IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: EXPRESS BRIEFS, VOL. 65, NO. 3, MARCH 2018
271
Multi-Stub-Loaded Differential-Mode Planar
Multiband Bandpass Filters
Roberto Gómez-García, Senior Member, IEEE, Raúl Loeches-Sánchez, Member, IEEE,
Dimitra Psychogiou, Member, IEEE, and Dimitrios Peroulis, Fellow, IEEE
Abstract—A new type of RF/microwave differential-mode
planar multiband bandpass filters (BPFs) are presented. Each
symmetrical half of the proposed balanced filtering architecture is composed of the in-series cascade of K N-stub-loaded
cells through K − 1 inter-connection transmission-line segments
to synthesize a differential-mode transfer function with N Kthorder passbands. Additional features of this balanced multiband
BPF topology are as follows: 1) generation of transmission
zeros at both sides of all differential-mode passbands; 2) high
common-mode power-rejection levels within the differential-mode
passband ranges; 3) scalability to any number of arbitraryorder differential-mode transmission bands; and 4) lack of
electromagnetic couplings in its physical structure. The theoretical foundations of the engineered balanced filter approach,
along with guidelines to design the differential-mode transfer function and to attain optimum in-band common-mode
power-attenuation characteristics, are expounded. Furthermore,
for experimental-demonstration purposes, a third-order tripleband microstrip prototype with differential-mode passbands that
are located within the range 1.4–3 GHz is manufactured and
characterized.
Index Terms—Balanced filters, bandpass filters (BPFs),
common-mode rejection, differential-mode filters, microstrip filters, microwave filters, multiband filters, planar filters, transmission zero (TZ), triple-band filters.
I. I NTRODUCTION
ESPITE their traditional use in low-frequency-analog
and digital applications—e.g., fully-differential modulators and operational transconductance amplifiers
(OTAs) [1], [2]—, balanced/differential-mode circuits and
systems are currently acquiring a great importance in highperformance RF/microwave transceivers. This is owing to
their higher immunity to undesired phenomena, such as
D
Manuscript received October 8, 2016; revised February 11, 2017; accepted
March 22, 2017. Date of publication March 28, 2017; date of current version March 8, 2018. This work was supported by the Spanish Ministry of
Economy and Competitiveness under Project TEC2014-54289-R. This brief
was recommended by Associate Editor S. Mirabbasi. (Corresponding author:
Roberto Gómez-García.)
R. Gómez-García is with the Department of Signal Theory and
Communications, University of Alcalá, 28871 Madrid, Spain (e-mail:
roberto.gomez.garcia@ieee.org).
R. Loeches-Sánchez is with Indra Sistemas S.A., 28850 Madrid, Spain
(e-mail: raul.loeches@gmail.com).
D. Psychogiou is with the Department of Electrical, Computer, and Energy
Engineering, University of Colorado Boulder, Boulder, CO 80309 USA
(e-mail: dimitra.psychogiou@colorado.edu).
D. Peroulis is with the School of Electrical and Computer Engineering,
Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47907
USA (e-mail: dperouli@purdue.edu).
Color versions of one or more of the figures in this paper are available
online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TCSII.2017.2688336
electromagnetic (EM) interference, crosstalk, and different
sources of noise—e.g., coupled noise from adjacent circuitry, environmental, and external noise—when compared
to their single-ended counterparts [3]. In particular, a large
interest has been recently detected in the design of highfrequency differential-mode bandpass filters (BPFs) as the
signal-preselection blocks of these balanced RF front-ends.
Desired electrical characteristics for these devices are high
selectivity for the differential-mode transfer function—through
transmission-zero (TZ) generation at both passband sides—
and high common-mode power-rejection levels within the
entire differential-mode passband range. Furthermore, due to
modern trends towards the development of highly-versatile
multi-mode RF architectures, these requisites have been
extended to balanced BPFs with multi-band operation [4], [5].
In relation to planar balanced single-band BPFs with
frequency-static and reconfigurable functionality, a large variety of solutions have been proposed [6]–[9]. However, much
fewer balanced BPFs with multi-band characteristics have
been reported. This is due to the difficulty of generalizing
available balanced single-band BPF configurations to exhibit
multi-band transfer functions. Recent examples of multiband balanced BPF schemes are limited to dual-passband
responses [10]–[14]. In [10], a balanced dual-band BPF
based on a double-layer structure was described. Although it
enables sharp-rejection differential-mode double-band transfer functions to be realized, the employment of a two-layer
arrangement makes it sensitive to manufacturing tolerances.
This shortcoming is resolved in the fully-planar balanced twoband BPF scheme in [11]. Nevertheless, its usefulness is
constrained to narrow-band specifications and limited number
of realizable bands (two in this case). In [12], a signalinterference differential-mode dual-band balanced BPF was
presented. Drawbacks of this filtering device is its relativelylarge physical size and the difficulty to synthesize more than
two passbands. This last shortcoming is also present in the
balanced dual-band BPF topology in [13] that makes use
of electrically-small resonators. Although it features compact size, the common-mode power-rejection levels within
the differential-mode passband widths are limited to 19 dB.
Finally, a balanced triple-band BPF component was described
in [14]. However, it does not exhibit TZs at both sides of
the three differential-mode passbands to obtain sharp-rejection
capabilities for all of them.
A new class of balanced planar multi-band BPFs is
presented in this brief. The proposed RF balanced filtering
architecture, which employs a multi-stub-loaded cell as basic
building block, allows to theoretically realize a differentialmode multi-band transfer function with an arbitrary number
of passbands. In addition, TZs at both sides of all these transmission bands and high common-mode power-rejection levels
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272
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: EXPRESS BRIEFS, VOL. 65, NO. 3, MARCH 2018
Fig. 1. (a) Proposed multi-stub-loaded balanced multiband BPF (differential-mode Kth-order N-band bandpass transfer function). (b) Equivalent circuit of
the N-stub-loaded cell for the differential-mode operation. (c) Equivalent circuit of the N-stub-loaded cell for the common-mode operation.
within their bandwidths can be obtained. Moreover, coupledline stages are avoided in their physical structure. This leads
to design simplicity, lower in-band insertion-loss levels in
the differential-mode operation, and size-miniaturization capability by applying line-meandering techniques as in [15] or
equivalent lumped-element-based implementations as in [16]
for the lower region of the microwave band.
The rest of the brief is organized as follows: the operational principles and design guidelines for the devised balanced
multi-band BPF are expounded in Section II. In Section III, the
experimental results of a proof-of-concept third-order tripleband microstrip prototype are shown. Finally, the main concluding remarks of this brief are summarized in Section IV.
where fd is the design frequency that can be arbitrarily
selected—but chosen in practice as the middle value of the
spectral range to be covered by the differential-mode bands.
Moreover, a total power-transmission frequency is obtained
between each pair of contiguous TZ frequencies in the
differential-mode N-stub-loaded cell. These maximum powertransmission frequencies { f0 } correspond to those spectral values at which the input admittances {Ysk } (k = 1, 2, . . . , N) of
the stubs cancel between them. This condition is analytically
expressed by means of the following implicit equation in f0 :
II. T HEORETICAL F OUNDATIONS
The circuit details of the proposed multi-stub-loaded balanced multi-band BPF are given in Fig. 1(a). As shown, each
half of its symmetrical electrical network is formed by the
in-series cascade connection of K N-stub-loaded cells through
K − 1 transmission-line segments to synthesize a differentialmode Kth-order N-band bandpass filtering transfer function.
The stubs in each cell are joined at their ends to those of
their peers in the symmetry plane of the filter either through
direct connection—i.e., virtual ground and open circuit for the
differential- and common-mode operations, respectively—or
by means of a physical short circuit—i.e., physical ground for
both the differential- and common-mode operations—. Note
that, as it will be further explained in Section II-B, a maximum
of N−1 physical ground connections can be considered in each
cell to obtain distinct differential- and common-mode behaviors. In Fig. 1, Z denotes characteristic impedance, whereas θ
refers to the electrical-length variable of a transmission line.
From the above, it is derived that a differential-mode multipassband filtering transfer function with TZs at both sides
of all transmission bands is synthesized through the N-stubloaded cell in Fig. 1(b). Specifically, (1) and (2) can be used to
obtain its design parameter values so that the prefixed specifications for the passband center frequencies and TZ positions
are fulfilled. Note that degrees of freedom are involved in this
process that can be exploited to adjust the bandwidths of the
differential-mode passbands as desired. It should be remarked
upon that although an infinite number of passbands and TZs
are created through the N-stub-loaded cell in Fig. 1(b), only N
passbands can be flexibly designed and matched for N stubs
in a higher-order multi-stage filter arrangement as in Fig. 1(a).
For illustration purposes, Fig. 2 depicts the theoretical
differential-mode power transmission and reflection responses
of two triple-band examples with nearly-equal passband widths
that are synthesized through the differential-mode N-stubloaded cell (i.e., N = 3) in Fig. 1(b). As shown, broader
bandwidths for the differential-mode transmission bands
are obtained as higher values for characteristic-impedance
variables are selected. Furthermore, Fig. 3 represents the
theoretical differential-mode power transmission and reflection parameters of two second-order dual-band examples
with equal and asymmetrical passband widths—synthesized
through two inter-cascaded replicas of the differential-mode
N-stub-loaded cell (i.e., N = 2) in Fig. 1(b)—. It reveals
how differential-mode multi-passband filtering transfer functions with arbitrary specifications can be designed through the
balanced filter architecture in Fig. 1(a). Note finally that each
stub in Fig. 1(b) can be equivalently replaced by an impedance
inverter and a parallel-type resonator with natural frequency
equal to the TZ frequency produced by this stub. Thus,
although beyond the scope of this brief, coupling-matrixsynthesis approaches as in [17] for the basic multi-band cell
A. Differential-Mode Operation
For the differential mode of operation, a virtual ground is
created in the symmetry plane of the balanced multi-band BPF
scheme in Fig. 1(a). Thus, as shown in Fig. 1(b), all the stubs
associated to the building N-stub-loaded cell of its symmetrical
halves are ended in a—virtual or physical—short circuit.
It is direct to deduce that TZs are generated by the Nstub-loaded cells of the balanced filter in Fig. 1(a) for the
differential-mode operation. The spectral positions { fz } of
these TZs for the example cell in Fig. 1(b), which depend
on the values of the electrical lengths of its constituent shortended stubs, are given by the following analytical formula:
2nπ
{ fz } ≡ 0,
fd , k = 1, 2, . . . , N, n ∈ N
(1)
θsk ( fd )
N
k=1
Ysk ( f0 ) =
N
k=1
jZsk tan
1
f0
fd θsk ( fd )
= 0.
(2)
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GÓMEZ-GARCÍA et al.: MULTI-STUB-LOADED DIFFERENTIAL-MODE PLANAR MULTI-BAND BPFs
273
dd | and
Fig. 2. Theoretical power transmission and reflection parameters (|S21
dd |) of two triple-passband (i.e., N = 3) examples synthesized with the
|S11
differential-mode N-stub-loaded cell in Fig. 1(b) (example 1: Zs1 = Z0 , Zs2 =
Z0 , and Zs3 = Z0 /2; example 2: Zs1 = Z0 /2, Zs2 = Z0 /2, and Zs3 = Z0 /4;
θs1 ( fd ) = π , θs2 ( fd ) = 2π/3, and θs3 ( fd ) = π/3 for both examples; Z0 is
the reference impedance).
Fig. 4.
Theoretical differential- and common-mode power transmission
dd | and |Scc |) for a synthesized two-stub-loaded cell (Z = Z ,
parameters (|S21
s1
0
21
Zs2 = Z0 /2, θs1 ( fd ) = π , and θs2 ( fd ) = π/2; Z0 is the reference impedance):
influence of the stub-ending conditions on the common-mode operation.
dd | and
Fig. 3. Theoretical power transmission and reflection parameters (|S21
dd |) of two second-order dual-passband (i.e., N = 2) examples synthesized
|S11
with two inter-cascaded replicas of the differential-mode N-stub-loaded cell in
Fig. 1(b) through a transmission-line segment of Zc characteristic impedance
and θc electrical length (example 1: Zc = Z0 , θs1 ( fd ) = π , θs2 ( fd ) = π/2,
θc ( fd ) = π/2; example 2: Zc = 1.014Z0 , θs1 ( fd ) = π , θs2 ( fd ) = π/3, and
θc ( fd ) = 0.4372π ; Zs1 = Z0 and Zs2 = Z0 /2 for both examples; Z0 is the
reference impedance).
and in-series cascades of its replicas can be applied to them
for a complete theoretical design of their differential-mode
filtering transfer function.
B. Common-Mode Operation
As previously mentioned, the transmission-line segments of
the K N-stub-loaded cells in each half of the balanced multiband BPF in Fig. 1(a) can be ended in a physical ground or
directly connected at their edges to those of their symmetrical counterparts. Although such stub-termination conditions
do not have influence on the differential-mode behavior of
the overall balanced filtering architecture—all the stubs of
the N-stub-loaded cell appear ended in a virtual or a physical short circuit for the differential-mode operation as shown
in Fig. 1(b)—, different common-mode filtering transfer functions are obtained in each case. This provides design flexibility
for the common mode of operation. Thus, the terminations of
the transmission-line segments that shape the N-stub-loaded
cell must be appropriately selected in order to maximize the
common-mode power-rejection levels within the differentialmode passband widths. Note that, as shown in Fig. 1(c) where
the equivalent circuit of the common-mode N-stub-loaded
cell is provided, a physical-ground termination of the stub
means a short-circuit-ended stub whereas a direct connection to its peer stub in the filter symmetry plane results in
an open-circuit-ended stub in the common mode of operation.
As an illustrative example, Fig. 4 represents the theoretical differential- and common-mode power transmission
parameters for a synthesized two-stub-loaded cell for different stub-ending conditions. Note that a total of three cases
are contemplated since no more that one physical ground
connection can be considered to obtain distinct transfer functions for the differential- and common-mode operations. As
proven in Fig. 4, there is an optimum case—case 1—in which
higher common-mode attenuation levels are obtained throughout the bandwidths of the differential-mode dual passbands. In
general, for a Kth-order N-band BPF in which different termination conditions are allowed for the K N-stub-loaded cells
of each half, a total of (2N − 1)K cases must be evaluated.
III. E XPERIMENTAL R ESULTS
To validate the practical usefulness of the engineered
multi-stub-loaded balanced multi-band BPF architecture, a
proof-of-concept triple-band BPF microstrip prototype has
been designed, built, and tested. This circuit was ideally
synthesized so that its lower, middle, and upper differentialmode third-order passbands exhibit center frequencies equal
to 1.55 GHz, 2.1 GHz, and 2.8 GHz and 3-dB absolute bandwidths of 200 MHz, 155 MHz, and 215 MHz, respectively
(i.e., 3-dB relative bandwidths equal to 12.9%, 7.4%, and
7.7%, respectively).
In the design process of this filter, the guidelines expounded
in Section II were followed for the synthesis of its constituent
triple-stub-loaded cells. Subsequently, a fine-optimization step
of the whole circuit was carried out. Specifically, three triplestub-loaded cells were inter-cascaded in series in each half of
the overall balanced filtering device to attain high-selectivity
capabilities for the differential mode of operation. Note also
that, in order to maximize the power-attenuation levels for
the common mode within the three differential-mode passbands as explained in Section II-B, two of the stubs in each
cell were physically grounded at their extremes; the remaining stub was connected at its end to that of its peer in the
symmetry plane of the balanced structure (i.e., virtual-groundended stub for the differential mode). Furthermore, as can be
seen in Fig. 1(a), two transmission-line segments were inserted
at the filter input/output accesses to increase the in-band
power-matching levels in the differential-mode operation.
The theoretical differential-mode power transmission and
reflection parameters of the synthesized balanced triple-band
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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: EXPRESS BRIEFS, VOL. 65, NO. 3, MARCH 2018
Fig. 5.
Theoretical differential-mode power transmission and reflection
dd | and |Sdd |) and common-mode power transmission parameter
parameters (|S21
11
cc |) of the synthesized
balanced triple-band BPF.
(|S21
Fig. 7. Simulated and measured S-parameters of the manufactured balanced
triple-band BPF microstrip prototype. (a) Differential-mode power transmisdd | and |Sdd |) and common-mode power
sion and reflection parameters (|S21
11
cc |). (b) Differential-to-common
and common-totransmission parameter (|S21
dc | and |Scd |).
differential mode-conversion power transmission parameters (|S21
21
(c) Differential-mode group delay.
Fig. 6.
Manufactured balanced triple-band BPF microstrip prototype.
(a) Layout (dimensions in mm: w0 = 3.35, w1 = 1.74, w2 = 0.54, w3 = 0.47,
w4 = 0.61, w5 = 6.5, w6 = 0.63, w7 = 0.79, w8 = 7.1, l0 = 10, l1 = 23.78,
l2 = 23.82, l3 = 37.2, l4 = 52.1, l5 = 18.12, l6 = 36.2, l7 = 51.4,
l8 = 18.72, and l9 = 1). (b) Photograph.
BPF, along with its theoretical common-mode transfer function, are represented in Fig. 5. The final values for its design
parameters are as follows (Z0 = 50 and fd = 2 GHz):
(1)
(3)
• Triple-stub-loaded cells #1 and #3: Zs1 = Zs1 = 2.2Z0 ,
(1)
(3)
(1)
(3)
(1)
Zs2 = Zs2 = 2.4Z0 , Zs3 = Zs3 = 0.64Z0 , θs1 ( fd ) =
(3)
(1)
(3)
θs1 ( fd ) = 1.1π , θs2 ( fd ) = θs2 ( fd ) = 0.8056π , and
(1)
(3)
θs3 ( fd ) = θs3 ( fd ) = 4π/9.
(2)
(2)
• Triple-stub-loaded cell #2: Zs1 = 2.02Z0 , Zs2 = 2.18Z0 ,
(2)
(2)
(2)
Zs3 = 0.6Z0 , θs1 ( fd ) = 1.1π , θs2 ( fd ) = 0.8056π , and
(2)
θs3 ( fd ) = 4π/9.
• Inter-cell in-series cascading transmission-line segments:
Zc1 = Zc2 = 2.3Z0 and θc1 ( fd ) = θc2 ( fd ) = 0.5π .
• Input/output in-band power-matching transmission-line
segments: Zm = 1.44Z0 and θm ( fd ) = 0.5167π .
As shown in Fig. 5, a differential-mode triple-band filtering transfer function with equirriple-type third-order passbands is obtained. These transmission bands have 20-dB
minimum input-power-matching levels and TZs at both
sides. Furthermore, the common-mode power-rejection levels throughout the lower, middle, and upper differential-mode
3-dB passband widths are higher than 38.5 dB, 75 dB, and
38 dB, respectively.
The layout and a photograph of the constructed microstrip
prototype are given in Fig. 6. For circuit manufacturing, a
RO4003 microstrip substrate with the following parameters
was used: relative dielectric permittivity εr = 3.38, dielectric
thickness H = 1.52 mm, metal thickness t = 35 μm, and
dielectric loss tangent tan δD = 0.0027. The physical ground
connections of short-circuit-ended stubs were implemented by
means of 1-mm-diameter metallic via holes.
The simulated and measured S-parameters of the developed microstrip circuit are depicted in Fig. 7. The simulations
were performed through EM analysis in the software package Keysight ADS, whereas measurements were done by
means of a four-port Agilent-E8361A network analyzer. As
observed, a fairly-close agreement between measurements and
simulations was obtained. The main measured characteristics
for the lower, middle, and upper differential-mode passbands
are as follows: center frequencies of 1.51 GHz, 2.13 GHz,
and 2.78 GHz, 3-dB absolute bandwidths equal to 183 MHz,
155 MHz, and 195 MHz (i.e., 3-dB relative bandwidths of
12%, 7.3%, and 7%), minimum in-band power-insertion-loss
levels of 0.74 dB, 1.29 dB, and 1.41 dB, in-band input-powermatching levels higher than 20.4 dB, 15.7 dB, and 12.8 dB,
and maximum in-band differential-mode group-delay variations of 3.9 ns, 2.7 ns, and 4.3 ns, respectively. The measured
common-mode power-rejection levels within the 3-dB bandwidths of the three differential-mode transmission bands are
respectively above 36.7 dB, 59 dB, and 48.7 dB. Furthermore,
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GÓMEZ-GARCÍA et al.: MULTI-STUB-LOADED DIFFERENTIAL-MODE PLANAR MULTI-BAND BPFs
275
TABLE I
C OMPARISON W ITH S TATE - OF - THE -A RT P LANAR BALANCED M ULTI -BAND BPF S
minimum isolation levels of 35.4 dB, 29 dB, and 30 dB for the
differential-to-common mode-conversion power transmission
and equal to 39.5 dB, 30.7 dB, and 29.3 dB for the commonto-differential mode-conversion power transmission within the
first, second, and third differential-mode 3-dB passband widths
were measured. Note that these values correspond to average
in-band phase-distortion metrics for the realized differentialmode transfer-function selectivity since no self-equalization
techniques were introduced in this balanced filter design.
Finally, Table I provides a comparison between the manufactured balanced triple-band BPF prototype and recent
previously-published differential-mode multi-band bandpass
filtering devices. With regard to most of state-of-the-art components, the developed circuit shows the following merits:
i) larger number of differential-mode passbands (theoretically generalizable to an arbitrary number of them), ii) high
common-mode power-rejection levels within their bandwidths,
iii) increased selectivity that is obtained by means of TZ
generation at both sides of all the differential-mode passbands, and iv) design and fabrication simplicity that is
attributed to the lack of EM couplings in its physical structure. Furthermore, circuit-size miniaturization techniques, such
as the one reported in [18] based on fractal-shape arrangements, could be applied to this filter approach for reduced-area
realizations.
IV. C ONCLUSION
A novel class of balanced planar multi-band BPFs that feature a number of differential-mode passbands larger than in
most related prior-art devices have been reported. The engineered balanced RF/microwave filtering topology is shaped
by two symmetrical halves based on the in-series cascade
of several multi-stub-loaded cells. It allows to synthesize
differential-mode quasi-elliptic-type multi-band filtering transfer functions with any number of arbitrary-order transmission
bands. Moreover, TZs at both sides of all the differential-mode
passbands and high common-mode rejection levels throughout their bandwidths are obtained. An added advantage of the
proposed multi-band BPF approach is the lack of coupledline sections that leads to lower insertion-loss levels, reduced
design complexity, and suitability for lumped-element realizations. The operational principles and guidelines for the design
of the devised differential-mode multi-passband filter architecture have been described. Moreover, as experimental proof-ofconcept demonstrator, a triple-band microstrip prototype with
differential-mode third-order passbands positioned within the
frequency interval 1.4–3 GHz has been developed and tested.
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