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Medical Instrument
Dynamic Characteristics & Biopotential
Group 3 : 김제선
김준범
김현준
김한울(1등)
노재선
Medical Instrumentation
Contents
1
2
Transient response
Steady state response
3
Distortionless Mearsurment
4
Biopotential
Medical Instrumentation
Dynamic Characteristic
Time dependency
 Most medical instruments must process
signals that are functions of time. It is this
time-varying property of medical signals
that requires us to consider dynamic
instrument characteristics.
Medical Instrumentation
Transient response
CASE1
Step Response
x(t)
H
y(t)
The transfer function for a linear instrument or system expresses the relationship
Between the input signal and the output signal mathematically.
Medical Instrumentation
Transient response
System behavior
Dependence of the system behavior on the
value of the damping ratio ζ, for underdamped, critically-damped ,over-damped, and
undamped cases, for zero-velocity initial
condition. The behavior of the system depends
on the relative values of the two fundamental
parameters, the natural requency ω0 and the
damping ratio ζ. In particular, the qualitative
behavior of the system depends crucially on
whether the quadratic equation for γ has one
real solution, two real solutions, or two
complex conjugate solutions.
Medical Instrumentation
Dynamic Characteristic
Critical damping (ζ = 1)
When ζ = 1, there is a double root γ (defined above), which is real. The
system is said to be critically damped. A critically damped system converges
to zero faster than any other, and without oscillating.
Medical Instrumentation
Transient response
Over-damping (ζ > 1)
When ζ > 1, the system is over-damped and there are two different real roots. An
over-damped door-closer will take longer to close than a critically damped door
would.
Medical Instrumentation
Transient response
Under-damping (0 ≤ ζ < 1)
Finally, when 0 ≤ ζ < 1, γ is complex, and the system is under-damped. In this
situation, the system will oscillate at the natural damped frequency ωd, which is a
function of the natural frequency and the damping ratio.
Medical Instrumentation
Transient response
Under-Damping
ζ <1
Critical-Damping
ζ =1
Over-Damping
ζ >1
Medical Instrumentation
Dynamic Characteristic
System
First-order system
Second-order system
Exponential
Time constant
Natural frequency
Under-damping
Critical-damping
Over-damping
Medical Instrumentation
Dynamic Characteristic
x
x
y
3차
1차
*인수분해에 의해서 3차는 1차, 2차로 표현 가능
2차
y
Medical Instrumentation
Steady state response
CASE2
Sinusoidal Steady State Frequency Response
System
Medical Instrumentation
Steady state response
Linear system(Principal of superposition)
Linear
System
Linear combination
Set of all x(t) is X,
Basis of X =
x(t) is a linear combination-dependent frequency
Medical Instrumentation
Steady state response
Impulse response
Convolution - LTI(Linear time invariant)
Fourier Transform
Frequency transfer function
Amplitude response
Phase response
Medical Instrumentation
Steady state response
Review
Euler’s law
Medical Instrumentation
Steady state response
Example
Medical Instrumentation
Steady state response
|H|
ω
ω
H(jw
)
각각의 주파수에 대한 출력을 알고 있으므로 입력의 합에 대한 결과 역시 알 수 있다.
(Superposition)
Medical Instrumentation
Steady state response
Input
output
주파수는 같고 크기와 위상만 달라짐
[주파수에 따라 출력의 모양이 달라진다.
]
Medical Instrumentation
Distortionless Measurment
Time delay
System
Instrument elements that give an output that is exactly the same as the input,
Except that is delayed in time by
, are defined as time-delay elements.
Medical Instrumentation
Distortionless Measurment
transposition
|H|
A
Flat amplitude response
ω
ω
Linear phase response
Medical Instrumentation
Distortionless Measurment
Example
X(t)
H*(jw
)
Y(t)
“Phase = Frequency X Time”
Medical Instrumentation
Example of distortion(amplitude)
+
X(t)
Medical Instrumentation
Example of distortion(phase)
Medical Instrumentation
Example of distortion
입력의 주파수 범위가 w1에서 w2일때 무왜곡을 측정하기 위한 H(jw)?
ω1
ω2
ω
ω1
ω2
Non-causal
존재할 수 없다
빛의 속도보다 빠르면 존재
ω
Medical Instrumentation
Biopotential
Insulating Membrane
V
Insulating membrane
Voltage is zero.
Na+
ClNeutral(1%)
Na+
Cl-
Neutral(10%)
*Half-cell potential is zero.
Medical Instrumentation
Biopotential
Permeable Membrane
V
Na+
ClNeutral(1%)
Na+
Cl-
Voltage is zero.
Membrane is permeable to both Na+ & Cl-
Neutral(10%)
*Half-cell potential is zero.
Medical Instrumentation
Biopotential
Semi-permeable Membrane
V
Na+
Diffusion
ClNeutral(1%)
Na+
Repulsive
Cl-
Neutral(10%)
Semi-permeable Membrane
(Only to Na+)
*Half-cell potential is zero.
Medical Instrumentation
Biopotential
Electronic Coulomb force < Diffusion force
-> Na+ permeate.
V
Dynamic Equilibrium
Na+
Diffusion
ClNeutral(1%)
Na+
Repulsive
Cl-
Neutral(10%)
Electronic Coulomb force = Diffusion force
-> Na+ stop permeating
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Medical Instrumentaiton