phase-sensitive demodulation 2006200401 tae-eui, kim
DESCRIPTION
MEDICAL INSTRUMENTATION II. PHASE-SENSITIVE DEMODULATION 2006200401 Tae-eui, Kim. Phase-sensitive Demodulation. ; 10Hz Sinusoid (Tx = 0.1s). ; High Freq. Signal (Tx = 0.02s). X(t). X(t) c(t). X O. 1. 0.1s. 0.05s. 0.1s. 0.05s. -1. -X O. Phase-sensitive Demodulation. - PowerPoint PPT PresentationTRANSCRIPT
PHASE-SENSITIVE DEMODULATION
2006200401 Tae-eui, Kim
( ) sin(2 10 )ox t X t
( ) sin(2 50 )c t t
; 10Hz Sinusoid (Tx = 0.1s)
; High Freq. Signal (Tx = 0.02s)
X(t) X(t) c(t)
XO
-XO
1
-1
0.05s 0.1s 0.05s 0.1s
Phase-sensitive DemodulationPhase-sensitive Demodulation
Phase-sensitive DemodulationPhase-sensitive Demodulation
< MATLAB CODE > < MATLAB PLOT >
( ) sin(2 10 )ox t X t
( ) sin(2 50 )c t t
< MATLAB CODE > < MATLAB PLOT >
Phase-sensitive DemodulationPhase-sensitive Demodulation
< MATLAB CODE > < MATLAB PLOT >
( ) ( )x t c t
Phase-sensitive DemodulationPhase-sensitive Demodulation
With Freq. 50Hz
< MATLAB CODE > < MATLAB PLOT > < MATLAB PLOT WITH HIGH MAGNITUDE >
Phase-sensitive DemodulationPhase-sensitive Demodulation
( ) ( )x t c t With Freq. 1000Hz
( )y t
2( ) ( )x t c t
( ) sin(2 50 )c t t
( )O tLPF
xf 2 cf
Given x(t) c(t) = y(t), find x(t)Phase-sensitive DemodulationPhase-sensitive Demodulation
X LPF
2 2( ) ( ) sin (2 )cx t c t x t f t cos( ) cos cos sin sin
2 2cos(2 ) cos sin 2 21 cos sin 21 cos 2 2sin
2 1sin (1 cos 2 )
2
1( ) 1 cos(2 2 )
2 cx t f t
1 1( ) ( ) cos(2 2 )
2 2 cx t x t f t
1( ) ( )
2O t x t
Phase Demodulation
After LPF
Phase-sensitive DemodulationPhase-sensitive Demodulation
Capacitive Sensor – Problem 9 (a)Capacitive Sensor – Problem 9 (a)
( ) 1 0.2sin(2 )x t ft
60 1HR bpm f Hz
( )( )x o
Lc t
x t
Change of distance
Metal plate
AB
L
25A cm 128.8 10 /o F m
; Capacitive is dependent on changing distance between chest and metal plate
iVoC
xC
oV
A B
4( ) sin(2 10 )iV t t 4.4oC pF
1
1o x o
i x
o
V j C C
V Cj C
o o
i i
V Z
V Z
Capacitive Sensor – Problem 9 (b)Capacitive Sensor – Problem 9 (b)
( ) ( )oo i
x
CV t V t
C
( ) ( ) ( )oo i
o
CV t x t V t
A
Capacitive Sensor – Problem 9 (b)Capacitive Sensor – Problem 9 (b)
( ) ( ) ( )oo i
o
CV t x t V t
A
( )oV t
( )iV t
1( )
2o
o
Cx t
A
LPF
10Hz
Capacitive Sensor – Problem 9 (c)Capacitive Sensor – Problem 9 (c)
X LPF
( )oV t ( ) ( )o iV t V t1
( )2
o
o
Cx t
A
Air
A B C
P1 P2
Atmospheric pressure
X1 X2
Chamber
rigid rigid
Diaphragm
1 1 1 2( )x x P P
2 2 1 2( )x x P P One is increased,The other is decreased At the same amount
How to express by using equation from the sensor in order to analyze it is crucial
11
AC
x 2
2
AC
x
00
AC
x
1 2P P(when )
1 2C C A B C
1C 2CGoal is to measure “ “
1 2P P
Capacitive Sensor – Problem 10 (a)Capacitive Sensor – Problem 10 (a)
Capacitive Sensor – Problem 10 (a)Capacitive Sensor – Problem 10 (a)
A
AC(Capacitor)
C
1C
2C
oC
oCD
sV oV
B
1
1 2c s
CV V
C C
2
1 2
1
1 1c s
j CV V
j C j C
1
2D sV V1
( )2o o sC C V
0s sV V 3( ) sin(2 10 )s sV t V t
i D CV V V
Capacitive Sensor – Problem 10 (a)Capacitive Sensor – Problem 10 (a)
0 1 2
0 1 2 0 1 2
( )1
2( ) ( )
i s
Ax P P
V VA A
x P P x P P
0 1 2
0 1 2 0 1 2
( )1
2 ( ) ( ) s
x P PV
x P P x P P
0 1 2
0
( )1
2 2 s
x P PV
x
1 2( )2 s
o
P P Vx
1
1 2
1
2i s
CV V
C C
Capacitive Sensor – Problem 10 (a)Capacitive Sensor – Problem 10 (a)
31 2( ) sin(2 10 )
2i so
V P P V tx
31 2( )sin(2 10 )
2s
o
VP P t
x
Constant
x High Freq.
Something we would like to measure
Constant
Capacitive Sensor – Problem 10 (b)Capacitive Sensor – Problem 10 (b)
1[ ]sV V
100[ ]ox m
2[ ]m mmHg
31 2( ) ( )sin(2 10 )
2s
io
VV t P P t
x
31 2( ) ( ) ( )sin(2 10 )
2s
o io
VV t GV t G P P t
x
Constant
Unit less
Capacitive Sensor – Problem 10 (c)Capacitive Sensor – Problem 10 (c)
( )oV t
3sin(2 10 )t
1 2
1( )
2 2s
o
VG P P
x
LPF
10Hz