This paper presented a novel approach for the design of a tunable dualband bandpass filter (BPF) with independently tunable passband center frequencies and bandwidths. The newly proposed dualband filter principally comprised two dualmode single band filters using common input/output lines. Each single BPF was realized using a varactorloaded transmission line resonator. To suppress the harmonics over a broad bandwidth, a defected ground structure was used at the input/output feeding lines. From the experimental results, it was found that the proposed filter exhibited the first passband center frequency tunable range from 1.48 to 1.8 GHz with a 3dB fractional bandwidth (FBW) variation from 5.76% to 8.55%, while the second passband center’s frequency tunable range was 2.40 to 2.88 GHz with a 3dB FBW variation from 8.28% to 12.42%. The measured results of the proposed filters showed a rejection level of 19 dB up to more than 10 times the highest center frequency of the first passband.
Ⅰ. Introduction
Various wireless communication standards, such as wireless local area networks (WLANs), worldwide interoperability for microwave access (WiMAX), wideband code division multiple access (WCDMA), longterm evolution (LTE), etc., have been developed throughout the world and more standards will likely emerge in the near future. The integration of separate standards into one unit increases the size, cost, and complexity of wireless systems. The need for the design of lowcost, compact robust radio frequency components such as tunable bandpass filters (BPFs) operating at multiple frequency bands to meet the demands of next generation wireless systems have become apparent.
In some applications of wireless communication systems, radios themselves sense the available spectrum and decide on the communications channel (frequency, bandwidth, and modulation scheme) to be used. Therefore, it is important to design a multiband BPF with a tunable center frequency and bandwidths. To meet these requirements, various approaches have been applied to design tunable BPFs using different kinds of tuning devices, such as microelectromechanical system (MEMS) devices
[1
,
2]
, ferroelectric devices/capacitors
[3]
, PIN diodes
[4]
, and semiconductor varactor diodes
[5

9]
. These tuning devices allow tunability of the center frequency of filters by changing the effective length of their resonators and the variation of the bandwidth by changing coupling between resonators.
Semiconductor varactors are widely used in designing tunable BPFs due to high tuning speed and reliability
[5

9]
. In comparison to the design of singleband tunable filters, only a limited number of studies have been undertaken to design filters with a tunable center frequency and bandwidth independent of one another
[10
,
11]
. There have been some attempts to design tunable dualpassband filters
[12
,
13]
. However, no studies have addressed the design of a tunable dualband BPF with independently tunable center frequencies and bandwidths.
With the tunable passband frequency, the harmonic bands that degrade the outofpassband characteristics are also tuned. Thus, the suppression of harmonics is one of the critical issues related to tunable filters. This issue has rarely been addressed in the design of tunable dualband filters.
In this paper, dualband BPFs with independently tunable passband center frequencies and bandwidths are presented. From theoretical even and oddmode analysis, it is found that the passband center frequencies can be varied by controlling the odd and evenmode resonant frequencies. The separation between the odd and evenmode resonant frequencies is proportional to the bandwidths of passbands; these can be controlled independently by the evenmode resonant frequencies by keeping the oddmode resonant frequencies constant. To suppress the harmonics, the defected ground structure (DGS) is used at the input/output feeding lines. The bandrejection characteristics of the DGS are utilized to suppress the harmonics of the proposed BPF.
Ⅱ. Design and Implementation
Fig. 1
(a) shows the proposed twopole varactortuned dualband BPF. It consists of two singleband BPFs combined with common input and output ports. Each single band BPF comprises dualmode resonators that contain a transmission line and three varactor diodes. The coupling scheme of the proposed filter is shown in
Fig. 1
(b), where
S
and
L
denote input and output ports. Nodes 1 and 3 denote the odd modes and nodes 2 and 4 denote the even modes at the first passband (
f
_{1}
) and second passband (
f
_{2}
) center frequencies, respectively. Since these two operating modes do not couple to each other, a simple tuning scheme can be obtained.
(a) Layout of the proposed twopole dualband tunable filter I and (b) its coupling scheme.
(a) Basic structure of the proposed resonator, (b) oddmode excitation equivalent circuit, and (c) evenmode excitation equivalent circuit.
Fig. 2
(a) shows the basic structure of the proposed resonator. Two varactor diodes are the attached at ends of the transmission line with tunable capacitances
C_{v}
_{1}
and one varactor diode with tunable capacitance
C_{v}
_{2}
is placed at a center point of transmission line. The DC block capacitor is placed at the center point of the transmission. For the theoretical analysis, the lossless transmission line of characteristic admittance
Y
and physical length
L
is assumed. Since the structure is symmetrical, the even and oddmode analysis method can be applied to obtain the resonant frequencies
[13]
. When the oddmode excitation is applied to the ends of the proposed resonator shown in
Fig. 2
(a), there is a voltage null along the symmetry plane. Under oddmode excitation, this can be represented by the half circuit, as shown in
Fig. 2
(b). Therefore, the oddmode resonant frequency can be determined as follows:
where
v_{p}
is the phase velocity. From (1), it is concluded that the oddmode resonant frequency fully depends on the capacitance
C_{v}
_{1}
of varactor diodes connected at the ends of the transmission line. Moreover, the oddmode resonant frequencies are not affected by the varactor diode connected at the center of the transmission line.
For evenmode excitation, there is no current flowing through the center of the transmission line. Under this condition, the proposed resonator can be represented by the equivalent half circuit shown in
Fig. 2
(c). For the resonance condition, the evenmode resonant frequency can be determined as follows:
where
C_{v}
_{2_t}
is the total capacitance for series connection of DC block capacitor and varactor diode. This is given as follows:
From (2) and (3), it can be observed that the evenmode resonant frequency depends on
C_{v}
_{1}
and
C_{v}
_{2}
. Moreover, when
C_{v}
_{1}
is fixed, the evenmode resonant frequency can be tuned with
C_{v}
_{2}
alone. This characteristic of the proposed resonator can be used to design a BPF with tunable bandwidth.
To verify the theoretical analysis, a fullwave electromagnetic (EM) simulation was carried out using HFSS
_{v11}
by Ansys. Two microstrip lines with a characteristic impedance of 50 Ω were utilized to feed the proposed resonator using loose coupling to investigate its resonant behavior. The characteristic impedance of resonators is fixed at 76 Ω.
Fig. 3
shows the simulated resonant characteristics according to different capacitances (
C_{v}
_{1}
and
C_{v}
_{2}
) of the varactor diodes and length (
L
). As
C_{v}
_{1}
and
C_{v}
_{2}
are varied, the odd and evenmode resonant frequencies are tuned simultaneously. This characteristic of the proposed resonator can be utilized in the design of BPFs with tunable passband center frequencies. If the capacitances
C_{v}
_{1}
of the varactor diodes connected at the ends of the transmission line are fixed, it is obvious that the oddmode resonant frequency is fixed and the evenmode resonant frequency can be tuned by varying the capacitance
C_{v}
_{2}
of the varactor diode connected at the center of the line. The separation between the modal frequencies is proportional to the bandwidth. This characteristic of proposed resonator can be utilized in the design of BPF with tunable bandwidths.
Resonant frequencies of single dualmode resonator according to capacitances and length at (a) the first passband and (b) the second passband.
 1. Design Method
First, the requirement of the ideal dualmode filter at each passband should be determined; this may be derived from its fixed frequency response centering at the highfrequency edge of a given tuning range. Then the separation of odd and evenmode resonant frequencies and the required
Q_{exo}
and
Q_{exe}
for ideal tunable filter can be determined at each passband.
Second, the tuning rate of the oddand evenmode resonant frequencies should be determined by selecting
Y
,
L
,
C_{v}
_{1}
, and
C_{v}
_{2}
using Eqs. (1) and (2) separately at each passband. Third, the coupling network should be designed to maintain the shape and bandwidth of oddand evenmode frequency responses over the tuning range.
To demonstrate the described design method, filter centerings at
f
_{1}
=1.80 GHz and
f
_{2}
=2.9 GHz with 3dB FBWs of 5.8% and 9.5% have been designed. The desired parameters can be derived from a target coupling matrix corresponding to specified response
[14]
, which are given as
f_{oddf}
_{1}
=1.74 GHz,
f_{evenf}
_{1}
=1.94 GHz,
Q_{exof}
_{1}
= 20.5, and
Q_{exef}
_{1}
=40.2 at the lower passband (
f
_{1}
) and
f_{oddf}
_{2}
=2.76 GHz,
f_{evenf}
_{2}
=3.04 GHz,
Q_{exof}
_{2}
=23.5, and
Q_{exef}
_{2}
=29.5 at the higher passband (
f
_{2}
). With these design parameters, the lengths and characteristic impedances of resonators at the first (
f
_{1}
) and second (
f
_{2}
) passbands are selected as 51 mm, 24.8 mm, and 76 Ω, respectively. In addition, according to the external quality factors, the values of
g
_{1}
,
g
_{2}
,
W
_{2}
, and
L
_{3}
are taken as 0.12 mm, 0.14 mm, 0.4 mm, and 17.5 mm, respectively.
 2. Analysis of Center Frequency and Bandwidth Tunability
Fig. 4
(a) presents the tunability of center frequency of passbands according to capacitances
C
_{v1f1}
,
C
_{v2f1}
,
C
_{v1f2}
, and
C
_{v2f2}
. The first passband center frequency (
f
_{1}
) can be tuned from 1.41.82 GHz by adjusting
C
_{v1f1}
from 0.4 to 0.9 pF and
C
_{v2f1}
from 5.1 to 10.2 pF. Similarly, the second passband center frequency (
f
_{2}
) can be varied from 2.26 to 3 GHz by changing
C
_{v1f2}
from 0.4 to 0.9 pF and
C
_{v2f2}
from 2.2 to 6.7 pF.
Fig. 4
(b) presents the 3dB FBWs verses capacitances (keeping
C
_{v1f1}
and
C
_{v1f2}
constant and varying
C
_{v2f1}
and
C
_{v2f2}
) for
f
_{1}
=1.531.82 and
f
_{2}
=2.383 GHz. From the simulation, it is found that the 3dB FBW results are in the tunable range of 5%9% for
f
_{1}
=1.531.82 GHz and 6%12% for
f
_{2}
=2.383 GHz.
Ⅲ. Simulation and Measurement Results
To verify the analysis of the proposed resonators, two types of tunable dualband BPF were designed, simulated, and measured.
Fig. 1
(a) depicts the configuration of microstrip dualmode tunable dualband filter I. In the proposed filter, two dualmode resonators are combined with common input/output ports. The inner resonators are designed for higher passbands, whereas the outer resonator is designed for lower passbands. The resonators are folded in order to reduce the size. The substrate is RT/Duriod 5880 made by Rogers with a dielectric constant (
ε_{r}
) of 2.2 and thickness (
h
) of 31 mils.
Simulated results for the tunability of the center frequencies and bandwidths of passbands according to capacitances: (a) passband center frequency tunability and (b) bandwidth tunability. Refer to Fig. 1 for notation. FBW=fractional bandwidth.
The proposed filter employs two types of varactor diodes from Skyworks: SMV1231011LF for tuning
C
_{v1f1}
and
C
_{v1f2}
, and SMV1233079LF for tuning
C
_{v2f1}
and
C
_{v2f2}
. After the simulation, the physical parameters and component values of the filter were determined as shown in
Table 1
.
Dimensions for fabricated filter I (unit=mm; refer toFig. 1for notation)
Dimensions for fabricated filter I (unit=mm; refer to Fig. 1 for notation)
Simulation (Sim) and measurement (Meas) results of filter I with both tunable passbands. Bias voltage variation: V_{Cv1_f}_{1}=3.78 to 15 V, V_{Cv2_f}_{1}= 0.59 to 15 V, V_{Cv1_f}_{2}=4 to 15 V, and V_{Cv2_f}_{2}=4 to 15 V.
 1. Filter I: Tunable Center Frequencies
Fig. 5
shows the simulation and measurement results of filter I for several typical bias voltages. The measurement results agree well with the simulation results. The measurement results show that the first passband center frequency can be tuned from 1.48 to 1.8 GHz and the second passband center frequency can be tuned from 2.40 to 2.88 GHz.
The return loss is better than 12 dB in the overall tuning range of both passbands. The insertion loss varies from 1.99 to 4.4 dB at the first passband, whereas it varied 1.60 to 4.2 dB at the second passband. As the passbands are tuned towards lower frequencies, the insertion loss becomes higher. Because of decreasing bias voltages, the Q value of varactors becomes lower.
Fig. 6
shows the simulation and measurement results of filter I with the fixed second passband and tunable first passband center frequencies. The second passband center frequency is fixed at 2.88 GHz and the first passband center frequency is tuned from 1.48 to 1.8 GHz. The return loss is better than 12 dB over the entire tuning range of the first passband. The insertion loss varies from 1.99 to 4.42 dB.
Simulation and measurement results of filter I with a tunable first passband and fixed second passband. Bias voltage variation: V_{Cv1f1}=3.78 to 15 V, V_{Cv2f1}= 0.59 to 15 V, V_{Cv1f2}=15 V, and V_{Cv2f2}=15 V.
Simulation and measurement results for filter I with a fixed first passband and tunable second passband. Bias voltage variation: V_{Cv1f1}=15 V, V_{Cv2f1}=15 V, V_{Cv1f2}=4 to 15 V, and V_{Cv2f2}=4 to 15 V.
Fig. 7
shows the simulation and measurement results of filter I with the fixed first passband and tunable second passband center frequencies. The first passband center frequency is fixed at 1.74 GHz, and the second passband center frequency is tuned from 2.40 to 2.88 GHz with the return loss better than 12 dB over the entire tuning range.
The insertion loss varies from 1.64 to 4.2 dB. From these results, it is clear that the center frequencies of proposed filter can be tuned independently. However, the differences in insertion loss between the simulation and measurement results are due to the use of ideal capacitances in EM simulation.
 2. Filter I: Tunable Bandwidths
Fig. 8
shows the simulation and measurement results of filter I with both tunable passband bandwidths. As seen in this figure, the first passband’s 3dB FBWs could be tuned from 5.76% to 8.55% at 1.74 GHz and the second passband’s 3dB FBW variation was from 8.28% to 12.42% at a center frequency of 2.80 GHz.
Figs. 9
and
10
show the simulation and measurement results for filter I, which independently verify the tunable 3dB FBWs of the passbands. As seen in
Fig. 9
, the 3dB FBW of the first passband is tunable with the fixed second passband bandwidth. Similarly,
Fig. 10
shows the simulation and measurement results for the tunable 3dB FBWs of the second passband with the fixed first passband bandwidth. A photograph of the fabricated filter I is shown in
Fig. 11
.
 3. Filter Ⅱ: The Tunable DualBand Bandpass Filter with Harmonic Suppression
It can be observed from the simulation and measurement results in the previous section that the two passbands have several harmonics.
These harmonics are also tuned by varying the passband frequencies and must be suppressed for overall system performance.
A simple method of suppressing the harmonics is the introduction of a transmission zero at the harmonic frequency
[15]
. However, this method would be inefficient, because it can only suppress the harmonics around a specific frequency. Due to a broad range of variation in the harmonic frequency in the case of a tunable dual band BPF, it is not possible to cancel harmonics sufficiently by a simple transmission zero circuit. The DGS of the microstrip line is implemented by making artificial defects on the ground plane; it provides bandrejection characteristics corresponding to the size and shape of defects on the ground plane. The DGS also provides an additional effective inductance in the transmission line, which enables the slowwave factor of line to be increased. These bandrejection properties and the slowwave effect of DGS have been applied in the design of various microwave circuits, including filters, dividers, and amplifiers
[16
,
17]
.
Simulation and measurement results for filter I with tunable bandwidths (BWs) in both passbands simultaneously. (a) both passbands, (b) magnified first band characteristics, and (c) magnified second band characteristics. Bias voltage variation: V_{Cv1f1}=15 V, V_{Cv2f1} =6 to 15 V, V_{Cv1f2}=15 V, and V_{Cv2f2}=8 to 15 V.
Simulation and measurement results for filter I with a fixed second passband bandwidth (BW) and tunable first passband BW: (a) both passbands and (b) magnified first band characteristics. Bias voltage variation: V_{Cv1_f1} =15 V, V_{Cv2f1}=6 to 15 V, V_{Cv1f2}=15 V, and V_{Cv2f2}= 15 V.
Simulation and measurement results of filter I with the fixed first passband bandwidth (BW) and tunable second passband BW: (a) both passbands and (b) magnified second band characteristics. Bias voltage variation: Bias voltage variation: V_{Cv1_f1}=15 V, V_{Cv2f1}=15 V, V_{Cv1f2}= 15 V, and V_{Cv2f2} =8 to 15 V.
In microwave circuit design, the bandrejection property of the DGS can also be utilized in the suppression of harmonics
[13
,
17]
.
Fig. 12
shows the proposed configuration and photograph of fabricated harmonic suppressed tunable dual band filter Ⅱ. In this structure, DGS is used at the input/output feeding lines for inducting coupling and acts as a broad bandrejection resonator to suppress the harmonics of filter I. The methods for finding the equivalent circuits of DGS are detailed in
[16]
. The physical parameters and component values of filter Ⅱ are shown in
Table 2
.
Photograph of fabricated filter I.
Proposed structure and photograph of fabricated filter II: (a) configuration, (b) top view, and (c) bottom view of fabricated filter Ⅱ. DGS=defected ground structure.
Fig. 13
(a) shows the narrowband characteristics of the simulation and measurement results for filter Ⅱ. The passband frequencies are tuned with the help of the bias voltages of the varactor diodes. From the measurement results, the first passband frequency can be tuned from 1.5 to 1.8 GHz and the second passband frequency can be tuned from 2.45 to 2.80 GHz. The return loss is better than 11 dB over the entire tuning range of the passbands. The insertion loss varies from 3.02 to 4.8 dB at the first passband and 2.78 to 4.6 dB at the second passband. These measurement results for filter Ⅱ are almost similar to the filter I results in the previous section, except for the suppression of the harmonic characteristics.
Simulation and measurement results for filter Ⅱ with two tunable passbands: (a) narrowband and (b) wideband characteristics. Bias voltage variation: Bias voltage variation: V_{Cv1_f1}=4.09 to 13 V, V_{Cv2f1}=0.93 to 15 V, V_{Cv1f2}=5.60 to 15 V, and V_{Cv2f2}=3.21 to 15 V.
Dimensions for fabricated filter Ⅱ (unit=mm; refer toFig. 12for notation)
Dimensions for fabricated filter Ⅱ (unit=mm; refer to Fig. 12 for notation)
In order to verify the harmonic suppression characteristics of filter Ⅱ, the broadband harmonic suppression characteristics are shown in
Fig. 13
(b). The harmonic suppression characteristics for the fabricated filter Ⅱ are better than 19 dB up to 18 GHz over the entire tuning range of the passbands. This means that the proposed structure can suppress more than 10th order harmonics of the highest center frequencies of the first passbands due to the bandrejection characteristics of DGS. This confirmed that the proposed method can achieve broadband harmonic suppression without degrading any passbands performances. Performance comparisons of the proposed tunable filter with other tunable filters reported in the literature are summarized in
Table 3
. The proposed filter can provide dualpassbands with independently tunable center frequencies and bandwidths in addition to broadband harmonic rejection characteristics.
Performance comparison of tunable filter with independent control of center frequency and bandwidthFBW=fractional bandwidth, A=independently tunable center frequency and bandwidth, Y=yes, N=no,f1_max=highest center frequency of first passband,f2_max=highest center frequency of second passband,*=1dB FBW,**=suspendedstripline rings in microelectromechanical system technology.
Performance comparison of tunable filter with independent control of center frequency and bandwidth FBW=fractional bandwidth, A=independently tunable center frequency and bandwidth, Y=yes, N=no, f_{1_max}=highest center frequency of first passband, f_{2_max}=highest center frequency of second passband, ^{*}=1dB FBW, ^{**}=suspendedstripline rings in microelectromechanical system technology.
Ⅳ. Conclusion
In this paper, the design of tunable dualband BFPs with independently tunable center frequencies and bandwidths was demonstrated. The proposed structure is validated by both theoretical analysis and experiments. Defected ground structures were utilized to reject the harmonics. The experimental results are in good agreement with the theoretical predictions. These experimental results showed that the first passband can be tuned from 1.48 to 1.8 GHz with a 3dB fractional bandwidth tunability of 5.76% to 8.55%, while the second passband can be tuned from 2.40 to 2.88 GHz with a 3dB fractional bandwidth tunability of 8.25% to 12.42%. The proposed filter also offers switchable passband characteristics.
The proposed method can suppress more than 10th order harmonics of second passbands, thereby ensuring broad harmonic rejection characteristics without any degradation of the passband characteristics. The proposed filter topology is simple to implement and a good candidate for communication systems requiring multiband tunable filters with center frequency and bandwidth control. The proposed filter design method can be applied to selectable multimode or multiband applications that have different operating frequencies and bandwidths.
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