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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 8, AUGUST 2005
A 12–18-GHz Three-Pole RF MEMS Tunable Filter
Kamran Entesari, Student Member, IEEE, and Gabriel M. Rebeiz, Fellow, IEEE
Abstract—This paper presents a state-of-the-art RF microelectromechanical systems (MEMS) wide-band tunable filter designed
for the 12–18-GHz frequency range. The coplanar-waveguide filter,
fabricated on a glass substrate using loaded resonators with RF
MEMS capacitive switches, results in a tuning range of 40% with
very fine resolution, and return loss better than 10 dB for the whole
0.4%
tuning range. The relative bandwidth of the filter is 5.7
over the tuning range and the size of the filter is 8 mm
mm.
The insertion loss is 5.5 and 8.2 dB at 17.8 and 12.2 GHz, respectively, for a 2-k sq bias line. The loss improves to 4.5 and 6.8 dB
at 17.8 and 12.2 GHz, respectively, if the bias line resistance is increased to 20 k sq. The measured
3 level is 37 dBm for
kHz. To our knowledge, this is the widest band planar
tunable filter to date.
excellent performance [7], but the filter results in four separate
frequency responses, which are not contiguous. There is a need
for a completely contiguous filter design at 8–18 GHz, and this
paper addresses this problem.
In this paper, we present a three-pole RF MEMS digital tunable filter with 40% tuning range from 12.2 to 17.8 GHz. The
frequency band is covered by 16 filter responses (states) with
very fine frequency resolution so as to behave as a continuoustype filter. To achieve this high tuning resolution, a novel 4-bit
MEMS distributed capacitor bank is used in the resonator. A
nonlinear study of the tunable filter is presented in Section IV.
Index Terms—Coplanar-waveguide (CPW) filter, loaded resonators, microelectromechanical systems (MEMS), RF MEMS,
wide-band tunable filter.
II. FILTER DESIGN
1
200
4
IIP
I. INTRODUCTION
R
F microelectromechanical systems (MEMS) tunable filters have been developed in the past few years for multiband communication systems, radars, and wide-band tracking
receivers [1]. MEMS switches and varactors have very low loss,
therefore, resulting in relatively high- designs. RF MEMS
also offer outstanding linearity with a measured overall
40–50 dBm [2]–[4]. Electrostatic RF MEMS switches do not
require any dc current and, therefore, offer a very low power
approach for tuning applications.
There are two different types of frequency-tuning methods
for MEMS-based filters: analog and digital. Analog tuning is
relatively easy with MEMS varactors and provides continuous
frequency variation, but the tuning range has been limited
to 5%–15% [3]. In digital-type tuning, where a capacitor is
switched in and out of the circuit, discrete center frequencies
and wide tuning ranges are possible (20%–60%), and several
designs are currently available at 0.1–10 GHz [4]–[6]. The main
advantage of digital-type designs is that they are less sensitive
to bias and Brownian noise [2], and the center frequency is
well known (little drift with temperature). However, due to the
size of the switching capacitor bank, it has been hard to design
filters using the digital approach above 8 GHz. Recently, a
2-bit (four states) 10–14-GHz MEMS filter was presented with
Manuscript received September 23, 2004. This work was supported by the
National Science Foundation under Contract ECS9979428.
K. Entesari is with the Radiation Laboratory, Department of Electrical
Engineering and Computer Science, The University of Michigan at Ann Arbor,
Ann Arbor, MI 48109-21222 USA (e-mail: kentesar@umich.edu).
G. M. Rebeiz was with the Radiation Laboratory, Department of Electrical
Engineering and Computer Science, The University of Michigan at Ann Arbor,
Ann Arbor, MI 48109-21222 USA. He is now with the Electrical and Computer
Engineering Department, University of California at San Diego, La Jolla, 92037
CA USA (e-mail: rebeiz@ece.ucsd.edu).
Digital Object Identifier 10.1109/TMTT.2005.852761
A. Topology
Fig. 1 presents the circuit model for a three-pole loaded
resonator tunable filter. Each coplanar-waveguide (CPW)
resonator is periodically loaded by four switched MEMS
capacitors pairs (eight in total), which results in a slow-wave
structure with a smaller effective wavelength and lower characteristic impedance in comparison to the unloaded resonator.
Every switched capacitor is built as a series combination of
a MEMS switch with a capacitance ratio of 30–40 and a
.
fixed metal–air–metal (MAM) capacitor
The loaded MEMS resonators are coupled through inductive
impedance inverters and form a three-pole bandpass filter. The
inductive impedance inverters are T-combinations of a shunt
inductor and two series transmission lines with negative lengths
[3].
The response of the filter can be tuned over a wide frequency range by changing the effective electrical length of the
resonators using 16 different combinations (4-bit) of pairs of
MEMS switches in the up- and down-state positions. Due to the
filter topology, the shape and fractional bandwidth of the filter
is approximately fixed over the tuning range, and the inductive
couplings between the resonators compensate the increasingly
capacitive behavior of the resonators when they are tuned
toward the lower frequencies [9]. It is also known that the inductive coupling along with capacitive loading provides closer
spurious passbands and lower rejection at higher frequencies
[1], [8]. However, for a loaded resonator, this negative effect is
not observed because the second resonance is eliminated due
to loading effect at the center of the resonator.
B. Resonator Design
The circuit model of a capacitively loaded resonator is shown
in Fig. 2 The loading capacitors are placed in a symmetrical
fashion around the middle of the resonator and are actuated in
pairs. This results in a symmetrical shape of the standing-wave
voltage on the loaded resonator and, therefore, for each state,
the maximum voltage level always occurs at the middle point
0018-9480/$20.00 © 2005 IEEE
ENTESARI AND REBEIZ: 12–18-GHz THREE-POLE RF MEMS TUNABLE FILTER
2567
Fig. 1. Circuit model of a three-pole loaded resonator tunable filter.
Fig. 2.
Circuit model of a capacitive resonator loaded with eight capacitive MEMS switches.
TABLE I
RESONATOR CIRCUIT MODEL ELEMENT VALUES
EXTRACTED FROM ADS SIMULATIONS
Fig. 3. Circuit model and practical realization of a unit cell in a loaded
resonator. The biasing resistance is grounded in the simulations.
of the resonator. For example, to change the resonant frequency
from State-0000 (all the switches are in the up-state position) to
State-0001, the two MEMS switches, which are in series with
are pulled down. Table I shows the values
MAM capacitor
for the MEMS capacitors in up- and down-state positions (
and
) and the MAM capacitors
. The
in series with the
largest loading unit cells (MAM capacitors
MEMS switches) are placed close to the middle of the resonator
and can shift the resonant frequency from 18 GHz to around
14 GHz when they are pulled down. The smallest loading unit
cells are placed farther from the middle of the resonator and
are for fine tuning. All loading unit cells have the same elecwith an unloaded t-line
trical distance from each other
impedance of 78 . This distance is simulated to be 4.4 (or
120 m) at the design frequency (18 GHz) with Agilent’s ADS1
when a lumped capacitor model is used as a loading unit cell.
A practical realization of a unit cell is shown in Fig. 3, and
the physical length of each unit cell is 140 m. The finite width
of the bridge and MAM capacitors and the current path over
the bridge result in a phase delay, which reduces the effective
1Agilent
Technol. Inc., Palo Alto, CA, 2002.
physical length of a unit cell to 100 m, and the spacing between
m at
two adjacent unit cells is 20 m and, hence,
18 GHz. Table I also shows the electrical length of the unloaded
sections for each resonator simulated in ADS
. The real physical lengths of the unloaded sections will
be reduced in the practical realization due to the negative t-line
lengths of the inductive inverters.
All resonators are simulated using Sonnet2 with CPW dimensions of 70/120/70 m on a 500- m glass substrate (
and
at 18 GHz). The dimensions of the CPW line
are chosen to minimize the conductor loss [11]. The measured
,
, and
unloaded CPW line parameters are
dB/m at 18 GHz with 2- m electroplated gold. Table II
shows the transmission-line parameters for the four different
and
are the
loaded sections of the resonator [3].
equivalent capacitor values for each loading cell
and are calculated from
(1)
2Sonnet
8.52, Sonnet Software Inc., Syracuse, NY, 2003.
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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 8, AUGUST 2005
TABLE II
UNIT CELL CIRCUIT MODEL ELEMENT VALUES EXTRACTED FROM ADS SIMULATIONS AT 18 GHz (Z
= 78
; = 2:8; = 42 dB/m, Q = 65)
ripple Chebyshev filter. Canonical equations result in input and
pH and interstage inverters
output inverters with
pH at 18 GHz. The series transmission lines
with
with negative electrical lengths are absorbed in the unloaded
sections of each resonator [3] (
at 18 GHz). The physical realization of shunt inductors in
CPW transmission lines is shown in Fig. 5. The length and width
of the inductive short-circuit slots are found using a full-wave
simulation (Sonnet). Fig. 6 shows the simulated insertion loss
k sq, and is 5.4 and
for 16 different states with
8 dB at 17.8 and 12.2 GHz, respectively. The higher insertion
loss at 12.2 GHz is due to the higher loss factor of a loaded
transmission line and the low-resistivity bias line, which has a
strong loading effect when all the switches are in the down-state
position.
III. FABRICATION AND MEASUREMENT
A. Fabrication, Implementation, and Biasing
Fig. 4. Simulated: (a) unloaded quality factor and (b) resonant frequency for
a tunable loaded resonator.
The quality factor for an unloaded resonator is calculated from
(2)
and is 65 at 18 GHz for the unloaded CPW resonator. For the
loaded sections, the quality factor is calculated in the up- or
)
down-state positions using [10] (assuming
(3)
These values all are presented in Table II. Fig. 4(a) and (b)
shows the simulated unloaded quality factor of the loaded resonator and the resonant frequency for 16 different combinations
of the switches, respectively. This is done using a single resonator, which is weakly coupled to the input and output ports,
and the simulated resonant frequency and quality factor for each
different state is obtained using ADS based on the values on
Table I.
C. Complete Filter Design and Simulations
The final section of the filter design is the inductive inverter
implementation. The goal is to design a three-pole 6% 0.1-dB
The tunable filter is fabricated on a 500- m glass substrate
(
and
) using CPW lines and MEMS
switches with a standard RF MEMS process developed at The
University of Michigan at Ann Arbor [12]. The MEMS capacitive switch is based on a 8000- sputtered gold layer and is
suspended 1.4–1.6 m above the pull-down electrode. The dielectric Si N layer is 1800- thick and the bottom electrode
thickness is 6000 (underneath the bridge). The MAM capacitors are suspended 1.5 m above the first metal layer. The CPW
conductor, bridge anchor, and top plate of the MAM capacitors
are electroplated to 2- m thick using a low-stress gold solution.
The bias lines are fabricated using an 800- -thick SiCr layer
with a resistivity of approximately 2 k /square.
The width, length, and thickness of the MEMS bridge are 60,
280, and 0.8 m, respectively, and the gap is 1.5 m for the
bridge and MAM capacitors [see Fig. 3]. The bottom plate of
one of the MAM capacitors is connected to the thin-film resistor
to bias the bridge. The release height of the MEMS bridge and
MAM capacitor is 1.5 m measured by a light-interferometer
V, with
microscope. The measured pull-in voltage is
N/m, and a residual
a corresponding spring constant of
stress of
MPa. The mechanical resonant frequency and
kHz and
,
quality factor of the switch are
respectively [2].
The photograph of the complete 12–18-GHz filter is shown
in Fig. 5. It is composed of three resonators, each one loaded
with eight unit cells, two inductive inverters at the input and
output of the filter, and two inductive inverters between loaded
resonators. Each switch has a separate SiCr dc-bias line for
ENTESARI AND REBEIZ: 12–18-GHz THREE-POLE RF MEMS TUNABLE FILTER
2569
Fig. 5. Complete 12–18-GHz filter fabricated on a glass substrate.
Fig. 6. Simulated: (a) insertion loss and (b) return loss of the tunable three-pole
12–18-GHz filter.
independent control. The center conductor of the coplanar
loaded resonators is connected to the dc ground pad through
the RF probe using a bias tee. The filter is excited using
ground–signal–ground (GSG) single-ended probes with a pitch
of 150 m.
B. Measurements
The tunable filter is measured using CPW probes and TRL
calibration. The measured results are shown in Fig. 7 for 16 different states. The insertion loss [see Fig. 7(a)] is 5.5 and 8.2 dB
at 17.8 and 12.2 GHz, respectively, and the relative bandwidth
Fig. 7. Measured: (a) insertion loss and (b) return of the tunable three-pole
12–18-GHz filter.
is approximately fixed for the whole tuning range, as expected
from the simulation results. The return loss [see Fig. 7(b)] is
better than 10 dB over the whole tuning range. The measured
center frequency and loss for each of the 16 different states is
presented in Fig. 8(a). Fig. 8(b) shows the relative bandwidth
variation for all responses, and is 6.1% at 17.8 GHz (State 0),
and 5.3% at 12.2 GHz (State 15). Fig. 9 compares the measured and simulated insertion loss for three arbitrary states at
17.8 (State 0), 14 (State 8), and 12.2 GHz (State 15), and the
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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 8, AUGUST 2005
Fig. 10. Experimental setup for intermodulation measurements
f .
f
Fig. 8. (a) Measured center frequency and loss. (b) Measured relative
bandwidth of the 16-filter responses 5.7 0.4% .
( 6
)
Fig. 9. Comparison between the measured and simulated insertion loss for
three arbitrary states at 12.8 (State 15), 14.0 (State 8), and 17.8 GHz (State 0).
simulated and measured responses agree very well. For the case
k sq , the simulated insertion loss is 1.0 dB
of
better at 17.8 GHz, 1.4 dB better at 14 GHz, and 2.2 dB better
at 12.2 GHz, as compared with the measurements with
k sq. The measured response of a fabricated filter without
any bias lines also confirms that the insertion loss improves by
0.8 dB at 17.8 GHz (all the switches are electroplated in the
up-state position) to 2.0 dB at 12.2 GHz (all the switches are
electroplated in the down-state position).
IV. NONLINEAR CHARACTERIZATION
The nonlinear analysis of MEMS switches, varactors, and
tunable filters has been presented in [13]. For high level RF
signals, this analysis shows that the MEMS bridge capacitance
self-pull-down results in a nonlinear behavior of the tunable
0 )
= 0
(1f =
Fig. 11. Nonlinear measurements at V
V: the fundamental and
intermodulation components versus the input power, and the two-tone
versus the beat frequency.
IM
filter. In the case of two RF signals, third-order intermodulation
is generated. To measure the intermodulation components at the
output of the tunable filter, the setup shown in Fig. 10 is used.
Fig. 11 shows the measured output power for the fundamental
and intermodulation components for several values of
. The measured
is 37 dBm for
kHz. The
since this state
measurement is in the up-state position
products. Tunable filters with diode vargives the worse
(12 dBm in [14] and
actors have much lower values of
28 dBm in [15]). Fig. 11 also shows the intermodulation component versus the difference frequency between input tones
for
dBm (no bias voltage on the bridges). The intermodulation component follows the mechanical response of the
level drops by 40 dB/decade for
,
bridge, and the
which is in agreement with theory [13]( is the mechanical resis 77 dBm at a differonant frequency). This means that
ence frequency of 2 MHz, which is very hard to measure and is
quite impressive.
V. CONCLUSION
The paper has demonstrated a wide-band tunable filter on
a glass substrate from 12.2 to 17.8 GHz (40% tuning range).
Four different unit-cell pairs (MEMS capacitive switches in series with high- MAM capacitors) have been used to load the
CPW resonators to reduce their effective length and make them
tunable in a very wide range. This resulted in a tunable filter
with very fine tuning resolution. The return loss is better than
10 dB over the whole band, and it is possible to achieve a better
return loss, especially at lower frequencies, if the inductive inverters are made tunable. The measured results are very close
to full-wave simulations. This study has shown that RF MEMS
ENTESARI AND REBEIZ: 12–18-GHz THREE-POLE RF MEMS TUNABLE FILTER
2571
tunable filters are excellent for wide-band designs and result in
very low intermodulation levels.
[15] A. R. Brown and G. M. Rebeiz, “A varactor-tuned RF filter,” IEEE
Trans. Microwave Theory Tech., vol. 48, no. 7, pp. 1157–1160, Jul. 2000.
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Ka
X
Kamran Entesari (S’03) received the B.S. degree
in electrical engineering from Sharif University of
Technology, Tehran, Iran, in 1995, the M.S. degree
in electrical engineering from Tehran Polytechnic
University, Tehran, Iran, in 1999, and is currently
working toward the Ph.D. degree in electrical
engineering (with an emphasis on applied electromagnetics and RF circuits) at The University of
Michigan at Ann Arbor.
His research area includes RF MEMS for
microwave and millimeter-wave applications, microwave tunable filters, and packaging structures.
Gabriel M. Rebeiz (S’86–M’88–SM’93–F’97) received the Ph.D. degree in electrical engineering from
the California Institute of Technology, Pasadena.
He is a Full Professor of electrical engineering
and computer science (EECS) with the University
of California at San Diego, La Jolla. He authored
RF MEMS: Theory, Design and Technology (New
York: Wiley, 2003). His research interests include
applying MEMS) for the development of novel
RF and microwave components and subsystems.
He is also interested in SiGe RF integrated-circuit
(RFIC) design, and in the development of planar antennas and millimeter-wave
front-end electronics for communication systems, automotive collision-avoidance sensors, and phased arrays.
Prof. Rebeiz was the recipient of the 1991 National Science Foundation
(NSF) Presidential Young Investigator Award and the 1993 International Scientific Radio Union (URSI) International Isaac Koga Gold Medal Award. He
was selected by his students as the 1997–1998 Eta Kappa Nu EECS Professor
of the Year. In October 1998, he was the recipient of the Amoco Foundation
Teaching Award, presented annually to one faculty member of The University
of Michigan at Ann Arbor for excellence in undergraduate teaching. He was the
corecipient of the IEEE 2000 Microwave Prize. In 2003, he was the recipient
of the Outstanding Young Engineer Award of the IEEE Microwave Theory
and Techniques Society (IEEE MTT-S). He is a Distinguished Lecturer for the
IEEE MTT-S.