The development and testing of a miniaturized, high-Q, broadly tunable resonator is described. An exemplary device, with a center frequency that is continuously tunable from 1.2 to 2.6 GHz, was tested in detail. Experimental results demonstrated a resonator Q of up to 380, and typical insertion loss of -1.9 dB for a 25 MHz 3-dB bandwidth. These resonators have been used to stabilize a broadly-tunable oscillator with phase noise of -132 dBc/Hz at 100-kHz offset, with a center frequency tunable from 1.2-2.6 GHz, and a tuning speed of 1 GHz/ms

Slocum, Alexander H.

White, Christopher J.

White, James R.

English

Caltech Authors - Main

IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 15, NO. 11, NOVEMBER 2005 793
Octave-Tunable Miniature RF Resonators
James R. White, Christopher J. White, and Alexander H. Slocum
Abstract—The development and testing of a miniaturized,
high- , broadly tunable resonator is described. An exemplary
device, with a center frequency that is continuously tunable
from 1.2 to 2.6 GHz, was tested in detail. Experimental results
demonstrated a resonator of up to 380, and typical insertion
loss of 1.9 dB for a 25 MHz 3-dB bandwidth. These resonators
have been used to stabilize a broadly-tunable oscillator with phase
noise of 132 dBc/Hz at 100-kHz offset, with a center frequency
tunable from 1.2–2.6 GHz, and a tuning speed of 1 GHz/ms.
Index Terms—Microelectromechanical system (MEMS), res-
onators, voltage controllable oscillators (VCOs).
I. INTRODUCTION
TUNABLE radio frequency devices have long relied onnonlinear elements such as ferrites [1], ferroelectrics
[2], or varactors [3] to implement frequency-tuning. A central
weakness of all these approaches is the nonlinearity of the
tuning element, and the resulting performance degradation
such as intermodulation at high power levels. For example, a
700 MHz to 1.33 GHz varactor-tuned filter with 3-dB insertion
loss for a 16% bandwidth was demonstrated by [4], but IP3 in-
termodulation was poor at 17.9 dBm. A ferrite-tuned 4–40 GHz
wide bandwidth filter was demonstrated by [5], however band-
width was not constant over the tuning range and the tuning
current was 1.5 A, indicating a large power requirement, and
the use of tuning magnets suggests a large mass. Magneti-
cally-tuned superconducting filters were demonstrated by [6],
with 10-GHz center frequency, 1% BW, and 13% frequency
tuning, using a superconducting Yttrium barium copper oxide
(YBCO) stripline and very small tuning field to vary the ferrite
magnetization. This filter demonstrates IP3 intermodulation of
approximately 40 dBm but the filter response degrades above
10 dBm input power, a limitation of the superconducting
stripline. A three-pole Ka-band filter [7] made by the EFAB
process demonstrated insertion loss of 1.74 dB at 29 GHz for
a 6-GHz BW, indicating an unloaded resonator of approxi-
mately 50.
A widely promoted alternative to the classical approach is the
use of micromachined variable-capacitive elements [8]. Several
groups have also demonstrated micromachined fixed-frequency
cavities in the mm-wave bands, for example a two-pole band-
pass filter with 3% BW at 12.7 GHz and insertion loss of 1.88 dB
Manuscript received April 4, 2005; revised July 15, 2005. The work was sup-
ported in part by the MIT Deshpande Center for Technological Innovation. The
review of this letter was arranged by Associate Editor M. Mozowski.
J. R. White and A. H. Slocum are with the Massachusetts Institute of Tech-
nology, Cambridge, MA 02139 USA (e-mail: jwhite@mit.edu).
C. J. White is with the California Institute of Technology, Pasadena, CA
91125 USA.
Digital Object Identifier 10.1109/LMWC.2005.859012
Fig. 1. Packaged S-band tunable resonator.
[9]. An electrostatically tuned cavity resonator at mm-wave fre-
quencies was proposed [10] but not reduced to practice. Such
an electrostatically-tuned arrangement would present a limita-
tion on power handling due to pull-in at high radio frequency
(RF) power, and intermodulation due to self-excitation around
the mechanical resonant frequency of the cavity.
Resonators tuned by micromachined capacitive elements
have also often fallen short of required performance metrics
such as immunity to self-excitation and manufacturability,
leading to a dearth of frequency agile MEMS devices in
commercial use [11]. This has prompted the development of
the “Octave ” miniaturized mechanically tunable resonator,
shown in packaged form in Fig. 1. The resonator design was
based on classical precision-mechanism design principles [12],
[13], resulting in a simplified manufacturing process, and
excellent mechanical and electrical performance. The resonator
consists of a copper cavity loaded by a capacitive gap. The
resonator is tuned using a piezo disc to deform the cavity, as
shown in Fig. 1.
II. ELECTRICAL DESIGN
The tunable resonator is a flexible copper re-entrant cavity,
whose physical dimensions are sufficiently small compared to
an electrical wavelength, that there exist identifiable inductive
and capacitive regions. An outer toroidal region with fixed ge-
ometry contains only the magnetic field and is therefore mod-
eled as an inductor. An inner region with opposed parallel plates
with variable separation contains the oscillating electric field
and is modeled as a tunable capacitor. Thus, the device can be
accurately modeled as a tunable parallel-LC circuit for all res-
onant frequencies, as shown in Fig. 2. In the exemplary imple-
mentation described in this letter, the input and output signals
are capacitively coupled into the resonator, and the capacitive
coupling elements vary in concert with the tank capacitance.
1531-1309/$20.00 © 2005 IEEE
794 IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 15, NO. 11, NOVEMBER 2005
Fig. 2. Equivalent circuit model (two port S-band resonator).
III. MECHANICAL DESIGN
A piezoelectric d31-mode bending unimorph actuator was
designed as the tuning element. Piezoelectric actuators offer the
advantage of robustness, high precision and relative simplicity
when compared to, for example, electrostatic or magnetostric-
tive elements. Notwithstanding their advantages, piezoelectric
devices suffer from well known nonlinearities such as hysteresis
and creep that are readily compensated using external feedback
control [14].
The -band tunable resonators are assembled using conduc-
tive epoxy, although solder joints can also be employed. In op-
eration, they are tuned by applying an electric field across a
.004 in thick disk of piezoelectric material bonded with conduc-
tive epoxy1 to the top surface of the .0032 in thick electroformed
copper resonator. A cross section of this arrangement is shown
in Fig. 3. The electroformed parts are plated off a machined and
polished aluminum mandrel, and released in caustic solution.
An earlier resonator design used etched silicon [15].
Finite-element analysis (FEA) was used to predict the static
deflection of the piezoelectric unimorph structure. This anal-
ysis employed a convenient analogy to thermal bimorph struc-
tures, as in [16], where the piezoelectric charge constant is
analogous to the thermal expansion coefficient, and the applied
electric field is analogous to temperature. This technique can be
used to model low frequency actuation. An actuator response of
0.16 m/V was predicted for the fabricated resonator structure,
however the measured results gave a response of .07 m/V. The
large discrepancy has been attributed to the low shear stiffness
of the adhesive layer between the resonator and the piezoelectric
disc. However, the FEA was useful in predicting the optimal di-
mensions of the piezoelectric disks and the optimal wall thick-
ness of the electroformed copper cavity. The initial capacitor
gap was 12.8 m, corresponding to a resonator center frequency
of 2.30 GHz.
IV. DYNAMICS
The dynamic response of the mechanical structure was also
modeled by finite-element methods. The lowest resonant mode
occurs at 5.32 kHz. The static stiffness of the resonator structure
(open-loop piezo) was 7.6 10 N/m. A second-order lumped-
1Epotek H20E, Epotek Inc., Billerica, MA.
Fig. 3. Perspective view of tunable resonator.
parameter model was then constructed to model the resonator’s
sweep rate, settling time and sensitivity to self-excitation
(1)
Here, is the displacement of the parallel-plate capacitor,
is the equivalent lumped-parameter mass, is the nonlinear
damping coefficient, is the stiffness of the actuator (calculated
from the measured resonant frequency), is the permittivity
of free space, is the area of the capacitor, V is the the
slowly-varying envelope of the RF field, since the mechanical
structure acts as a low-pass filter, is the initial capacitor gap,
is the acoustic pressure due to microphonic disturbances,
is the projected area of the resonator, is the measured
response coefficient of the piezoelectric actuator, and V is
the voltage applied to the piezo diaphragm. The damping of the
system is modeled as squeeze-film damping [17]. The damping
coefficient is given by
(2)
where is the separation of the capacitor plates, is the radius
of the capacitor plates, and is the viscosity of air. The damping
force is strongly dependent on the capacitor plate radius and
the gap, thus to reduce the damping force, an array of small
holes was machined into the capacitor plate by excimer laser
machining.
The open-loop step response of the resonator was calculated
using Matlab. The open-loop settling time (in ambient air) was
less than 10 ms for a 10- m displacement (frequency step from
2.5 GHz to 1.5 GHz), and the maximum sweep rate of the device
was 10 m/ms, corresponding to a continuous frequency sweep
rate of 1 GHz/ms.
V. ELECTRICAL TESTING RESULTS
The tunable resonator had a resonant of up to 380 at
2.5 GHz, although this measurement was conservative as it did
not account for the insertion loss of the sub-miniature version A
(SMA) connectors on the input and output ports (approximately
0.1 dB each). Fig. 4 shows measured for a range of tuning
voltages. Out-of-band isolation was better than 30 dB up to
4 GHz.
WHITE et al.: OCTAVE-TUNABLE MINIATURE RF RESONATORS 795
Fig. 4. Typical S responce for two-port S-band resonator, IL <   2.0 dB,
center frequency swept from 1.3 to 2.6 GHz.
Fig. 5. Phase noise of oscillator loaded by two-port resonator.
A typical plot of phase noise versus offset frequency, Fig. 5,
shows phase noise of 132 dBc/Hz at 100-KHz offset, at
2.0 GHz.
The third-order intermodulation was measured to have an IP3
intercept at 41 dBm for a 10-dBm carrier power and 5.3-kHz
offset [18]. For larger frequency offset the IP3 intercept rises to
above 47 dBm (the limit of the sensitivity of the measurement
apparatus). The peak in the intermodulation products at 5.3-kHz
frequency offset is a consequence of the mechanical self-exci-
tation of the device at high power levels. No degradation of the
resonator response was observed at input power levels of up to
37 dBm (the limit of the amplifiers in the test setup), although
heating caused some drift of the resonator center frequency.
VI. CONCLUSION
Microphonics must be addressed for commercial-production
devices, as well as sensitivity to external vibrations and self-ex-
citation at high power. Further work in optimizing the thermal
response of the resonator is also necessary for the device to be
useable in harsh environments. To address these shortcomings,
a feedback controller will be built into the positioning system, in
addition to commercially-available packaging refinements (for
example a hermetic vacuum package) and a more judicious ma-
terials selection to minimize CTE mismatch between the elec-
troformed cavity and the ceramic substrate.
ACKNOWLEDGMENT
The authors wish to thank Dr. D. Ham, Harvard University,
for assistance with the microwave testing.
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