Multi-Domain Modeling: Electrical and Mechanical

Transcription

1 Filename: AET_lab6b ECE535 Smart Sensors and Fuel Cell Laboratory #6b Objectives: Multi-Domain Modeling: Electrical and Mechanical 1. To study Multi-Domain Modeling, using MEMS Accelerometer.. To learn typical sensing converts signal in one domain to another ( Mechanical to Electrical). 3. To learn how to write DAE in each own domain. I. MEMS Accelerometer Structure Sensing is typically performed in two steps: Transform acceleration to mechanical displacement Transform mechanical displacement to electrical signal environmental acceleration Primary Transducer tethered seismic mass mechanical displacement Secondary Transducer capacitive electrical signal

2 Microflexural Structure

3 Mechanical Domain Portion of MEMS Accelerometer Daspot: (D) Model frictional resistance as damping force proportional to rate of movement (velocity) Seismic Mass (M): Model inertia as force proportional to rate of velocity (acceleration) Spring (K): Model structural elasticity as spring force proportional to movement F applied = F mass + F damping + F spring d x dx F(t) = M + D + Kx dt dt Inertia, dissipative, elasticity characteristics determine transient (time domain) and bandwidth (frequency domain) response. F( t) d x dx = G( t) = + ξω 0 + ω0x M dt dt ω = 0 ξ = ω = ω x a 0 1 = ω 0 K M D KM 1 ξ

4 Where: ω 0 ξ ω x/a natural resonant frequency - oscillation with no damping/forcing damping factor actual damping/critical damping damped resonant frequency primary transducer transfer function displacement/unit acceleration Electrical Domain Portion of MEMS Accelerometer Capacitive Sensing Seismic mass forms one plate of a parallel plate capacitance. Movement of mass changes area/gap between parallel plates and, consequently the capacitance. Differential Capacitance Sensing Easier to detect relative (differential) change rather than absolute change Comb finger capacitances connected in parallel to add to form C 1 and C. Sensing requires a bridge circuit with complementary AC source VS.

5 VS V + C1 - + I C1 VX + VS C I = C C1C C1 + C 1sVS = svs V X = V S V C1 = V S I sc1 = V S 1 sc1 C1C C1- C svs = VS C1 + C C1 + C C 1 = C C 1 C => no acceleration => acceleration II. MEMS Simulation Using Simplorer VHDL-AMS Draw the schematic diagram of the mems accelerometer. It consists of three voltage sources and comb_drive, where: env_force1 is the low frequency 100Hz source, emulating earthquake signal. Vsource1, and Vsource are the high frequency 1MHz sources for the capacitor bridge circuit to convert mechanical motion to electrical signal. Comb_drive is the mems vhdl-ams model of the accelerometer. Task1: In LISTING1, the complete VHDL-AMS code has been provided for the3999 voltage sources. For the comb-drive, only the port, generic and quantities are provided. You need to complete the dynamic equations of the comb-drive to complete the code.

6 vsource1 env_force1 ENV_FORCE mag_ac := 0.16e-9*5*9.8 freq := comb_drive1 comb_drive m := 0.16e-9 k :=.6455 d := 4.0e-6 a :=.0e-6*110.0e-6 do := 1.5e-6 VSOURCE mag_ac := 300.0e-3 freq := 1.0 Meg vsource VSOURCE r1 mag_ac := e-3 freq := 1.0Meg Figure 1. MEM accelerometer schematic diagram. r := 3.0Meg LISTING1 LIBRARY IEEE; USE IEEE.ENERGY_SYSTEMS.ALL; USE IEEE.ELECTRICAL_SYSTEMS.ALL; USE IEEE.MECHANICAL_SYSTEMS.ALL; ENTITY comb_drive IS GENERIC(m : MASS := 0.16*nano; d : DAMPING := 4.0e-6; k : STIFFNESS :=.6455; a : REAL :=.0e-6 * 110.0e-6; do : REAL := 1.5e-6); PORT(TERMINAL proof_mass, ref : TRANSLATIONAL; TERMINAL top_el, mid_el, bot_el : ELECTRICAL); END ENTITY comb_drive; ARCHITECTURE bcr OF comb_drive IS --Free quantities QUANTITY vel : VELOCITY; QUANTITY qtm, qbm : CHARGE; QUANTITY dtm, dbm : DISPLACEMENT; QUANTITY ctm, cbm : CAPACITANCE; --branch quantities QUANTITY pos ACROSS force THROUGH proof_mass TO ref; QUANTITY vtm ACROSS itm THROUGH top_el TO mid_el; QUANTITY vbm ACROSS ibm THROUGH bot_el TO mid_el; BEGIN --mechanical dynamics --compute displacement of comb drive

7 Write the mechanical dynamic equation of the following: vel=f(pos) force=f(pos,vel,acc) dtm=f(do, pos) dbm=f(do, pos) where: vel is the velocity of the middle plate acc is the acceleration of the middle plaate dtm is the displacement between the top and middle plate dbm is the displacement between the bottom and middle plate do is the initial displacement of the middle plate pos is the position of the middle plate --electrical dynamics --compute change in capacitance Write the formula of the capacitance between two parallel plates ctm =f(a, epso,dtm) cbm=f(a,epso,dbm) where: a is the area of the capacitor plate epso is the permittivity constant of vacuum energy_systems package ctm is the capacitance between the top and middle plate (C1) cbm is the capacitance between the bottom and middle plate (C) --compute generated current Write the equations of the charge and current of the capacitors qtm =f(ctm, vtm) itm=f(qtm) qbm=f(cbm, vbm) ibm=f(qbm) where: vtm is the applied voltage between the top and middle plate vbm is the applied voltage between the bottom and middle plate qtm is the charge of the top and middle capacitor itm is the current of the top and middle capacitor qbm is the charge of the bottom and middle capacitor ibm is the current of the bottom and middle capacitor END ARCHITECTURE bcr;

8 LIBRARY IEEE; USE IEEE.MATH_REAL.ALL; USE IEEE.MECHANICAL_SYSTEMS.ALL; ENTITY ENV_FORCE IS GENERIC(MAG_AC, MAG_DC : FORCE :=0.0; FREQ : REAL := 0.0); --GENERIC Parameters are CONSTANT, and NO QUANTITY PORT(TERMINAL PT1, PT : TRANSLATIONAL); END ENTITY ENV_FORCE; ARCHITECTURE SINE OF env_force IS QUANTITY FORCE THROUGH PT1 TO PT; BEGIN FORCE == MAG_AC*SIN(MATH PI*FREQ*NOW); END ARCHITECTURE SINE; LIBRARY IEEE; USE IEEE.MATH_REAL.ALL; USE IEEE.ELECTRICAL_SYSTEMS.ALL; ENTITY vsource IS GENERIC(MAG_AC, MAG_DC : VOLTAGE := 0.0; FREQ : REAL := 0.0); PORT (TERMINAL p, m : ELECTRICAL); END ENTITY vsource; ARCHITECTURE sine OF vsource IS QUANTITY v across i THROUGH p TO m; BEGIN v == mag_ac*sin(math PI*freq*NOW)+mag_dc; END ARCHITECTURE sine; Task : Show the output waveforms of env_force1, comb_deive1.dtm, and r1.v are shown in the following three graphs.

9 II. Signal Detection The modulated signal in r1.v can be demodulated by mixing the signal with a local oscillator with the same frequency as the carrier. [A(t)Sin x] Sin y = 0.5A(t)[cos(x-y) cos(x+y)] If x=y [A(t)Sin x] Sin x =0.5A(t)[1-cosx]=0.5A(t)-0.5A(t)cosx A(t) can be recovered by low pass filtering.

10 vsource3 electricalsfg VSOURCE ElectricalSfg vsource1 env_force1 ENV_FORCE mag_ac := 0.16e-9*5*9.8 freq := comb_drive1 comb_drive m := 0.16e-9 k :=.6455 d := 4.0e-6 a :=.0e-6*110.0e-6 do := 1.5e-6 VSOURCE mag_ac := 300.0e-3 freq := 1.0 Meg vsource VSOURCE r1 r := 3.0Meg mag_ac := e-3 freq := 1.0Meg electricalsfg1 ElectricalSfg mul1 Figure. MEM accelerometer with signal recovery schematic diagram. gs1 G(s) Task3: Update the schematic in Figure 1 to that shown in Figure, by adding the following: Vource3 is a voltage whose frequency is selected to demodulate the modulated signal r1.v to its base-band signal, use signal detection theory. Mul1 is multiplier device, which performs the demodulation operation. Gs1 is low pass filter whose transfer function is given G(s)=w/(s+w), where w= πf. NOTE select f to recover the desired signal of env_fource, whose frequency is 100Hz.

11 Task4: Show that the ouput of the low pass,gs1.val, is as shown below: