Download A Differential 4-bit 6.5–10-GHz RF MEMS Tunable Filter

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 3, MARCH 2005
1103
A Differential 4-bit 6.5–10-GHz
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 wide-band miniature tunable filter
designed for 6.5–10-GHz frequency range. The differential filter,
fabricated on a glass substrate using digital capacitor banks and
microstrip lines, results in a tuning range of 44% with very fine
resolution, and return loss better than 16 dB for the whole tuning
range. The relative bandwidth of the filter is 5.1 0.4% over
the tuning range and the size of the filter is 5 mm 4 mm. The
insertion loss is 4.1 and 5.6 dB at 9.8 and 6.5 GHz, respectively,
for a 1-k sq fabricated bias line. The simulations show that, for
a bias line with 10- k sq resistance or more, the insertion loss
improves to 3 dB at 9.8 GHz and 4 dB at 6.5 GHz. The measured
45 dBm for
kHz, and the filter can
3 level is
handle 250 mW of RF power for hot and cold switching.
IIP
1
500
Index Terms—Differential filter, digital capacitor bank, microelectromechanical systems (MEMS), RF MEMS, wide-band tunable filter.
I. INTRODUCTION
IDE-BAND tunable filters are extensively used for
multiband communication systems and wide-band
tracking receivers. The most practical implementation is based
on yttrium–iron–garnet (YIG) resonators. They have multioctave bandwidths and are high quality-factor resonators [1],
[2]. However, they are bulky and cannot be easily miniaturized
for wireless communications. They also consume considerable
amount of dc power (0.75–3 W), and their linearity is not high
– dBm .1 An alternative to YIG filters is based on
miniaturized planar filters with solid-state or microelectromechanical systems (MEMS) devices. Solid-state varactors can
provide a wide tuning range, but they have loss and linearity
problems at microwave frequencies [3]–[5]. MEMS switches
and varactors have very low loss, they do not consume any dc
dBm [6], [7].
power, and their linearity is excellent
There are two different types of frequency-tuning methods for
MEMS-based filters, analog and digital. Analog tuning provides
continuous frequency variation of the passband, but the tuning
range is limited. For example, the tuning range in [8]–[10] is
W
Manuscript received April 12, 2004; revised September 9, 2004. This
work was supported by the National Science Foundation under Contract
ECS-9979428.
K. Entesari is with the Radiation laboratory, Department of Electrical Engineering and Computer Science, The University of Michigan at Ann Arbor, Ann
Arbor, MI 48109-2122 USA (e-mail: [email protected]).
G. M. Rebeiz was with the Radiation Laboratory, The University of Michigan
at Ann Arbor, Ann Arbor, MI 48109-2122 USA. He is now with the Department
of Electrical and Computer Engineering, University of California at San Diego,
La Jolla, CA 92093-0407 USA (e-mail: [email protected]).
Digital Object Identifier 10.1109/TMTT.2005.843501
1YIG
Fig. 1. Lumped model for a two-pole differential tunable filter.
4.2%, 10%, and 14%, respectively. In digital MEMS filters, discrete center frequencies and wide tuning ranges are possible.
Young et al. [16], and Brank et al. [17] presented excellent tunable filters with high-frequency resolution at 0.8–2 GHz. However, existing digital MEMS filters at microwave frequencies
GHz do not have enough resolution to result in near
continuous coverage of the frequency band. The MEMS filter in
[11] shows four states (2-bit filter) and a 44% tuning range with
poor frequency resolution. The filter in [12] has two states (1-bit
filter) and can switch from 15 to 30 GHz. Other designs have two
states and lower tuning range: 28.5% in [13] and 12.8% in [14].
In this paper, we will present a 4-bit digital differential tunable filter with 44% tuning range from 6.5 to 10 GHz. The frequency band is covered by 16 filter responses with very fine frequency resolution. Practically, this filter behaves like a continuous-type tunable filter. To achieve such a high tuning resolution, capacitive MEMS switches are connected in series with
high- metal–air–metal (MAM) capacitors to make a capacitor
bank. As a result, the capacitor variation can be controlled accurately by choosing the correct values for MAM capacitors. The
MEMS capacitor bank is inserted in a lumped differential filter
to result in a miniature 6.5–10-GHz tunable filter. A nonlinear
study of the differential tunable filter is presented in Section IV.
II. DESIGN
A. Design Equations
Fig. 1 presents a two-pole filter suitable for a differential implementation. This filter is a practical realization of a standard
Chebyshev bandpass filter with parallel resonators and -inverters [see Fig. 2(a)]. The element values for the normalized
bandpass filter are calculated from
(1)
(2)
(3)
tuned filters, Micro Lambda Inc., Fremont, CA.
0018-9480/$20.00 © 2005 IEEE
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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 3, MARCH 2005
Fig. 3. J -inverter implementation using a practical transformer.
Fig. 2. (a) Standard Chebyshev bandpass filter. (b) Admittance scaling.
(c) Practical transformer realization using capacitive dividers.
where
is the bandpass filter center frequency,
is the
and
are the parallel capacfractional bandwidth, and
itor and the admittance inverter for the normalized low-pass
prototype filter [15]. The shunt inductance is inversely proportional to and for narrow bandwidths; it can be too small to
be physically realizable. Therefore, the entire admittance of the
factor,
filter (including source and load) can be scaled by a
where is an arbitrary scaling factor to result in realizable element values, and an impedance transformer must be inserted
between the filter and its terminations [see Fig. 2(b)]. To realize this ideal transformer at high frequencies, a narrow-band
and
capacimpedance transformer is implemented using
itors [see Fig. 2(c)]. The values of
and
can be found using
the two conditions at the source and load
and
can be calculated based on the self-inductance of
and the transformer coupling factor
the transformer
(7)
(8)
(9)
Using (1)–(9), the values of
,
, , and
can be calfor a specific freculated based on , , , , , and
quency. The closed-form equations for the lumped elements of
the differential filter of Fig. 1 are summarized as follows:
(10)
(11)
(4)
(12)
is the differential line impedance at the input and
where
output of the filter (100 for this design). Solving (4) gives
the values of
and
[15]
(13)
B. Design
(5)
(6)
is a negative capacitor, but it is always smaller than
so
.
they can be absorbed into each other and form the capacitor
Fig. 3 shows the implementation of the -inverter and parallel
bandpass inductors using a practical transformer. The values of
The response of the differential filter of Fig. 1 can be tuned
over a wide frequency range by varying
. The shape and relative bandwidth of the filter is approximately fixed due to the
filter topology, i.e., capacitive tuning with an inductive inverter
[1]. The input/output matching is maintained better than 16 dB
. Table I presents the elover the tuning range by varying
ement values of a two-pole 5% (Chebyshev, equiripple bandwidth) 6.5–10-GHz differential tunable filter. The filter is first
and
designed at 10 GHz using (10)–(13) with
. Next,
and
capacitors are varied to achieve a
ENTESARI AND REBEIZ: DIFFERENTIAL 4-BIT 6.5–10-GHz RF MEMS TUNABLE FILTER
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TABLE I
ELEMENT VALUES FOR THE TUNABLE LUMPED FILTER
Fig. 5. Simulated values of C and C
C
Fig. 4.
(a) Simplified circuit model. (b) Layout for C as a capacitor bank.
filter response down to 6.5 GHz using Agilent ADS.2 To achieve
and
a 40% tuning range or more,
.
C. 3- and 4-Bit Digital MEMS Capacitors
The resonant capacitor
is substituted by a capacitor bank
with four unit cells (Fig. 4). This results in 16 different filter responses using 16 different combinations of switches in the up,
, and
repand down-state positions.
is half of the MAM
resent MEMS switches,
is the parcapacitor in series with the MEMS switch, and
asitic capacitance coming from the layout implementation of
. Each matching capacitor
is composed of three unit
cells, and provides enough capacitive variation to result in a
well-matched circuit over the whole tuning range.
and
for difFig. 5 shows the different values of
ferent combination of switches in the up- and down-states positions. These values are extracted from full-wave simulation of
2ADS
2002, Agilent Technol. Inc., Palo Alto, CA.
for different switch combinations.
TABLE II
ELEMENT VALUES EXTRACTED FROM SONNET SIMULATION
the capacitor bank layouts using Sonnet3 and fitted to a
model. The corresponding unit-cell values presented in Table II
, where
is found from the
are calculated using
full-wave simulations and includes all inductive (parasitic) efvaries between 140 fF (State 0, all the switches are
fects.
up) and 425 fF (State 15, all the switches are down), which is
varies from 95 (State 0) to
close to the range in Table I.
253 fF (State 7), which is higher than
in Table I and
provides a safe margin to match the return loss of the filter at
lower frequencies.
D. Effect of Bias Resistance on Capacitor
The resonant capacitor bank
quality factor has an important role in determining the unloaded of the resonators and
the insertion loss of the filter. The MEMS and MAM capacitors
as measured in [18], and do not
are high- elements
degrade the unloaded of the resonators. However, the bias line
resistor has a very strong loading effect on the quality factor of
(and the resonator). Fig. 6 shows the simulated quality factor
at an arbitrary frequency
GHz for different bias
of
line values. This is done using ADS, with the component values
in Table II placed in the circuit model of Fig. 4. The simulated
circuit ( is negligible), and
impedance is fitted to a simple
the quality factor is defined as [6]
(14)
3Sonnet
8.52, Sonnet Software Inc., North Syracuse, NY.
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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 3, MARCH 2005
Fig. 6. Simulated resonant capacitor quality factor for different switch
combinations, and bias resistances.
TABLE III
SIMULATED CENTER FREQUENCIES AND THE CORRESPONDING 16 DIFFERENT
STATES FOR C AND C . THE INDEXES U/L REFER TO THE UPPER (U)
AND LOWER (L) MATCHING CAPACITORS IN FIG. 1
Fig. 7. Simulated: (a) insertion loss and (b) return loss of the tunable two-pole
6.5–10-GHz filter.
where is the operation frequency, is the total series resistance including MEMS switches, MAM capacitors, and bias
line resistances, and is the equivalent capacitance. The
quality factor doubles if the bias line resistance changes from 1
to 10 k sq. For higher bias line resistances (up to 1 M sq),
the quality factor improvement is only 20%.
E. Tunable Filter Simulations
layout can change both the
The resonant capacitor
transformer coupling factor and inductor values. The amount
of desired coupling and inductance is adjusted by changing
the length of the inductors and the distance between the two
resonators are simulated
inductors when the coupled
together in Sonnet. The simulated
of the wide microstrip
m,
m) on the glass substrate
lines (
is around 78 at 8 GHz. The whole filter response is then
simulated in ADS by cascading -parameters of the matching
capacitors and resonators. The simulated center frequencies
and
are presented in
and the corresponding states of
Table III. Fig. 7 shows the insertion loss for 16 different states
k sq and is 4 and 5.6 dB at 9.8 and 6.5 GHz,
with
respectively. The higher insertion loss at 6.5 GHz is due to the
low-resistivity bias line, which has a strong loading effect when
the switches are all in the down-state position. If the value of
increases to 10 k sq, the insertion loss improves to
3 dB at 9.8 GHz and 4 dB at 6.5 GHz. The effective unloaded
of the two-pole filter is 45 and 60 for
k sq and
10 k sq, respectively, at 8 GHz.
III. FABRICATION AND MEASUREMENT
A. Fabrication, Implementation, and Biasing
The tunable filter is fabricated on a 500- m glass substrate
and
) using MEMS switches and
(
microstrip lines using a standard RF MEMS process developed
at The University of Michigan at Ann Arbor [18], [19]. 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
above the first
metal layer. The microstrip conductor, bridge anchor, and top
plate of MAM capacitors are electroplated to 2- m thick using
a low-stress gold solution. The bias lines are fabricated using a
1200- –thick SiCr layer with a resistivity of 1 k sq.
ENTESARI AND REBEIZ: DIFFERENTIAL 4-BIT 6.5–10-GHz RF MEMS TUNABLE FILTER
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Fig. 8. Photograph of a unit cell in a digital capacitor bank.
Fig. 9.
Photograph of the complete 6.5–10-GHz filter.
The center frequency of the tunable filter is directly related to
the accuracy of the MAM capacitors (obtained versus designed
values). Since the MAM capacitors are quite large and fully
electroplated and the sacrificial layer underneath them is uniform, one can build these capacitors quite uniformly throughout
the entire wafer with an accuracy around 5% in university laboratories. This can be clearly seen in the agreement between
measured versus simulated center frequencies [see Fig. 12(a)].
The photograph of a unit cell in a digital capacitor bank is
shown in Fig. 8. The width, length, and thickness of the bridge
are 70, 280, and 0.8 m, respectively, and the gap is 1.5 m
for the bridge and MAM capacitors. 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
a corresponding spring constant of
N/m and a residual
MPa. The mechanical resonant frequency and
stress of
kHz and
,
quality factor of the switch are
respectively [6].
The photograph of the complete 6.5–10-GHz filter is shown
in Fig. 9. It is composed of a transformer in the middle, two
, each with four unit cells, and four
resonant capacitors
, each with three unit cells. Each
matching capacitors
switch has a separate SiCr dc-bias line for independent control.
The center conductor of each capacitor bank is connected to the
dc ground pad through the SiCr line. The filter is excited using
differential input and output lines, which are compatible with
Fig. 10. Measured: (a) insertion loss and (b) return loss of the tunable two-pole
6.5–10-GHz filter.
a ground–signal–ground–signal–ground (GSGSG) differential
probe with a pitch of 150 m.
B. Measurements
The tunable filter is measured using a differential test setup:
two 0 –180 hybrid couplers and two differential probes are
used to provide differential excitation for the filters. As is well
known, only the odd mode should be generated for differential
circuits. The phase and amplitude imbalance for the couplers
should be as small as possible. (Gain Bal. 2 dB, Phase Bal.
10 ) for accurate differential measurements [20].
The measurement results are shown in Fig. 10 for 16 different
states. The insertion loss [see Fig. 10(a)] is 4.1 and 5.6 dB at
9.8 and 6.5 GHz respectively, and the relative bandwidth is approximately fixed for the whole tuning range, as expected from
the simulation results. The return loss [see Fig. 10(b)] is always better than 16 dB for the whole tuning range. Fig. 11 compares the measured and simulated insertion loss for two arbitrary
states at 8.6 GHz (State 4) and 7.1 GHz (State 13). The simulated and measured responses agree very well. For the case of
k sq , the simulated insertion loss is 1 dB better
at 8.6 GHz and 1.4 dB better at 7.1 GHz, as compared with the
k sq. The measured response of
measurements for
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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 53, NO. 3, MARCH 2005
Fig. 13.
.
f
)
Experimental setup for intermodulation measurements
(1f = f 0
Fig. 11. Comparison between the measured and simulated insertion loss for
two arbitrary states at 7.1 (State 13) and 8.6 GHz (State 4).
=0
Fig. 14. Nonlinear measurements at V
V. (a) The fundamental and
intermodulation components versus the input power and the two-tone
versus the beat frequency. (b) Filter insertion loss for different values of input
power.
Fig. 12. (a) Simulated and measured center frequency and loss. (b) Measured
relative bandwidth of the 16 filter responses 5.1 0.4 .
( 6 %)
a fabricated filter without any bias lines also confirms that the
insertion loss improves by 1 dB at 9.8 GHz (all the switches
are electroplated in the up-state position) to 1.6 dB at 6.5 GHz
(all the switches are electroplated in the down-state position).
The simulated and measured center frequency and loss for each
of the 16 different states is presented in Fig. 12(a). Fig. 12(b)
shows the relative bandwidth variation for all responses, and is
5.5% at 9.8 GHz (State 0) and 4.7% at 6.5 GHz (State 15).
IV. NONLINEAR CHARACTERIZATION
The nonlinear analysis of MEMS switches, varactors, and
tunable filters has been presented in [7]. This analysis shows that
IM
the mechanical force acting on the MEMS bridge is proportional
across the bridge. Under high RF drive conditions, the
to
MEMS bridge capacitance variation results in a nonlinear behavior of the tunable filter. In the case of two-tone excitation,
the mechanical force at the beat frequency changes the capacitance of the bridge and the presence of the input tones across
the variable capacitor generates the third-order intermodulation.
Fig. 13 shows the setup to measure the intermodulation components at the output of the tunable filter. Two tones generated
by two synthesizers are combined, and the combined signal is
delivered to the MEMS filter differentially through the baluns
(3-dB couplers) and differential RF probes. The output signals
are measured using a spectrum analyzer.
Fig. 14(a) shows the measured output power for the fundamental and the intermodulation components for several
ENTESARI AND REBEIZ: DIFFERENTIAL 4-BIT 6.5–10-GHz RF MEMS TUNABLE FILTER
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distorted. This filter can, therefore, handle an input power up
to 24 dBm (250 mW). If a higher bias MEMS switch is used
V , the RF power handling will increase to 1 W
before self-biasing becomes an issue.
The maximum power handling of the filter can be well predicted by studying the voltage and current across the MEMS
switch for an input power of 200 mW (Fig. 15). Using a linear
model in Agilent ADS, the rms voltage is calculated to be 12.5 V
, which is the switch with the largest loading MAM
across
]. The corresponding height change in
capacitor [State 0;
the MEMS switch is 0.055 m, and results in a 0.97-fF change
in the switch and a 0.7-fF change in the overall bit-4 capacitance.
This is small enough that it has no effect on the frequency response [see Fig. 14(b)]. In the down-state position, the rms curis 81 mA for
m , and is well within
rent in
the acceptable region [6]. However, the rms voltage across the
is 3.5 V, which is just below the hold-down voltage of
5 V (the switch remains down even if the dc actuation voltage
is removed). It is for these reasons that we predict a 250-mW
power-handling capacity for hot switching (RF is never shut
off).
V. CONCLUSION
Fig. 15. Simulated rms V and I for the input capacitor banks (C , C ). The
values for the output capacitive banks are lower by a factor of two due to the
filter loss.
values of
. The measured
is 45 dBm for
kHz. The measurement is in the up-state position
since this state gives the worse
products. Tunable
filters with diode varactors have much lower values of
(12 dBm in [3] and 28 dBm in [4]). Fig. 14(a) also shows the
intermodulation component versus the difference frequency
for
dBm (no bias voltage
between input tones
on the bridges). The intermodulation component follows the
level drops
mechanical response of the bridge, and the
by 40 dB/decade for
, which is in agreement with
theory [7].
Fig. 14(b) shows the measured insertion loss of the filter for
and dBm).
three different input power levels (
Due to the spectrum analyzer (a noncalibrated system), the
measured insertion loss value is not the same as Fig. 10. The
center frequency is at 9.8 GHz and the bias voltage is zero
]. For
dBm, there is no self-actuation
[State 0;
effect [6], [7], and the filter response does not change with
. For
dBm, the level of
increasing the level of
the RF voltage across the MEMS bridges is large enough to
self-bias the bridges. As a result, the shape of the filter gets
This paper has demonstrated a wide-band tunable filter on
a glass substrate from 6.5 to 9.8 GHz (44% tuning range). A
novel lumped differential topology is used to miniaturize the
filter structure. Resonant capacitor banks with four unit cells
(MEMS capacitive switches in series with high- MAM capacitors) result in 16 different filter responses next to each other
with very fine tuning resolution like a continuous tunable filter.
Matching capacitor banks with three unit cells result in a return
loss better than 16 dB over the whole band. The measured results
are very close to full-wave simulations. The loss of the filter can
be improved by 1–1.6 dB using 10-k sq bias lines or higher
instead of a 1-k sq fabricated SiCr line. We believe that the
lumped capacitor design can be extended to 18 GHz on glass
substrates. Above this frequency, the finite size of the MEMS
bridge results in a large parasitic inductance, which limits the
tuning performance of the 3- or 4-bit capacitors.
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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 includes RF MEMS for microwaves
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 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.