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Medical InstrumentDynamic Characteristics & Biopotential

김제선김준범김현준김한울 (1 등 )노재선

Group 3 :

Medical Instrumentation

Contents

Transient response 1

Steady state response2

Distortionless Mearsurment3

Biopotential4

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

x(t)

y(t)

H

CASE1

Step Response

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 under-damped, 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. I

n 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-DampingUnder-Damping

Critical-DampingCritical-Damping

Over-DampingOver-Damping

ζ = 1

ζ > 1

ζ < 1

Medical Instrumentation

Dynamic Characteristic

First-order system

ExponentialTime constant

System

Second-order system

Natural frequencyUnder-dampingCritical-dampingOver-damping

Medical Instrumentation

Dynamic Characteristic

3 차x y

x y1 차 2 차

*인수분해에 의해서 3 차는 1 차 , 2 차로 표현 가능

Medical Instrumentation

Steady state response

System

CASE2

Sinusoidal Steady State Frequency Response

Medical Instrumentation

Steady state response

Linear system(Principal of superposition)

LinearSystem

Linear combination

Basis of X =

Set of all x(t) is X,

x(t) is a linear combination-dependent frequency

Medical Instrumentation

Steady state response

Fourier Transform

Impulse response

Convolution - LTI(Linear time invariant)

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(jw)

각각의 주파수에 대한 출력을 알고 있으므로 입력의 합에 대한 결과 역시 알 수 있다 .(Superposition)

|H|

ω

ω

Medical Instrumentation

Steady state response

주파수는 같고 크기와 위상만 달라짐

Input

output

[ 주파수에 따라 출력의 모양이 달라진다 . ]

Medical Instrumentation

Distortionless Measurment

System

Time delay

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|

ω

ωA

Flat amplitude response

Linear phase response

Medical Instrumentation

Distortionless Measurment

H*(jw)

Example

X(t) Y(t)

“Phase = Frequency X Time”

Medical Instrumentation

Example of distortion(amplitude)

X(t)

+

Medical Instrumentation

Example of distortion(phase)

Medical Instrumentation

Example of distortion입력의 주파수 범위가 w1 에서 w2 일때 무왜곡을 측정하기 위한 H(jw)?

ω

ω

Non-causal

존재할 수 없다빛의 속도보다 빠르면 존재

ω1 ω2

ω1 ω2

Medical Instrumentation

Biopotential

Insulating Membrane

Insulating membrane

Na+

Cl-

Na+

Cl-

Neutral(1%) Neutral(10%)

V

Voltage is zero.

*Half-cell potential is zero.

Medical Instrumentation

Biopotential

Permeable Membrane

Na+ Na+

Cl- Cl- Membrane is permeable to both Na+ & Cl-

V

Voltage is zero.

Neutral(1%) Neutral(10%)*Half-cell potential is zero.

Medical Instrumentation

Biopotential

Semi-permeable Membrane

Na+

Cl-

Na+

Cl- Semi-permeable Membrane(Only to Na+)

V

*Half-cell potential is zero.

Diffusion Repulsive

Neutral(1%) Neutral(10%)

Medical Instrumentation

Biopotential

Na+

Cl-

Na+

Cl-

V

Diffusion Repulsive

Neutral(1%) Neutral(10%)

Electronic Coulomb force < Diffusion force -> Na+ permeate.

Electronic Coulomb force = Diffusion force -> Na+ stop permeating

Dynamic Equilibrium

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Medical Instrumentaiton