Medical Instrumentation II

Phase–sensitive Demodulation

Medical Instrumentation II

)102sin()( 0 txtx

)502sin()( ttc

: 10Hz sinusoid (Tx = 0.1s)

: 50Hz sinusoid (Tc = 0.02s)

0.05s

0.1s

t

x(t)x0

-x0

t

x(t)c(t)

0.05s

0.1s

Matlab 1.

Medical Instrumentation II

When Xo = 2, x(t) is figured byusing matlab

Medical Instrumentation II

c(t) is figured by

using matlab

Medical Instrumentation II

x(t)c(t) is figured by

using matlab

Medical Instrumentation II

When c(t) is changed, figured

by Matlab

Medical Instrumentation II

When c(t)’s frequency is

1000, x(t)c(t) is figured by

using matlab

)]22cos(1[2

1)( tftx c

Medical Instrumentation II

Gi ven x(t)c(t) = y(t) , find x(t) = ?

X LPF ?y(t)

c(t) = sin(2πx50t)

x(t)c(t)²

O(t)

)2(sin)()()( 22 tftxtctx c

)22cos()(2

1)(

2

1)()( 2 tftxtxtctx c

Because 2fc is High frequency, cut off by LPF

)(2

1)( txtO

Problem 9.

A conductor board is setting chest at 1mm, this is one of capacitor. Distance to chest and conductor board is changed by heart rate, A change is x(t) = 1 + 0.2sin(2πft) [mm]. At this time f is heart rate frequency. You measure x(t) that is chest’s motion by heart rate. A is 5cm² and dielectricconstant ε₀ is 8.8 x 10⁻¹² F/m, heart rate is 60bpm.

(a) represent Cx by x function. Desire for max and

min capacitance. (b) Vi(t) = sin(2π x 10⁴t) V, C₀ is 4.4pF, V ₀(t) = ? (c) Propose Phase-sensitive demodulator that

desire x(t) by amplifier output V ₀(t)

Medical Instrumentation II

Capacitive Sensor

Medical Instrumentation II

Chest

x(t)

Non contact measure ]/[108.8,5 120

2 mfcmA

])[2sin(2.01)( mmfttx

bpmHR 60 Hzf 1

x

ACx 0 ][

)()( 0 f

tx

AtCx

O PAMP

+

-

O U T

Vo

Cx

Co

Vi

AB

BA ])[102sin()( 4 vtVi

][4.40 pFC o

x

i

o

Cj

Cj

1

1

)()( tVC

CtV i

x

oo )()()( tVtx

A

CtV i

o

oo

Matlab 2.

Medical Instrumentation II

X LPFVi(t)

Vo(t) )(2

1

0

0 txA

C

Constant is calculated and Vo(t) is figured

byusing matlab

Problem 10.

This is x₁ = x₀ + α(P1-P2), x₂ = x₀ - α(P1-P2), C₁ = εA/x₁, C₂ = εA/x₂, C₀ = εA/x₀. Ѵs = Vs <0 M Phase is 1KHz.

(a) Instrument Amplifier’s input voltage is Vi. Represent x₀, α, (P1-P2) and Ѵs. (b) Ѵs = 1[v], x₀ = 100[μm], α = 2[μm/mmHg]. Define Instrument Amplifier gain that output voltage phasor, V₀ sensitive magnitude is 0.1 [v/mmHg] (c) For desire (P1-P2) in V₀, using phase-sensitive demodulator, Represent circuit and explain

drive principal

Medical Instrumentation II

X1

Problem 10. Solution

Medical Instrumentation II

P1 P2 open

rigid

Diaphragm = very flexible

X2

A BC

Blow air

P1 > P2 P1 < P2

X1 increase / X2 decrease

)( 211 PPxX o

)( 212 PPxX o

00

22

11 ,,

c

AC

X

AC

X

AC

A C BC1

C2

When P1 = P2, C1 = C2

Medical Instrumentation II

O PAMP

+

-

O U T

A

C

B

C1

C2

C0

C0

os

i so GIA

0 ss ])[102sin()( 3 vtVstVs

CDi

sD 2

1ssC CC

C

CjCj

Cj

21

1

21

2

11

1

si CC

C

)2

1(

21

1

Medical Instrumentation II

s

PPxA

PPxA

PPxA

]

)()(

)(

2

1[

210210

210

sPPxPPx

PPx

])()(

)(

2

1[

210210

210

sx

PP

]

2

)(

2

1

2

1[

0

21

sPPx

)(2 21

0

])[102sin()(2

)( 321

0

vtPPx

VtV s

i

Medical Instrumentation II

]/[2],[100],[1 0 mmHgmmxvVs

])[102sin()(2

)( 321

0

vtPPx

VGtV s

o

Because High frequency, cut off by LPF

XLPFy(t)

sin(2πx10³t)

)(22

121

0

PPx

VG s