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MEMS Accelerometer with Sigma-Delta control loop
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-- VHDL-AMS model of MEMS accelerometer
with Sigma-Delta control loop
-- (c) Southampton
University 2009
-- Southampton VHDL-AMS Validation Suite
-- author:
Chenxu Zhao and
Tom J Kazmierski
-- School of Electronics and Computer
Science, University of Southampton
-- Highfield, Southampton SO17 1BJ,
United Kingdom
-- Tel. +44 2380 593520 Fax +44
2380 592901
-- e-mail: cz05r@ecs.soton.ac.uk, tjk@ecs.soton.ac.uk
-- Created: 03 April 2009
-- Last revised:
03 April 2009 (by Chenxu Zhao)
-- Description
-- This is a distributed
model for MEMS sensing element. The model includes
-- sense finger dynamics which allow accurate performance prediction of a MEMS
-- accelerometer in a Sigma-Delta
control loop
--------------------------------------------------------------------------------
1. VHDL-AMS Model of
mechanical sensing element
library IEEE;
use IEEE.ENERGY_SYSTEMS.all;
use IEEE.ELECTRICAL_SYSTEMS.all;
use IEEE.MECHANICAL_SYSTEMS.all;
use IEEE.MATH_REAL.all;
entity COMB_DRIVE is
generic(
N1: real :=50.0;
--Number of sense fingers
N : real :=5.0;
--Number of sections
L : real :=1.50e-4;
--Finger length
E: real :=1.3e+11;
--Young's modulus
I: real:=0.17e-24;
--Moment of inertia
rou: real:=2330.0;
--Density
d0: real:=1.5e-6;
--Initial gap
K: STIFFNESS:=100.0;--Spring
stiffness
D:DAMPING:=0.005;
--Damping constant
S:real:= 2.0e-6*1.0e-6;
--Cross section area
C: real:=0.01e-20;
--Internal damping modulus of finger
M:MASS:=3.0e-7
--Mass
);
port(
terminal
PROOF_MASS,PROOF_MASS1,PROOF_MASS2,PROOF_MASS3: TRANSLATIONAL;
terminal PROOF_MASS4,PROOF_MASS5, REF : TRANSLATIONAL;
terminal MID_EL : ELECTRICAL
);
end entity COMB_DRIVE;
architecture BCR of COMB_DRIVE is
quantity FE1,FE2,FE3,FE4:REAL;
--Electrostatic force
quantity Y: REAL;
--Average position of sense fingers
quantity dx: REAL;
--Length of each section
quantity A:REAL;
--Area of each section
quantity VM across IM
through MID_EL to electrical_ref;
quantity x across F0 through PROOF_MASS to
REF;
quantity y0 across F through PROOF_MASS1 to
REF;
quantity y1 across F1 through PROOF_MASS2 to
REF;
quantity y2 across F2 through PROOF_MASS3 to
REF;
quantity y3 across F3 through PROOF_MASS4 to
REF;
quantity y4 across F4 through PROOF_MASS5 to
REF;
begin
dx==L/N;
A== 2.0e-6*L/N;
--Electrostatic forces along the finger--
FE1==0.5*8.85e-12*A* ( 9.0 /((d0-y1)**2)-9.0/((d0+y1)**2));
FE2==0.5*8.85e-12*A* ( 9.0 /((d0-y2)**2)-9.0/((d0+y2)**2));
FE3==0.5*8.85e-12*A* ( 9.0 /((d0-y3)**2)-9.0/((d0+y3)**2));
FE4==0.5*8.85e-12*A* ( 9.0 /((d0-y4)**2)-9.0/((d0+y4)**2));
-- Sense finger is diveded into 5 segments--
E*I*(Y3-4.0*Y2+6.0*Y1-3.0*Y0)/dx**4+ROU*S*Y1'DOT'DOT+C*(Y3'DOT-
4.0*Y2'DOT+6.0*Y1'DOT-3.0*Y0'DOT)/dx**4==(F1+FE1)/dx;
E*I*(Y4-4.0*Y3+6.0*Y2-4.0*Y1+Y0)/dx**4+ROU*S*Y2'DOT'DOT+C*(Y4'DOT-
4.0*Y3'DOT+6.0*Y2'DOT-4.0*Y1'DOT+Y0'DOT)/dx**4==(F2+FE2)/dx;
E*I*(-2.0*Y4+5.0*Y3-4.0*Y2+Y1)/dx**4+ROU*S*Y3'DOT'DOT+C*(-
2.0*Y4'DOT+5.0*Y3'DOT-4.0*Y2'DOT+Y1'DOT)/dx**4==(F3+FE3)/dx;
E*I*(Y4-2.0*Y3+Y2)/dx**4+ROU*S*Y4'DOT'DOT+C*(Y4'DOT-2.0*Y3'DOT+Y2'DOT)
/dx**4==(F4+FE4)/dx;
--Structural mass motion equation--
M*X'DOT'DOT+D*X'DOT+K*X==F0;
y0==X;
Y==(Y1+Y2+Y3+Y4+Y0)/5.0;
VM==N1*Y/D0;
end architecture BCR;
--------------------------------------------------------------------------------
2. Compensator
library IEEE;
use IEEE.math_real.all;
use IEEE.electrical_systems.all;
entity compensator is
generic (
K : real := 4.0; -- gain
Fp : real := 2.0e+4; -- pole frequency
Fz : real := 1000.0 -- zero frequency
);
port (terminal input, output : electrical);
end entity compensator;
architecture behavioral of compensator is
quantity vin across input to electrical_ref;
quantity vout across output to electrical_ref;
constant num : real_vector := (Fz, 1.0);
constant den : real_vector := (Fp, 1.0);
begin
vout == K * vin'ltf(num, den);
end architecture behavioral;
--------------------------------------------------------------------------------
3. Quantizer
LIBRARY IEEE;
USE IEEE.MATH_REAL.ALL;
USE IEEE.STD_LOGIC_1164.ALL;
USE IEEE.ELECTRICAL_SYSTEMS.ALL;
ENTITY quantizer IS
GENERIC(threshod : REAL := 0.0);
PORT(
SIGNAL clk : IN STD_LOGIC;
TERMINAL ip : ELECTRICAL; --input analog signal
SIGNAL op : OUT STD_LOGIC); --output digital signal
END ENTITY quantizer;
ARCHITECTURE bhv OF quantizer IS
QUANTITY vip ACROSS ip;
BEGIN
PROCESS(clk)
BEGIN
IF(rising_edge(clk)) THEN
IF vip>threshod THEN
op <= '1';
ELSE
op <= '0';
END IF;
END IF;
END PROCESS;
END ARCHITECTURE bhv;
--------------------------------------------------------------------------------
4. DAC
LIBRARY IEEE;
USE IEEE.MATH_REAL.ALL;
USE IEEE.STD_LOGIC_1164.ALL;USE IEEE.ELECTRICAL_SYSTEMS.ALL;
use IEEE.MECHANICAL_SYSTEMS.all;
ENTITY DAC IS
PORT(SIGNAL ip : IN STD_LOGIC; -- input digital signal
QUANTITY fin: force;
TERMINAL op1: TRANSLATIONAL); -- output analog signal
END ENTITY DAC;
ARCHITECTURE bhv OF DAC IS
SIGNAL Fe : force := 0.0;
QUANTITY F through op1;
BEGIN
Fe<=35.0E-6 WHEN ip <= '0' ELSE -35.0E-6;
F==-Fe+fin;
END ARCHITECTURE bhv;
--------------------------------------------------------------------------------
5. Top level
library IEEE;
use IEEE.ELECTRICAL_SYSTEMS.all;
use IEEE.MECHANICAL_SYSTEMS.all;
use IEEE.MATH_REAL.all;
use IEEE.STD_LOGIC_1164.all;
entity ACCELEROMETER is
PORT( SIGNAL clk : IN STD_LOGIC;
quantity f :IN force);
end entity ACCELEROMETER;
architecture TOP_LEVEL of ACCELEROMETER is
terminal SMASS,SMASS1,SMASS2,SMASS3,SMASS4,SMASS5: TRANSLATIONAL;
terminal MID,como: ELECTRICAL;
signal output: std_logic;
begin
A1:entity WORK.COMB_DRIVE
port map (
PROOF_MASS => SMASS,
PROOF_MASS1 => SMASS1,
PROOF_MASS2 => SMASS2,
PROOF_MASS3 => SMASS3,
PROOF_MASS4 => SMASS4,
PROOF_MASS5 => SMASS5,
REF => TRANSLATIONAL_ref,
MID_EL => MID);
COM: entity compensator
port map(input => MID, output => como);
Q : entity quantizer
generic map(threshod => 0.0)
port map(clk => clk,ip => como, op => output);
DAC2: entity WORK.DAC(bhv)
port map (ip=>output,fin=>f, op1=>smass);
end architecture TOP_LEVEL;
--------------------------------------------------------------------------------
6. Testbench
library IEEE;
use IEEE.math_real.all;
use IEEE.std_logic_1164.all;
use IEEE.ENERGY_SYSTEMS.all;
use IEEE.ELECTRICAL_SYSTEMS.all;
use IEEE.MECHANICAL_SYSTEMS.all;
entity test is
end entity test;
architecture bhv of test is
signal clk : std_logic;
quantity f: force;
begin
acc : entity ACCELEROMETER(top_level)
port map(clk =>clk,f=>f);
process
begin
clk <= '1';
wait for 0.5us;
clk <= '0';
wait for 0.5us;
end process;
f==-3.0E-7*10.0*9.8*sin(MATH_2_PI*1000.0*NOW); --Input sine wave force
end architecture bhv;
--------------------------------------------------------------------------------
3. Simulation Results
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