Therefore, the length of the resonators of type-III filters is about
two-thirds of those of type-I and type-II filters. This means the
circuit size of type-III filters is smaller.
It should be noted that the impedances of the stubs are smaller
than that of the termination, especially for a filter with a narrower bandwidth. Therefore, in order to realize the dual-band filters with more practicable impedances, additional coupled-line
LEE AND TSAI: DUAL-BAND FILTER DESIGN WITH FLEXIBLE PASSBAND FREQUENCY AND BANDWIDTH SELECTIONS
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Fig. 8. Type-III dual-band filter, where the open- and short-circuited stubs are
separated into two equal parts for the synthesis of the coupled-line circuits in
the middle stages.
be found by the design equations in Section III. In order to synthesize the coupled-line circuits in the middle stages, the openand short-circuited stubs with characteristic admittances of
and
are separated into two equal parts, i.e.,
and
, as shown in Fig. 8. As the discussion in Section II, the
admittance inverter and the open- and short-circuited stubs on its
sides can be equivalent to the stepped-impedance coupled-line
section. The circuit parameters of the stepped-impedance coupled lines can then be obtained by solving (4), (6), and (7), and
the results are given as
(19)
(20)
(21)
(22)
(
)
Fig. 7. Design curves of: (a) . (b) and (c) Admittance ratio G=Y for
type-III filter with absolute bandwidth ratios equal to 0.5, 1, and 1.5, and
(for third-order Chebyshev filter prototype with 0.1-dB ripple).
1 = 10%
sections in the outer stages that function as impedance transformers are required. The design procedure of the coupled-line
circuits in the middle and outer sections for the type-III dualband filter is discussed in Section IV.
IV. DESIGNS OF COUPLED-LINE SECTIONS
A. Coupled-Line Sections in the Middle Stages
The dual-band resonators for the type-III filter are selected
identical in each stage for simplicity, and their parameters can
.
where
In order to derive a practical coupled-line circuit, the parameter in the above equations should be real. However, an imaginary number would sometimes be obtained under the circumstance of the dual-band filters with large frequency ratio and
wide bandwidths in the two passbands. It was found that the
type-III filter has an upper limit of absolute bandwidth ratio for
.
a given frequency ratio and the first passband bandwidth
The limitation curves for a third-order Chebyshev filter with
0.1-dB ripple are plotted in Fig. 9, where is defined as the
maximum of the absolute bandwidth ratio. It is more limited
is
as the frequency ratio or the first passband bandwidth
increased. Although type-III filters have this limitation on the
absolute bandwidth ratio of the two passbands, just as type-II
filters do [12], it was found that the maximum of this ratio is
larger than that of type-II filters.
B. Coupled-Line Sections in the Outer Stages
Type-III dual-band filters need coupled-line sections in their
exterior stages, which are used to transform the impedances
of the system terminations to higher values, and they can be
achieved by employing the rest of the open- and short-circuited stubs with characteristic admittances of and in the
outer-stage resonators, as shown in Fig. 10(a). Two redundant
transmission-line sections with characteristic admittances of
and electrical lengths of
at
are inserted
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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 55, NO. 5, MAY 2007
Fig. 11. Equivalence between the open- and short-circuited stubs in parallel
and the stepped-impedance short-circuited stubs.
Fig. 9. Limitation curves of absolute bandwidth ratio for the third-order Chebyshev filter with 0.1-dB ripple.
circuit has a similar formation to that shown in Fig. 3; however,
it is generally not symmetrically configured. Therefore, its
realization using the stepped-impedance coupled-line section
shown in Fig. 2 (which is a symmetric circuit) is not practicable.
Instead, stepped-impedance coupled-line structures consisting
of two different asymmetric coupled-line sections, as shown
in Fig. 10(d), are required. The exact equivalent circuits and
design equations are much more complicated due to the increased variety. Therefore, a simple design procedure with
approximation is proposed, and it could still provide sufficient
accuracy to maintain the performance of the dual-band filters.
The design procedure of the coupled-line sections in the outer
stages of the filter is based on the equivalence between the openand short-circuited stubs in parallel and the stepped-impedance
short-circuited stub, as shown in Fig. 11. The first step of the design procedure is to set the transformed termination in Fig. 10(c)
equal to the system conductance
, and the characteristic admittance can be obtained as
(23)
is then set equal to so that the equivalent
The admittance
circuit can be simplified as shown in Fig. 12(a). It is clear that
the open- and short-circuited stubs on the left-hand side have
the same characteristic admittances. The same components are
then extracted from the stubs on the right-hand side, as shown
in Fig. 12(b). In Fig. 12(c), the open- and short-circuited stubs
are replaced
with characteristic admittances of
with a single short-circuited stub using the equivalence given in
Fig. 11. After that, the transmission line and the shunted shortcircuited stubs with electrical lengths of could be equivalent
to the short-circuited coupled lines, as shown in Fig. 12(d), and
their even- and odd-mode characteristic admittances are given
by
Fig. 10. Design procedure of the coupled-line sections in the outer stages of
type-III filters.
(24)
(25)
between the termination and stubs, and the open- and short-cirand
are separated from
cuited stubs with admittances of
and , respectively, as shown in Fig. 10(b). After applying
the Kuroda identities of the second kind [16], the separated
stubs can be transformed to the other side of the transmission-line sections, and the final equivalent circuit is given in
Fig. 10(c). It was found that the equivalent transmission-line
Thus far, the coupled-line circuit design is exact without any
approximation. However, there are still two stubs left on the
right-hand side of Fig. 12(d), and they are attempted to be included in the coupled-line circuit. This can be done approximately with the following procedure. Based on the admittances
and
derived in (24) and (25), the linewidths
and
LEE AND TSAI: DUAL-BAND FILTER DESIGN WITH FLEXIBLE PASSBAND FREQUENCY AND BANDWIDTH SELECTIONS
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TABLE I
CIRCUIT PARAMETERS OF THE FILTER DESIGN EXAMPLE
then available. Finally, the coupled-line circuit in the outer stage
for type-III filter is constructed by the short-circuited stub with
a linewidth of and a stepped-impedance short-circuited stub
and
, and the coupling gap between
with linewidths of
them is , as shown in Fig. 12(e).
Although the coupled-line circuit is designed approximately,
it is sufficient to provide appropriate couplings and impedances
for the input/output resonators. The design example in Section V
will show that this approximation is feasible, and only a few iterations of the optimization process is needed to make the coupling structure more accurate, if necessary.
V. FILTER DESIGN EXAMPLES
Fig. 12. Approximate design of the coupled-line sections in the outer stages of
type-III filters.
gap of the coupled-line circuit can be obtained with the help
of the computer-aided design (CAD) tools. One of the shorted
coupled-transmission lines, which is attached to the right-handside open- and short-circuited stubs, is supposed to be a single
short-circuited stub regardless of the coupling. The characteristic admittance of the short-circuited stub with a linewidth of
is then calculated. By means of the equivalence in Fig. 11,
the short-circuited stub is equivalent to the open- and short-circuited stubs with half the characteristic admittance and electrical length. Now they can be combined with the right-handside open- and short-circuited stubs shown in Fig. 12(d), and
could be further equivalent to a stepped-impedance short-circuited stub using the equivalence again. The required linewidths
and
for the stepped-impedance short-circuited stub are
A third-order type-III dual-band filter was designed for the
wireless LAN applications, and the prototype of a Chebyshev
filter with 0.1-dB ripple was chosen. The central frequencies at
the two passbands are 2.45 and 5.25 GHz, and both the bandwidths are 4%. It should be noted that for this specifications, the
absolute bandwidth ratio is 2.14, which is beyond the limitation
of bandwidth ratio for type-II filters [12] and, therefore, its realization using a type-II filter structure is not practicable. The
termination is determined for reasonable impedance values
of the resonators in the internal sections of the filter. In this design, the initial resistance of the terminations is chosen to be
, and the slope parameters at the two
250 , i.e.,
passbands and the admittance inverters are then calculated as
and
. The circuit parameters can be obtained by solving (9)–(12), (15), and (16), and the
results are given in Table I. The open- and short-circuited stubs
and
are then separated
with characteristic admittances of
into two equal parts, i.e.,
and
, as shown
in Fig. 8, which represent the components for the adjacent coupled-line circuits. By the derived , , and , the circuit parameters of the stepped-impedance coupled-line circuit in the
internal sections can be calculated using (19)–(22), and they are
also given in Table I.
The coupled-line sections at the outer stages of the filter are
designed to transform the termination to the system termination . In this design, the system conductance
is 0.02
and, thus, the characteristic admittance extracted from and
is obtained by (23) as 0.0025 . The equivalent circuit of the
outer coupled-line section with the symmetric short-circuited
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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 55, NO. 5, MAY 2007
Fig. 13. Equivalent circuits of the outer section of the filter design example
with the symmetric coupled lines and residual open- and short-circuited stubs.
Fig. 15. (a) Circuit configuration of the filter design. (b) Its passband and
(c) out-of-band measured results compared with the simulated responses.
Fig. 14. Circuit simulation results of the filter design. (a) Coupled-line sections
at the outer stages are designed approximately. (b) After optimization.
coupled lines and the residual open- and short-circuited stubs
are shown in Fig. 13, and the circuit parameters are also given.
Finally, the residual stubs can be approximately included in the
coupled-line circuit based on the discussion in Section IV.
The dual-band filter is implemented in an eight-layer
low-temperature co-fired ceramic (LTCC) structure, with a total
thickness of 1.2 mm and a dielectric constant of 7.8. Fig. 14(a)
shows the circuit simulation results of the filter design without
taking account of the conductor and dielectric losses, whose
coupled-line sections at the outer stages are designed approximately as discussed. It is obvious that only minor distortions
occur for the filter to deviate from the Chebyshev filter responses, and its performance is still very good. Optimization
process might be employed, if necessary, for the coupled-line
circuit, and in Fig. 14(b), it can be seen that the dual-band filter
design is much closer to a Chebyshev filter after optimization.
The complete circuit configuration of the filter is shown in
Fig. 15(a). In order to avoid any crossing, the open stubs are
implemented on the upper layer with via connections to the
coupled-line circuits. The passband and out-of-band measurement results compared with the simulated responses are shown
in Fig. 15(b) and (c), respectively. The conductor surface
roughness of approximately 10 m and dielectric loss tangent
of 0.005 have been included in the simulations. The measured
LEE AND TSAI: DUAL-BAND FILTER DESIGN WITH FLEXIBLE PASSBAND FREQUENCY AND BANDWIDTH SELECTIONS
passband central frequencies are at 2.42 and 5.24 GHz, and the
are 6 and 5.3 dB, respectively. Since
corresponding
the losses are high due to the LTCC process, the equal-ripple
bandwidth cannot be defined. The measured 3-dB bandwidths
are approximately 4.1% and 5.3%. The spurious response
around 6.5 GHz is thought to be caused by the cross coupling
between the input and output due to the test fixture. Generally,
the measurement results are well with the specifications, and
the type-III dual-band filter has been successfully achieved.
VI. CONCLUSIONS
A new dual-band filter structure, which is called a type-III
filter, has been studied in this paper. Type-III filters are built by
the dual-band resonators with open- and short-circuited stubs
in parallel. A new structure of two-section asymmetric coupled
lines is first proposed and studied, which can be used for the
realization of the short-circuited stubs and inverters. The basic
configuration of the type-III filter is modified based on the derived equivalent circuit of the coupled-line structure. It should
be noted that type-III filters can achieve relatively large practical
passband center frequency ratios (in theory infinite), whereas
type-I and type-II filters have an upper limit of three. Type-III
filters have more freedom of bandwidth ratio than type-II filters.
The total circuit size is also reduced. Type-III filters require the
redundant coupled-line circuits at the outer stages to ensure that
the interior transmission-line circuits have reasonable values of
impedances. The stepped-impedance coupled lines are used to
implement the exterior sections of type-III filters. Although the
design procedure reported in this paper for the outer-stage coupled lines is an approximation, it is sufficient to provide appropriate couplings and impedances for the input/output resonators.
If a more accurate coupled-line structure is needed, a few iterations of the optimization process can be employed. Finally, a
design example of the type-III filter has been given and its measured results show good agreement with the predictions.
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Hong-Ming Lee (S’03–M’06) was born in Nantou,
Taiwan, R.O.C. He received the B.S. and Ph.D.
degrees in electrical engineering from National
Cheng Kung University, Tainan, Taiwan, R.O.C., in
2002 and 2006, respectively.
From February of 2006 to July 2007, he was a
Post-Doctoral Research Fellow with the Institute
of Computer and Communication Engineering,
Department of Electrical Engineering, National
Cheng Kung University. He is currently serving his
compulsory military service. His research interests
include microwave passive components and measurements.
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Chih-Ming Tsai (S’92–M’94) received the B.S.
degree in electrical engineering from National Tsing
Hua University, Taiwan, R.O.C., in 1987, the M.S.
degree in electrical engineering from the Polytechnic
University, Brooklyn, NY, in 1991, and the Ph.D.
degree in electrical engineering from the University
of Colorado at Boulder, in 1993.
From 1987 to 1989, he was a Member of the
Technical Staff with Microelectronic Technology
Inc., Taiwan, R.O.C., where he was involved with
the design of digital microwave radios. In 1994,
he joined the Department of Electrical Engineering, National Cheng Kung
University, Tainan, Taiwan, R.O.C., where he is currently a Professor. His
research interests include microwave passive components, high-speed digital
design, and measurements.