L5%20LEM - Lumped-Element Modeling #! Agenda $! Intro to...

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1 Lecture 5 LEM EEL 5225, Fall 2010, David Arnold Lumped-Element Modeling ! Senturia, Ch. 5, Supplement: “Tilmans papers” " HW5 # Agenda $ Intro to LEM $ Lumped Assumption $ Conjugate Power Variables $ Single-Port Elements $ Circuit Connections $ Two-Port Elements
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2 Lecture 5 LEM EEL 5225, Fall 2010, David Arnold Approach to Transducer Design Ref. Senturia, Pg 19 System Device Physical Process Simulation Verification % Top-down design % System : block diagrams, system partitioning, etc. % Device : macromodels, LEM, “black boxes” % Physical : numerical modeling, finite- element methods % Process : photomasks, layout, microfabrication process modeling % Bottom-up verification
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3 Lecture 5 LEM EEL 5225, Fall 2010, David Arnold % Ideal Macromodel : % % % % % ± oversimplification, but provides physical insight” Macromodels
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4 Lecture 5 LEM EEL 5225, Fall 2010, David Arnold % Capacitive Accelerometer: “multi-energy domain problem” % % % % % Example: Capacitive Accelerometer
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5 Lecture 5 LEM EEL 5225, Fall 2010, David Arnold % Capacitive Accelerometer (continued): % Complex dynamics problem : (haven’t even considered circuitry yet!) % Coupled % Non-linear Need efficient, compact, insightful models % Distributed Physical Laws Continuum? Can it be lumped ? Energy-based models Example: Capacitive Accelerometer
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6 Lecture 5 LEM EEL 5225, Fall 2010, David Arnold % Question : % Given the fundamental equations governing the physical phenomena, how do we generate lumped-element models? 1. Identify energy storage/dissipation mechanisms 2. Establish limits of “lumped” assumption 3. Define ideal elements (single-port elements) 4. Build equivalent single-energy-domain circuits using appropriate connection laws (KCL/KVL) 5. Connect energy domains using appropriate transducer models (two-port elements) Lumped Element Modeling
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7 Lecture 5 LEM EEL 5225, Fall 2010, David Arnold Vent Channel ( 10 μ m x 10 m x 9.5 mm ) Diaphragm ( 1 mm x 1 m ) Bond Pad ( 250 m x 250 m ) Arc Resistor Taper Resistor Oxide± ( 7000 Å ) Nitride ( 1 m ) p+ Silicon ( 1 x 10 20 cm -3 ) Oxide ( 550 Å ) Aluminum ( 1 m ) n-Si Nitride ( 2000 Å ) Ex: Piezoresistive Microphone Ref. Arnold, ASME2001 % Device Structure
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8 Lecture 5 LEM EEL 5225, Fall 2010, David Arnold Ex: Piezoresistive Microphone % Device Model % Assumption: Wavelength much larger than microphone diameter
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9 Lecture 5 LEM EEL 5225, Fall 2010, David Arnold Acousto-mechanical Electrical % Equivalent Circuit Model Ex: Piezoresistive Microphone
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10 Lecture 5 LEM EEL 5225, Fall 2010, David Arnold Ex: Piezoresistive Microphone % Predicted Results Sensitivity: Greatest sensitivity when, Frequency Response:
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11 Lecture 5 LEM EEL 5225, Fall 2010, David Arnold % Question : % What does it mean to be “lumped”? % Lumped Assumption
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This note was uploaded on 01/17/2011 for the course EEL 5225 taught by Professor Arnold during the Fall '08 term at University of Florida.

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L5%20LEM - Lumped-Element Modeling #! Agenda $! Intro to...

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