Overview of PZFlex for MEMs
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PZFLEX APPLICATIONS
• Industries
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NDE
Biomedical
Geophysics
Automotive
Aerospace
Sonar
Oil and gas
Electronics (Filters)
Power generation
Sensors
Industrial Measurement
FBAR displacement @ 2.2 GHz
Sonar transducer displacement @ 2.2 kHz
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OVERVIEW OF PZFLEX
• Why use it?
• What makes it so fast?
• What do we use it for?
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WHY USE FEA?
• Analytical solutions are only valid for specific cases
– Often non-practical
– Ideal constraints
• Real world has arbitrary geometries/materials/loading
– Even simple problems would require complex boundary conditions to
be solved
• FEA ‘breaks’ down differential equations into algebraic expressions
that can be solved numerically
– Ideally suited to modern computers
• Structures can therefore be simulated under arbitrary conditions
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FEA FOR ULTRASOUND
• Wave propagation and piezoelectric materials present unique
challenges to solving via FEA:
– large size, broadband, transient, electro-mechanical
• Ultrasonic problems are often very large due as waves propagate on
the order of 1-250 wavelengths
• Over a single wavelength there are small changes in pressure that
have to be represented
• This requires a reasonable number of elements per wavelength to
accurate capture effects
– > 10 elements per wavelength
– Therefore, a small 3D problem of 10x10x10 wavelengths requires at
least 1 million elements to solve accurately
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WHAT CAN BE SIMULATED?
• 1D, 2D, and 3D structures:
– 2D -Plane Strain
• Assumes effectively infinite model in z-direction (into the page)
– 2D -Axisymmetric
• Assumes 360°rotation around x or y axis (no partial rotations)
– 3D
• Complete model geometry specified with no approximations
• Time domain solver allows all data to be generated in one run
• Concept of ‘virtual experiment’
• Outputs
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Spatial plots of pressure, displacement, velocity, stress etc.
Time histories of the above, and resulting spectra
Electrical impedance, voltage current etc.
Far field extrapolation, TVR, OCV, Directivity
Modal vibration shapes
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3D SAW – Comparison with COMSOL
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2-PORT SAW
• Typical SAW device consists of an input port and an output port
• The phase difference between the signals from these ports depend on the
material properties of the substrate and the gap between the ports
Output port
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Input port
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Piezoelectric
substrate
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MODEL DESCRIPTION
• The model shows a 128 degree YX-cut lithium niobate substrate
– Substrate thickness is set to twice the wavelength for computational efficiency
– This is based on the assumption that surface waves do not penetrate much into
the depth of the substrate
• The Inter-digitated Transducers (IDT) on this two-port SAW device are
modeled as:
– Perfect conductors using boundary conditions
– Assuming the IDTs to be very thin compared to the piezoelectric substrate, the
effect of their mass and stiffness on the dynamics of the device is not accounted
for
• Model is solved for a target frequency of 433 MHz
– Solved for 3 cycles over time
• Rayleigh wave on the surface is visualized
• Voltages at input and output ports are compared
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KEY MODEL FEATURES
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Rayleigh wavespeed = 3996 m/s
Each IDT has 3 electrodes
Electrode length = 5 x Rayleigh wavelength
Gap between ports = 3 x Rayleigh wavelength
Electrode pitch = 1 x Rayleigh wavelength
Electrode width = ¼ x Rayleigh wavelength
Vertical Gap = 5 x Rayleigh wavelength
Horizontal Gap = 5 x Rayleigh wavelength
Substrate thick = 2 x Rayleigh wavelength
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PZFLEX MODEL
• 10 elements per wavelength at centre frequency
• Total number of elements ~ 650,000
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DISPLACEMENT AND VOLTAGE
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COMPUTATIONAL METRICS
Model
Run Time
RAM
Comsol
Model Size
(elements)
~650k
150mins
38GB
PZFlex
~650k
15secs
300MB
x650
x150
Improvement
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Memory: PZFlex uses less than 0.75% of the RAM
Run Time: PZFlex takes less than 0.2% of the runtime
Hardware: 8 cores @ 2.9GHz
With larger/longer problems, these figures will favour PZFlex more
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SUMMARY
• PZFlex is designed and optimised for piezoelectric and wave-propagation
applications
• It offers orders of magnitude improvements in simulations time and memory
requirements over other FEA codes for these problems
• This opens up applications for simulation that are considered too
computationally intensive for FEA
• The rapid simulation times provide clients the opportunity to greatly
accelerate product design cycles in a competitive marketplace
• The combination of PZFlex solvers with cloud computing allows massive
design studies to be executed in parallel and delivered in hours, not months
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