Transcript Figure 1.1 Generalized instrumentation system The sensor

Control
And
feedback
Power
source
Sensor
Measurand
Primary
Sensing
element
Calibration
signal
Variable
Conversion
element
Signal
processing
Output
display
Data
storage
Data
transmission
Perceptible
output
Radiation,
electric current,
or other applied
energy
Figure 1.1 Generalized instrumentation system The sensor converts energy or information
from the measurand to another form (usually electric). This signal is the processed and
displayed so that humans can perceive the information. Elements and connections shown by
dashed lines are optional for some applications.
© From J. G. Webster (ed.), Medical instrumentation: application and design. 3rd ed. New York: John Wiley & Sons, 1998.
Electrodes
vecg
Z1
Z2
Zbody
+Vcc
60-Hz
ac magnetic
field
+
Differential
amplifier
-
Displacement
currents
vo
-Vcc
Figure 1.2 Simplified electrocardiographic recording system Two possible interfering
inputs are stray magnetic fields and capacitively coupled noise. Orientation of patient cables
and changes in electrode-skin impedance are two possible modifying inputs. Z1 and Z2
represent the electrode-skin interface impedances.
© From J. G. Webster (ed.), Medical instrumentation: application and design. 3rd ed. New York: John Wiley & Sons, 1998.
(xd – Hfy)Gd = y
(1.1)
xdGd = y(1 + HfGd)
(1.2)
Gd
xd
1  H h Gd
(1.3)
y
X 
X
(1.4)
i
n
GM  n X 1 X 2 X 3    X n
s
 X
i
-X
(1.5)

2
(1.6)
n -1
 s
CV   100%
X
r
 X
 X
i
i
(1.7)

- X Yi - Y
-X

  Y - Y 
2
(1.8)
2
i
© From J. G. Webster (ed.), Medical instrumentation: application and design. 3rd ed. New York: John Wiley & Sons, 1998.
Characteristic with zero and sensitivity drift
Total error due to drift
y (Output)
y (Output)
D x'd
+ Sensitivity
drift
D y'
-
Dy
Intercept b
Slope m =
Dxd
Dy
Dxd
+ Zero
drift
Zero drift
-
Sensitivity drift
y = mxd + b
xd (Input)
(a)
xd (Input)
(b)
Figure 1.3 (a) Static-sensitivity curve that relates desired input xd to output y. Static sensitivity
may be constant for only a limited range of inputs. (b) Static sensitivity: zero drift and sensitivity
drift. Dotted lines indicate that zero drift and sensitivity drift can be negative. [Part (b) modified
from Measurement Systems: Application and Design, by E. O. Doebelin. Copyright  1990 by
McGraw-Hill, Inc. Used with permission of McGraw-Hill Book Co.]
© From J. G. Webster (ed.), Medical instrumentation: application and design. 3rd ed. New York: John Wiley & Sons, 1998.
m
b
n xd y -  xd  y 
(1.9)
n xd2 -  xd 
2
 y  x  -  x y  x 
n x -  x 
2
d
d
2
d
d
2
(1.10)
d
y  mxd  b
(1.11)
© From J. G. Webster (ed.), Medical instrumentation: application and design. 3rd ed. New York: John Wiley & Sons, 1998.
x1
Linear
system
y1
(x1 + y2)
and
x2
Linear
system
(y1 + y2)
Linear
system
and
y2
Kx1
Ky1
Linear
system
(a)
Figure 1.4 (a) Basic definition of linearity
for a system or element. The same linear
system or element is shown four times for
different inputs. (b) A graphical illustration
of independent nonlinearity equals A% of
the reading, or B% of full scale, whichever
is greater (that is, whichever permits the
larger error). [Part (b) modified from
Measurement Systems: Application and
Design, by E. O. Doebelin. Copyright 
1990 by McGraw-Hill, Inc. Used with
permission of McGraw-Hill Book Co.]
Least-squares
straight line
y (Output)
B% of full scale
A% of reading
Overall tolerance band
xd (Input)
Point at which
A% of reading = B% of full scale
(b)
© From J. G. Webster (ed.), Medical instrumentation: application and design. 3rd ed. New York: John Wiley & Sons, 1998.
Zx 
X d1 effort var
iable

X d2
flow variable
P  X d1  X d2 
an
X d12
 Z x X d22
Zx
(1.13)
dny
dy
d mx
dx





a

a
y
(
t
)

b
     b1
 b0 x(t )
1
0
m
n
m
dt
dt
dt
dt
a D
n
(1.12)
n



     a1 D  a0 y(t )  bm D m      b1 D  b0 x(t )
y( D) bm D m      b1 D  b0

x( D) an D n      a1 D  a0
Y ( jω) bm ( jω) m      b1 ( jω)  b0

X ( jω) an ( jω) n      a1 ( jω)  a0
(1.14)
(1.15)
(1.16)
(1.17)
© From J. G. Webster (ed.), Medical instrumentation: application and design. 3rd ed. New York: John Wiley & Sons, 1998.
Figure 1.5 (a) A linear
potentiometer, an example
of a zero-order system. (b)
Linear static characteristic
for this system. (c) Step
response is proportional to
input. (d) Sinusoidal
frequency response is
constant with zero phase
shift.
© From J. G. Webster (ed.), Medical instrumentation: application and design. 3rd ed. New York: John Wiley & Sons, 1998.
a0 y(t )  b0 x(t )
(1.18)
y( D) Y ( jω) b0


 K  staticsensitivity
x( D) X ( j ) a0
(1.19)
© From J. G. Webster (ed.), Medical instrumentation: application and design. 3rd ed. New York: John Wiley & Sons, 1998.
Output y(t)
R
+
+
C
x(t)
Figure 1.6 (a) A low-pass RC
filter, an example of a firstorder instrument. (b) Static
sensitivity for constant inputs.
(c) Step response for larger
time constants (L) and small
time constants (S). (d)
Sinusoidal frequency response
for large and small time
constants.
Slope = K = 1
y(t)
-
-
Input x(t)
(a)
(b)
Log
scale
x(t)
1
Y (jw
X (jw
1.0
0.707
y(t)
S
L
t
(c)
wL
Log scale w
(d)
f
y(t)
0°
1
0.63
- 45°
S
wS
L
L
S
-90°
t
© From J. G. Webster (ed.), Medical instrumentation: application and design. 3rd ed. New York: John Wiley & Sons, 1998.
Log scale w
a1
dy (t )
 a 0 y (t )  b0 x(t )
dt
τD  1y(t )  Kx(t )
y ( D)
K

x( D) 1  τ D

(1.21)
(1.22)
Y  jω
K
K


X  jω 1  jωτ
1  ω2 τ 2
f  arctan- ωτ/1
yt   K 1 - e -t / 
(1.20)

(1.23)
(1.24)
© From J. G. Webster (ed.), Medical instrumentation: application and design. 3rd ed. New York: John Wiley & Sons, 1998.
Figure 1.7 (a) Force-measuring
spring scale, an example of a
second-order instrument. (b)
Static sensitivity. (c) Step
response for overdamped case
 = 2, critically damped case
 = 1, underdamped case  = 0.5.
(d) Sinusoidal steady-state
frequency response,  = 2,  = 1,
 = 0.5. [Part (a) modified from
Measurement Systems:
Application and Design, by E. O.
Doebelin. Copyright  1990 by
McGraw-Hill, Inc. Used with
permission of McGraw-Hill
Book Co.]
Output
displacement
0
y(t)
Input
Force x(t)
Output y(t)
Slope K =
(a)
1
Ks
Input x(t)
(b)
Y (jw
Log
scale X (jw
K
2
x(t)
1
(d)
y(t)
yn
0.5
1
Log scale w
wn
t
(c)
Resonance
f
wn
Log scale w
0°
yn + 1
0.5
2
1
Ks
1
-90°
1
2
0.5
t
-180°
© From J. G. Webster (ed.), Medical instrumentation: application and design. 3rd ed. New York: John Wiley & Sons, 1998.
a2
d 2 y t 
dyt 
 a1
 a0 yt   b0 xt 
2
dt
dt
(1.25)
 D 2 2ζD 
 1 y t   Kx t 
 2 
ω
ω
n
 n

(1.26)
where
K
ωn 
ζ
b0
 staticsensitivity, output units defined by input units
a0
a0
 undampednaturalfrequency,rad/s
a2
a1
2 a0 a 2
 dampingratio,dimensionless
y D 
K
 2
x D  D
2ζD

1
2
ωn
ωn
Y  jω
K


2
X  jω  jω / ωn   2ζjω / ωn   1
(1.27)
K
1 - ω / ω    4ζ
2 2
n
2
ω 2 / ωn2
(1.28)
2ζ
ω / ω n - ωn / ω
f  arctan
© From J. G. Webster (ed.), Medical instrumentation: application and design. 3rd ed. New York: John Wiley & Sons, 1998.
xt  - B
dyt 
d 2 yt 
- K s yt   M
dt
dt 2
(1.29)
(1.30)
K  1/ K s
ωn 
Ks
M
ζ 
B
(1.31)
(1.32)
2 KmM
Overdamped,
ζ  1:
y t   -
ζ  ζ 2 -1
2 ζ 2 -1
 - ζ  ζ 2 -1  ω t
 n
Ke 

ζ - ζ 2 -1
2 ζ 2 -1
 - ζ - ζ 2 -1  ω t
 n
- Ke 
K
(1.33)
Critically damped,
ζ  1:
yt   -1  ωn t Ke -ωnt  K
(1.34)
Underdamped,
ζ  1:
y t   -
e - ζω nt
1- ζ 2


K sin 1 - ζ 2 ωn t  f  K
(1.35)
f  arcsin 1 - ζ 2
© From J. G. Webster (ed.), Medical instrumentation: application and design. 3rd ed. New York: John Wiley & Sons, 1998.
t n1 
7π / 2 - f
ωn 1 - ζ 2
tn 
and
3π / 2 - f
ωn 1 - ζ 2




 exp- ζω  3π / 2 - f    
n
2

 ωn 1 - ζ   




 7π / 2 - f    
K 
exp- ζω n 


 ωn 1 - ζ 2   
1 - ζ 2 

(1.36)
 K

 1- ζ 2

yn

y n 1 



(1.37)
 2πζ 

 exp
 1- ζ 2 


 y 
2πζ
ln n    
1- ζ 2
 y n 1 
ζ 

(1.38)
4π 2  2
yt   Kxt - τ d ,
Y  jω
 Ke - jωωd
X  jω
t  τd
(1.39)
(1.40)
© From J. G. Webster (ed.), Medical instrumentation: application and design. 3rd ed. New York: John Wiley & Sons, 1998.
Figure 1.8 Design process for medical
instruments Choice and design of
instruments are affected by signal
factors, and also by environmental,
medical, and economic factors.
(Revised from Transducers for
Biomedical Measurements: Application
and Design, by R. S. C. Cobbold.
Copyright  1974, John Wiley and
Sons, Inc. Used by permission of John
Wiley and Sons, Inc.)
© From J. G. Webster (ed.), Medical instrumentation: application and design. 3rd ed. New York: John Wiley & Sons, 1998.
© From J. G. Webster (ed.), Medical instrumentation: application and design. 3rd ed. New York: John Wiley & Sons, 1998.