Online proceedings - EDA Publishing Association

11-13
May 2011, Aix-en-Provence, France
102
430
101
100
Simulation
Analytic
425
420
Simulation
Analytic
Curling of this Self-Assembly
electrode is made intentional
Frequency [kHz]
99
98
97
96
Frequency [kHz]
415
410
405
95
400
94
395
93
0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75
V [V] P
(a)
390
0.2 0.4 0.6 0.8 1 1.2 1.4
V [V] P
(b)
)"
3
)'
3
Fig. 12. Self-Assembly beams shows lateral curling
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+,-./012,-34,113567)"8
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!"
!#
+,-./012,-34,113567*#8
*%
*'
!#
!*
#"
!"
##
A B
C"D%#A
A B
C"D*A
!%
!'
A B
C)D$A
A B
C)D#A
Narrow 200
nm gap
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90/:;/-?@8
(c)
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90/:;/-?@8
Fig. 14. Frequency tune range and AC plot for the PPTF and CC resonator
The simulated range of the frequency tuning is shown in
fig. 14 a) and b) while fig. 14 c) and d) show the transfer
function characteristics for the PPTF and CC resonator
respectively. A larger VP results in a reduced resonator loss,
thus reducing the impedance rz that the resonator represents
at the resonance frequency.
(d)
A
Fig. 13. Clamped-clamped beam with Self-Assembly beam
Table III describes the dimensions, parameters and results
of these two soft-tunable MEMS resonators. The PPTF
occupies more space and has less tunability compared to the
CC-beam, however the electromechanical coupling
coefficient is better and the input and output electrode is
clearly separated from each other.
TABLE III
Resonator dimensions and results
PPTF CC
Resonator dimensions
Resonator length, LR [!m]
Resonator width, WR [!m]
LFRAME=100
LCANTILEVER=50
WFRAME=2
WCANTILEVER=1
100
Electrode length, WE [!m] 100 100
Resonator-to-electrode gap, g [nm] 200 200
Resonator results
Nominal resonance frequency [kHz] 102.84 424.73
Frequency tuning range [kHz] 7.12 27.35
Tunability in percentage [%] 6.92 6.43
Effective beam stiffness [N/m] 4.30 4.74
Electromechanical coupling [nN/V] 55.34 35.24
1
x(t)
B FDSM y[n]
V CLK
R
V P
Fig. 15. System overview of resonator in an oscillator loop and with a FDSM
The MEMS resonator is put in a feedback loop with an
amplifier to make it oscillate naturally, shown in fig. 15. The
output of the oscillator is buffered to digital logic levels. A
Frequency Delta Sigma Modulator (FDSM) [12] was
included on-chip in order to show CMOS circuit
compatibility with the MEMS etch, and to demonstrate
CMOS and MEMS interoperability. The FDSM is a
frequency to digital converter, used here to generate a
quantized digital bitstream output from the MEMS oscillator
signal. This bitstream can be post processed offline to
recover the spectral contents of the oscillator output. The
FDSM was designed to operate with sampling frequencies
up to 20 MHz. The amplifier A in the oscillator loop consists
of a common-source amplifier set up in a Pierce amplifier
configuration with a loop gain of more than one in order to
initiate and sustain oscillation.
The clamped-clamped resonator is quite soft and has a
tuning-range of slightly more than 20 kHz using VP from
0.4 V to 1.4 V. For the PPTF resonator, the tuning range
would be from 0.3 V to 0.75 V with a 7 kHz tuning range.
120