simulating rf mems - cornell universitybindel/present/2004-03-bascd.pdf · ink jet printers, biolab...
TRANSCRIPT
Simulating RF MEMSDavid Bindel
UC Berkeley, CS Division
Simulating RF MEMS – p.1/21
Collaborators
Faculty Grad students
A. Agogino (ME) D. Bindel (CS)
Z. Bai (Math/CS) J.V. Clark (AS&T)
J. Demmel (Math/CS) D. Garmire (CS)
S. Govindjee (CEE) T. Koyama (CEE)
R. Howe (EE) R. Kamalian (ME)
J. Nie (Math)
S. Bhave (EE)
Simulating RF MEMS – p.2/21
MEMS Basics
Micro-electro-mechanical systemsChemical, fluid, thermal, optical (MECFTOMS?)
Applications:Sensors (inertial, chemical, pressure)Ink jet printers, biolab chipsRF devices
Use IC fabrication technology
Large surface area / volume ratio
Still mostly classical (vs. nanosystems)
Simulating RF MEMS – p.3/21
SUGAR
Goal: “Be SPICE to the MEMS world”
Fast enough for early design stages
Simple enough to attract users
Support design, analysis, optimization, synthesis
Verify models by comparison to measurement
System assembly
Models
Solvers
Matlab Web Library
Sensitivity analysis
Static analysis
Steady−state analysis
Transient analysis
Results
Netlist
Interfaces
Simulating RF MEMS – p.4/21
SUGAR: Analysis of a micromirror
(Mirror design by M. Last)
Simulating RF MEMS – p.5/21
SUGAR: Design synthesis
Simulating RF MEMS – p.6/21
SUGAR: Comparison to measurement
Simulating RF MEMS – p.7/21
Why RF resonators?
Microguitars from Cornell University (1997 and 2003)
Frequency references
Sensing elements
Filter elements
Neural networks
Really high-pitch guitars
Simulating RF MEMS – p.8/21
Micromechanical filters
Mechanical filter
Capacitive senseCapacitive drive
Radio signal
Filtered signal
Mechanical high-frequency (high MHz-GHz) filter
Saves power and cost over electronic filters
Advantage over piezo-actuated quartz SAW filtersIntegrated into chipLow power
Simulating RF MEMS – p.9/21
Governing equations
Time domain:
Mu′′ + Cu′ + Ku = Pφ
y = V T u
Frequency domain:
H(ω) = V T (−ω2M + iωC + K)−1P
y = Hφ
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.510
−4
10−2
100
102
104
106
108
Simulating RF MEMS – p.10/21
First proposed design: Checkerboard
� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �� � � � � � � � � � � � � � �
� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �� � � � � � � � � � � � � �
����
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� �� �� �� ����
�
� � � �� �
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� �� � � �� �� �� �� ����
�� �� �� �� �
D+
D−
D+
D−
S+ S+
S−
S−
Array of loosely coupled resonators
Anchored at outside corners
Excited at northwest corner
Sensed at southeast corner
Surfaces move only a few nanometers
Simulating RF MEMS – p.11/21
Design questions
−8 −6 −4 −2 0 2 4 6 8
x 10−5
−8
−6
−4
−2
0
2
4
6
8x 10−5
−8 −6 −4 −2 0 2 4 6 8
x 10−5
−8
−6
−4
−2
0
2
4
6
8x 10−5
Where should drive and sense be placed?
How should the individual resonators be connected?
How should the system be anchored?
How many components? What topology?
Simulating RF MEMS – p.12/21
Checkerboard response
95 MHz 100 MHz
Simulating RF MEMS – p.13/21
Checkerboard response
0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2
x 108
−550
−500
−450
−400
−350
−300
−250
Hz
dB
Corner−connected response
0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2
x 108
−550
−500
−450
−400
−350
−300
Hz
dB
Beam−connected response
Corner-connected details Beam-connected details
Simulating RF MEMS – p.14/21
Current questions
How do we model damping?
How do we compute frequency response quickly?
How do we track dependence on geometry?
How do we optimize designs?
Simulating RF MEMS – p.15/21
Energy loss and Q
Goal: strong output signal and high Q
Challenge: Model details of energy lossAnchor lossThermoelastic dampingAkheiser dampingAir damping
How are losses affected by fabrication errors (e.g.anchor misalignment)?
Simulating RF MEMS – p.16/21
Model reduction
Sun Ultra 10Sec n
ROM: 28 4834Full: 1474 50
Project onto an unusual Krylov subspace
Preserve second order system structure
Plan to use substructuring
Simulating RF MEMS – p.17/21
Mode tracking: Shear ring resonator
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9hw = 5.000000e−05
Value = 2.66E+07 Hz.
Ring is driven in a shearing motion
Can couple ring to other resonators
How do we track the desired mode?
Simulating RF MEMS – p.18/21
Mode tracking: Results
2 2.5 3 3.5 4 4.5 5 5.5 6
x 10−5
2.5
3
3.5
4
4.5
5
5.5x 107
Half width of annulus
Fre
quen
cy (
Hz)
Finite elementAnalytic result
Predictor-corrector iteration
Convergence criteria, step control based on|q(sk)
T q(sk+1)|
Simulating RF MEMS – p.19/21
Transfer function optimization
Choose geometry to make a good bandpass filter
What is a “good bandpass filter?”|H(ω)| is big on [ωl, ωr]
|H(ω)| is tiny outside this interval
How do we optimize?Overton’s gradient sampling methodUse Byers-Boyd-Balikrishnan algorithm for distanceto instability to minimize |H(ω)| on [ωl, ωr]
Small Hamiltonian eigenproblem (with ROM)
Simulating RF MEMS – p.20/21
Conclusions
RF MEMS are an interesting source of problemsUnderstanding the physicsApplying numerical tools
http://bsac.berkeley.edu/cadtools/sugar/sugar/
http://www.cs.berkeley.edu/∼dbindel/feapmex.html
Simulating RF MEMS – p.21/21