Download Medical Instrumentation Application Lecture #1

Principles of Bioelectronics Design
Lecture #1
‫יסודות תכן ביו‪-‬חשמלי ‪ 3.5- 334011‬נקודות זיקוי‬
‫מרצה‪ :‬פרופסור ראמז דאניאל‬
‫בניין אמרסון קומה ‪7‬‬
‫שעות קבלה‪:‬לפי תיאום מראש‬
‫‪[email protected]‬‬
‫מתרגל ‪ :‬ירון רם‬
‫בודק תרגילים‪ :‬לונא ריזק‬
‫עבודות בית ‪- 8 :‬הגשה חובה ‪10%‬‬
‫תרגיל מחשב‪ -2 :‬הגשה חובה ‪10%‬‬
‫בוחן – מגן – ‪20%‬‬
‫בחינה‪60% -‬‬
‫אתר הקורס‪:‬‬
‫מקצועות קדם‪ :‬תורת המעגלים החשמליים‬
‫מקצועות מקביל‪ :‬אותות ומערכות‬
‫חומרי לימוד‪:‬‬
‫• ‪Medical Instrumentation Application and Design, 4th Edition, John G. Webster 2009‬‬
‫‪• Foundations of Analog and Digital Electronic Circuits, 1st Edition, Agarwal & Lang‬‬
‫‪• Physics of Semiconductor Devices by S.M. Sze‬‬
‫ נקודות זיקוי‬3.5- 334011 ‫חשמלי‬-‫יסודות תכן ביו‬
Syllabus:
1. General introduction
2. Introduction to semiconductor
3. PN Junction
4. Diode
5. MOS capacitor
6. MOS Transistor
7. Circuits - Small signal analysis
7. Circuits – MOSFET amplifier
8. Circuits - MOSFET advanced
9. Differential amplifier
10.Negative feedback
11.Digital circuits
Devices
Analog
Design
Digital
Design
Why should we study electronic devices and circuits
imaging capsule
Electrocardiogram
potential (EKG)
Electroencephalography
(EEG)
Ultrasound
Glucose biosensor
Why should we study electronic devices and circuits
Simply it is the best way to measure and display biological signals
Biological Signals are often analog continues in time
Computation and signal processing in computers are often digital discrete in time
OFF State “0”
ON State “0”
Analog and Digital
Biological Signals are often analog continues in time
Frequency Response
Every signal can be represented
as a Sum of periodic signals with
different frequency and
amplitude (linear operation).
The amplitude value is Fourier
Transform
Analog and Digital
Sampling the analog signal (fs ≥BW)
Digitized signal  sequence of numbers that
represents the magnitudes of signal samples
Computation and signal processing in computers are often digital discrete in time
Biosenors
Converts Biological signal to electrical signal. Requirements:
1. Specificity
2. Can track the changes in the biological signals , faster than the biological
signal (BWBiosen >BWSignal)
3. Sensitivity
4. linearity
5. Noise
Transfer function
of sensor
Biosenors
Linearization - Small Signal Analysis
𝑉=𝑓 𝑥
∆𝑣 =
𝑑𝑓
𝑑𝑥
∙ ∆𝑋
𝑋𝐷
For example:
𝑉 = 𝑉0 𝑒 𝑥/𝑋0
1
∆𝑉 =
𝑉0 𝑒 𝑋𝐷 /𝑋0 ∙ ∆𝑋
𝑋0
𝑆𝑙𝑜𝑝𝑒 =
∆𝑉 𝑉𝐷
=
∆𝑋 𝑋0
Biosenors
First Order Biosensor:
R and C are patristic
𝐼𝐵 = 𝐼𝑅 + 𝐼𝐶
𝐼𝐵 = 𝑓 𝑥
𝑉
𝐼𝑅 = ,
𝑅
𝑑𝑉
𝐼𝐶 = 𝐶
𝑑𝑡
𝑑𝑉 𝑉
𝐶
+ =𝑓 𝑥
𝑑𝑡 𝑅
𝑑𝑉 𝑓(𝑥)
𝑉
=
−
𝑑𝑡
𝐶
𝑅𝐶
𝜏 = 𝑅𝐶
For constant IB:
𝑡
−𝜏
𝑉 𝑡 = 𝐼𝐵 ∙ 𝑅(1 − 𝑒 )
𝑉 𝑡 = 𝜏 = 𝐼𝐵 ∙ 𝑅 1 − 𝑒 −1 = 0.63𝐼𝐵 ∙ 𝑅
Biosenors
First Order Biosensor: Frequency response
For constant IB:
𝑑𝑉 𝐼𝐵 𝑉
= −
𝑑𝑡
𝐶 𝜏
Fourier transform
𝑗𝜔𝑣 =
𝑖𝐵 𝑣
−
𝐶 𝜏
𝑣(𝜔 = 0) = 𝑅 ∙ 𝐼𝐵
𝑣 𝑗𝜔𝜏 + 1 = 𝑅 ∙ 𝑖𝐵
𝑣(𝜔) =
𝑣(𝜔 = 𝜔𝑐 ) =
𝑅 ∙ 𝑖𝐵 (𝜔)
(𝑗𝜔𝜏 + 1)
𝑣(𝜔) =
𝜔𝑐 = 1/𝜏
𝑣(𝜔 → ∞) = 0
𝑅 ∙ 𝐼𝐵
𝜔 𝜔𝑐
𝑅 ∙ 𝐼𝐵
2
+1
2
Biosenors
First Order Biosensor: Frequency response
𝑣(𝜔) =
𝑅 ∙ 𝐼𝐵
𝜔 𝜔𝑐
2
+1
𝜔𝑐 = 1/𝑅𝐶
𝑣(𝜔 = 0) = 𝑅 ∙ 𝐼𝐵
𝑣(𝜔 = 𝜔𝑐 ) =
𝑅 ∙ 𝐼𝐵
2
𝑣(𝜔 → ∞) = 0
Low pass filter: every
input signal with
frequency higher ωC
will be cut-off
log 1/ 2 ≈ −0.15
Biosenors
Low pass filter
𝑣(𝜔) =
𝑅 ∙ 𝑖𝐵 (𝜔)
(𝑗𝜔𝜏 + 1)
𝑣 𝜔 = 𝑖𝐵 (𝜔) ∙ 𝐻𝐿𝑃𝐹 (𝜔)
sin 𝜔𝑏 𝑡
𝛿(𝜔 − 𝜔𝑏 )
Fourier transform
ωb > ωc  V=0
ωb < ωc  V=Biological
Signal
Therefore it is important to
design the biosensor physical
parameters to set the value of
RC (e.g., dimensions )
Biosenors
First Order Biosensor: Frequency response
We can arrive to the same results by KCL and KVL
The impedance of R does not depend on the
frequency (ZR=R)
The impedance of C depends on the frequency
(ZC=1/jωC)
𝑉 = 𝐼𝐵 ∙ (𝑍𝑅 ||𝑍𝐶 )
𝑉 = 𝐼𝐵
𝑉 = 𝐼𝐵
𝑉 = 𝐼𝐵
𝑍𝑅 ∙ 𝑍𝐶
𝑍𝑅 + 𝑍𝐶
1
𝑅 ∙ 𝑗𝜔𝐶
1
𝑅 + 𝑗𝜔𝐶
1
𝑅 ∙ 𝑗𝜔𝐶
𝑗𝜔𝐶𝑅 + 1
𝑗𝜔𝐶
𝑉 = 𝐼𝐵
𝑉 = 𝐼𝐵
𝑅
𝑗𝜔𝑅𝐶 + 1
𝑅
(𝜔𝑅𝐶)2 +1
Biosenors -Photodiode
Biosensor converts one type of energy to electrical energy
Photodiode: is pn junction that converts light to electrical energy
Light increases the
dark current
𝐶
𝑑𝑉 𝑉
+ = 𝐼𝐿𝑖𝑔ℎ𝑡 − 𝐼𝐷𝑖𝑜𝑑𝑒
𝑑𝑡 𝑅
𝐼𝐷𝑖𝑜𝑑𝑒 = 𝐼𝑑𝑎𝑟𝑘 (𝑒 𝑞𝑉
𝑅=
Low pass filter
𝐾𝑇
− 1)
𝑑𝑉
𝐾𝑇
=
𝑑𝐼 𝑞 ∙ 𝐼
C is the junction capacitance
Biosenors - Piezoelectricity
Biosensor converts one type of energy to electrical energy
Piezoelectricity: convert mechanical energy to electrical energy
Measure pressure and ultrasound waves
It is reversbile: an applied mechanical stress will generate a voltage and an applied voltage
will change the shape of the solid by a small amount (up to a 4% change in volume).
Convert deflection/displacement to charge generator:
q  Kx
K is a constant depends on the material
X is a deflection
R Sensor leakage resistance
C   0 r
C Sensor capacitance
Piezoelectric crystal (quartz)
A
x
Biosenors - Piezoelectricity
Changes in x cause to change in the charge and producing a current.
Convert charge generator to current generator:
𝐼𝐵 =
𝐶
𝑑𝑞
𝑑𝑥
=𝐾
𝑑𝑡
𝑑𝑡
𝑑𝑉 𝑉
𝑑𝑥
+ =𝐾
𝑑𝑡 𝑅
𝑑𝑡
𝑑𝑉
𝑑𝑥 𝑉
= 𝐾𝑆
−
𝑑𝑡
𝑑𝑡 𝜏
Ks = K/C, sensitivity, V/m
 = RC, time constant
Fourier transform
𝑗𝜔𝑣 = 𝐾𝑆 ∙ 𝑗𝜔𝑥(𝜔) −
𝑣
𝜏
𝐾𝑆 𝑗𝜔𝜏
𝑣(𝜔) =
∙ 𝑥(𝜔)
1 + 𝑗𝜔𝜏
Biosenors - Piezoelectricity
𝑣(𝜔) =
𝐾𝑆 ∙ 𝜔 𝜔𝑐
𝜔 𝜔𝑐
2
+1
∙ 𝑥(𝜔)
Ks = K/C, sensitivity, V/m
 = RC, time constant
High Pass filter (HPF)
ωb < ωc  V=0
ωb > ωc  V ~ x
Electrochemical Biosenors
Convert biochemical reactions to electrical signal
Electrochemistry: interfacing electrode with electrolyte
Oxidation: Ions that lose their electrons
Reduction: Ions that gain new electrons
Electrochemical Biosenors
Equivalent electrical circuit of electrochemical cells
Rct: Charge transfer resistance due to transfer of electrons from ions to
electrode
Cdl: Double layer capacitor –accumulation of charge in the interface
between the electrolyte and electrode
RS: series resistance – electrolyte solution resistance
𝑍𝑒𝑞
𝑅𝑐𝑡
= 𝑅𝑠 +
1 + 𝑗 ∙ 𝜔 ∙ 𝑅𝑐𝑡 ∙ 𝐶𝑑𝑙
LPF
Amplifier
An input signals (current/voltage) is amplified to a larger output
signals (current/voltage)
Features:
1. Linearity (wide linear range)
2. High Gain
3. Vin=0  Vout=0
4. High signal to noise ratio
5. Stability at time (One dominant half time)
6. Stable gain (not depend on circuit parameters, VDD, temperature …)
Amplifier
Amplifier
• Voltage amplifier
𝑣𝑜𝑢𝑡 = 𝐴𝑣 ∙ 𝑣𝑖𝑛
Vin –input
Vout –output
Av – voltage gain [db]
Ri is input resistance
Ro output resistance
RS source resistance
RL Load Resistance
𝑣𝑖𝑛
𝑅𝑖
= 𝑣𝑠 ∙
𝑅𝑖 + 𝑅𝑆
𝑅𝐿
𝐿 +𝑅𝑂
𝑣𝑜𝑢𝑡 = 𝐴𝑣 𝑣𝑖𝑛 ∙ 𝑅
𝑅
𝑅𝐿
𝐿 +𝑅𝑂
𝑖
𝑣𝑜𝑢𝑡 = 𝐴𝑣 𝑣𝑠 ∙ 𝑅 +𝑅
∙𝑅
𝑖
𝐴𝑣𝑒𝑓𝑓 =
𝑣𝑜𝑢𝑡
𝑣𝑠
𝑆
𝑅
𝑅𝐿
𝐿 +𝑅𝑂
𝑖
= 𝐴𝑣 ∙ 𝑅 +𝑅
∙𝑅
20 log 𝐴𝑣 [𝑑𝐵]
𝑖
𝑆
decibels
Amplifier
Differential amplifier
𝑉𝑜𝑢𝑡 = 𝐴 ∙ (𝑉𝑖𝑛1 − 𝑉𝑖𝑛2 )
Reject common noise:
∆𝑉𝑖𝑛 = 𝑉𝑖𝑛1 − 𝑉𝑖𝑛2 = 𝑉𝑖𝑛1 + ∆ − 𝑉𝑖𝑛2 − ∆
 ∆𝑉𝑖𝑛 = 𝑉𝑖𝑛1 − 𝑉𝑖𝑛2
Negative feedback
Negative feedback loop: when the output of the system feed it
back to control and reduce his activity
Open loop equation:
𝑉𝑜𝑢𝑡 = 𝐴 ∙ (𝑉𝑖𝑛1 − 𝑉𝑖𝑛2 )
Negative feedback loop equation:
𝑉𝑖𝑛2 = 𝛽 ∙ 𝑉𝑜𝑢𝑡
⇒ 𝑉𝑜𝑢𝑡 = 𝐴 ∙ 𝑉𝑖𝑛1 − 𝛽 ∙ 𝑉𝑜𝑢𝑡
𝑽𝒐𝒖𝒕
𝑨
= 𝑽𝒊𝒏𝟏 ∙
𝟏+𝜷∙𝑨
β∙A>>1  Vout=Vin1/β
Black’s Formula
Negative feedback can increase the
stability
Analog-to-digital converts
Noise accumulated in analog circuits
noise hampers our ability to distinguish between small differences in
value —e.g. between 3.1V and 3.2V.
Solution : Digital circuit
Digital circuits
1. Device of two states (OFF/ON) or (0/1)
𝑉𝑂𝑁
𝑉𝑜𝑢𝑡 = 𝑉
𝑜𝑓𝑓
𝑉𝑖𝑛 > 𝑉𝑡ℎ
𝑉𝑖𝑛 < 𝑉𝑡ℎ
2. Computation arises from logic functions (Boolean algebra) using
basic logic gates: