Principles of Bioelectronics Design Lecture 1

נקודות זיקוי334011-35חשמלי -יסודות תכן ביו

פרופסור ראמז דאניאל מרצה

7אמרסון קומה בניין

לפי תיאום מראשקבלהשעות

ramizdabmtechnionacil

ירון רם מתרגל

לונא ריזק בודק תרגילים

10הגשה חובה -8 עבודות בית

10הגשה חובה -2 תרגיל מחשב

20ndashמגן ndashבוחן

60-בחינה

אתר הקורס

תורת המעגלים החשמליים מקצועות קדם

ומערכותאותות מקצועות מקביל

חומרי לימודbullMedical Instrumentation Application and Design 4th Edition John G Webster 2009

bull Foundations of Analog and Digital Electronic Circuits 1st Edition Agarwal amp Langbull Physics of Semiconductor Devices by SM Sze

נקודות זיקוי334011-35חשמלי -יסודות תכן ביו

פרופסור ראמז דאניאל מרצה

7אמרסון קומה בניין

לפי תיאום מראשקבלהשעות

ramizdabmtechnionacil

ירון רם מתרגל

לונא ריזק בודק תרגילים

10הגשה חובה -8 עבודות בית

10הגשה חובה -2 תרגיל מחשב

20ndashמגן ndashבוחן

60-בחינה

אתר הקורס

תורת המעגלים החשמליים מקצועות קדם

ומערכותאותות מקצועות מקביל

חומרי לימודbullMedical Instrumentation Application and Design 4th Edition John G Webster 2009

bull Foundations of Analog and Digital Electronic Circuits 1st Edition Agarwal amp Langbull Physics of Semiconductor Devices by SM Sze

נקודות זיקוי334011-35חשמלי -יסודות תכן ביו

Syllabus

1 General introduction2 Introduction to semiconductor3 PN Junction 4 Diode5 MOS capacitor6 MOS Transistor7 Circuits - Small signal analysis 7 Circuits ndash MOSFET amplifier8 Circuits - MOSFET advanced 9 Differential amplifier10Negative feedback11Digital circuits

Devices

Analog Design

Digital Design

Why should we study electronic devices and circuits

Electrocardiogram potential (EKG)

Electroencephalography(EEG)

imaging capsule Glucose biosensor

Ultrasound

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 ldquo0rdquo ON State ldquo0rdquo

Analog and DigitalBiological Signals are often analog continues in time

Every signal can be represented as a Sum of periodic signals with different frequency and amplitude (linear operation) The amplitude value is Fourier Transform

Frequency Response

Analog and DigitalSampling the analog signal (fs geBW)

Digitized signal sequence of numbers that represents the magnitudes of signal samples

Computation and signal processing in computers are often digital discrete in time

Converts Biological signal to electrical signal Requirements1 Specificity 2 Can track the changes in the biological signals faster than the biological

signal (BWBiosen gtBWSignal)3 Sensitivity4 linearity5 Noise

Biosenors

Transfer function of sensor

Linearization - Small Signal Analysis

Biosenors

119881 = 119891 119909

∆119907 =119889119891

119889119909119883119863

∙ ∆119883

119881 = 11988101198901199091198830

∆119881 =1

11988301198810119890

1198831198631198830 ∙ ∆119883

For example

119878119897119900119901119890 =∆119881

∆119883=

119881119863

1198830

First Order Biosensor

R and C are patristic

Biosenors

119868119861 = 119868119877 + 119868119862

119868119861 = 119891 119909

119868119877 =119881

119877 119868119862 = 119862

119889119881

119889119905

119862119889119881

119889119905+119881

119877= 119891 119909

119889119881

119889119905=

119891(119909)

119862minus

119881

119877119862

120591 = 119877119862

For constant IB

119881 119905 = 119868119861 ∙ 119877(1 minus 119890minus119905

120591)

119881 119905 = 120591 = 119868119861 ∙ 119877 1 minus 119890minus1 = 063119868119861 ∙ 119877

First Order Biosensor Frequency response

Biosenors

For constant IB

119889119881

119889119905=

119868119861119862minus119881

120591

119895120596119907 =119894119861119862minus119907

120591

119907 119895120596120591 + 1 = 119877 ∙ 119894119861

119907(120596) =119877 ∙ 119894119861(120596)

(119895120596120591 + 1)

120596119888 = 1120591

Fourier transform

119907(120596 = 0) = 119877 ∙ 119868119861

119907(120596 rarr infin) = 0

119907(120596) =119877 ∙ 119868119861

120596 1205961198882 + 1

119907(120596 = 120596119888) =119877 ∙ 119868119861

2

First Order Biosensor Frequency response

Biosenors

119907(120596) =119877 ∙ 119868119861

120596 1205961198882 + 1

120596119888 = 1119877119862

119907(120596 = 0) = 119877 ∙ 119868119861

119907(120596 rarr infin) = 0

Low pass filter every input signal with frequency higher ωC

will be cut-off

119907(120596 = 120596119888) =119877 ∙ 119868119861

2

log 1 2 asymp minus015

Low pass filter

Biosenors

ωb gt ωc V=0

sin 120596119887119905

Fourier transform

120575(120596 minus 120596119887)

ωb lt ωc V=Biological Signal

Therefore it is important to design the biosensor physical parameters to set the value of RC (eg dimensions )

119907(120596) =119877 ∙ 119894119861(120596)

(119895120596120591 + 1)

119907 120596 = 119894119861(120596) ∙ 119867119871119875119865(120596)

First Order Biosensor Frequency response

Biosenors

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=1jωC)

119881 = 119868119861 ∙ (119885119877||119885119862)

119881 = 119868119861119885119877 ∙ 119885119862119885119877 + 119885119862

119881 = 119868119861

119877 ∙1

119895120596119862

119877 +1

119895120596119862

119881 = 119868119861

119877 ∙1

119895120596119862119895120596119862119877 + 1

119895120596119862

119881 = 119868119861119877

119895120596119877119862 + 1

119881 = 119868119861119877

(120596119877119862)2+1

Biosensor converts one type of energy to electrical energyPhotodiode is pn junction that converts light to electrical energy

Biosenors -Photodiode

119862119889119881

119889119905+119881

119877= 119868119871119894119892ℎ119905 minus 119868119863119894119900119889119890

119868119863119894119900119889119890 = 119868119889119886119903119896(119890 119902119881 119870119879 minus 1)

Low pass filter

Light increases the

dark current

119877 =119889119881

119889119868=

119870119879

119902 ∙ 119868

C is the junction capacitance

Biosensor converts one type of energy to electrical energy

Piezoelectricity convert mechanical energy to electrical energyMeasure pressure and ultrasound waves

Biosenors - Piezoelectricity

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 deflectiondisplacement to charge generator

Kxq K is a constant depends on the material

X is a deflection

R Sensor leakage resistance

C Sensor capacitance

Piezoelectric crystal (quartz)

x

AC r0

Biosenors - Piezoelectricity

Changes in x cause to change in the charge and producing a current

Convert charge generator to current generator

119868119861 =119889119902

119889119905= 119870

119889119909

119889119905

119862119889119881

119889119905+119881

119877= 119870

119889119909

119889119905

119889119881

119889119905= 119870119878

119889119909

119889119905minus119881

120591

Ks = KC sensitivity Vm

= RC time constant

Fourier transform

119895120596119907 = 119870119878 ∙ 119895120596119909(120596) minus119907

120591

119907(120596) =119870119878119895120596120591

1 + 119895120596120591∙ 119909(120596)

Biosenors - Piezoelectricity

Ks = KC sensitivity Vm

= RC time constant

119907(120596) =119870119878 ∙ 120596 120596119888

120596 1205961198882 + 1

∙ 119909(120596)

ωb lt ωc V=0

ωb gt ωc V ~ x

High Pass filter (HPF)

Electrochemical Biosenors

Electrochemistry interfacing electrode with electrolyte Oxidation Ions that lose their electronsReduction Ions that gain new electrons

Convert biochemical reactions to electrical signal

Electrochemical Biosenors

Equivalent electrical circuit of electrochemical cells

Rct Charge transfer resistance due to transfer of electrons from ions to electrodeCdl Double layer capacitor ndashaccumulation of charge in the interface between the electrolyte and electrodeRS series resistance ndash electrolyte solution resistance

119885119890119902 = 119877119904 +119877119888119905

1 + 119895 ∙ 120596 ∙ 119877119888119905 ∙ 119862119889119897

LPF

Amplifier

An input signals (currentvoltage) is amplified to a larger output signals (currentvoltage)

Features1 Linearity (wide linear range)2 High Gain3 Vin=0 Vout=04 High signal to noise ratio5 Stability at time (One dominant half time)6 Stable gain (not depend on circuit parameters VDD temperature hellip)

Amplifier

Amplifier

bull Voltage amplifier

119907119900119906119905 = 119860119907 ∙ 119907119894119899

Vin ndashinputVout ndashoutputAv ndash voltage gain [db]Ri is input resistanceRo output resistanceRS source resistanceRL Load Resistance

119907119894119899 = 119907119904 ∙119877119894

119877119894 + 119877119878 119907119900119906119905 = 119860119907119907119894119899 ∙119877119871

119877119871+119877119874

119907119900119906119905 = 119860119907119907119904 ∙119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

119860119907119890119891119891 =119907119900119906119905

119907119904= 119860119907 ∙

119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

20 log 119860119907 [119889119861] decibels

Amplifier

Differential amplifier

Reject common noise

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992 = 1198811198941198991 + ∆ minus 1198811198941198992 minus ∆

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

Negative feedbackNegative feedback loop when the output of the system feed it back to control and reduce his activity

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

1198811198941198992 = 120573 ∙ 119881119900119906119905

Open loop equation

Negative feedback loop equation

rArr 119881119900119906119905= 119860 ∙ 1198811198941198991 minus 120573 ∙ 119881119900119906119905

119933119952119958119957 = 119933119946119951120783 ∙119912

120783 + 120631 ∙ 119912Blackrsquos Formula

β∙Agtgt1 Vout=Vin1βNegative feedback can increase the stability

Analog-to-digital converts

Noise accumulated in analog circuits

Solution Digital circuit

noise hampers our ability to distinguish between small differences in value mdasheg between 31V and 32V

Digital circuits1 Device of two states (OFFON) or (01)

119881119900119906119905 = 119881119874119873 119881119894119899gt 119881119905ℎ119881119900119891119891 119881119894119899 lt 119881119905ℎ

2 Computation arises from logic functions (Boolean algebra) using basic logic gates

Why should we study electronic devices and circuits

Electrocardiogram potential (EKG)

Electroencephalography(EEG)

imaging capsule Glucose biosensor

Ultrasound

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 ldquo0rdquo ON State ldquo0rdquo

Analog and DigitalBiological Signals are often analog continues in time

Every signal can be represented as a Sum of periodic signals with different frequency and amplitude (linear operation) The amplitude value is Fourier Transform

Frequency Response

Analog and DigitalSampling the analog signal (fs geBW)

Digitized signal sequence of numbers that represents the magnitudes of signal samples

Computation and signal processing in computers are often digital discrete in time

Converts Biological signal to electrical signal Requirements1 Specificity 2 Can track the changes in the biological signals faster than the biological

signal (BWBiosen gtBWSignal)3 Sensitivity4 linearity5 Noise

Biosenors

Transfer function of sensor

Linearization - Small Signal Analysis

Biosenors

119881 = 119891 119909

∆119907 =119889119891

119889119909119883119863

∙ ∆119883

119881 = 11988101198901199091198830

∆119881 =1

11988301198810119890

1198831198631198830 ∙ ∆119883

For example

119878119897119900119901119890 =∆119881

∆119883=

119881119863

1198830

First Order Biosensor

R and C are patristic

Biosenors

119868119861 = 119868119877 + 119868119862

119868119861 = 119891 119909

119868119877 =119881

119877 119868119862 = 119862

119889119881

119889119905

119862119889119881

119889119905+119881

119877= 119891 119909

119889119881

119889119905=

119891(119909)

119862minus

119881

119877119862

120591 = 119877119862

For constant IB

119881 119905 = 119868119861 ∙ 119877(1 minus 119890minus119905

120591)

119881 119905 = 120591 = 119868119861 ∙ 119877 1 minus 119890minus1 = 063119868119861 ∙ 119877

First Order Biosensor Frequency response

Biosenors

For constant IB

119889119881

119889119905=

119868119861119862minus119881

120591

119895120596119907 =119894119861119862minus119907

120591

119907 119895120596120591 + 1 = 119877 ∙ 119894119861

119907(120596) =119877 ∙ 119894119861(120596)

(119895120596120591 + 1)

120596119888 = 1120591

Fourier transform

119907(120596 = 0) = 119877 ∙ 119868119861

119907(120596 rarr infin) = 0

119907(120596) =119877 ∙ 119868119861

120596 1205961198882 + 1

119907(120596 = 120596119888) =119877 ∙ 119868119861

2

First Order Biosensor Frequency response

Biosenors

119907(120596) =119877 ∙ 119868119861

120596 1205961198882 + 1

120596119888 = 1119877119862

119907(120596 = 0) = 119877 ∙ 119868119861

119907(120596 rarr infin) = 0

Low pass filter every input signal with frequency higher ωC

will be cut-off

119907(120596 = 120596119888) =119877 ∙ 119868119861

2

log 1 2 asymp minus015

Low pass filter

Biosenors

ωb gt ωc V=0

sin 120596119887119905

Fourier transform

120575(120596 minus 120596119887)

ωb lt ωc V=Biological Signal

Therefore it is important to design the biosensor physical parameters to set the value of RC (eg dimensions )

119907(120596) =119877 ∙ 119894119861(120596)

(119895120596120591 + 1)

119907 120596 = 119894119861(120596) ∙ 119867119871119875119865(120596)

First Order Biosensor Frequency response

Biosenors

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=1jωC)

119881 = 119868119861 ∙ (119885119877||119885119862)

119881 = 119868119861119885119877 ∙ 119885119862119885119877 + 119885119862

119881 = 119868119861

119877 ∙1

119895120596119862

119877 +1

119895120596119862

119881 = 119868119861

119877 ∙1

119895120596119862119895120596119862119877 + 1

119895120596119862

119881 = 119868119861119877

119895120596119877119862 + 1

119881 = 119868119861119877

(120596119877119862)2+1

Biosensor converts one type of energy to electrical energyPhotodiode is pn junction that converts light to electrical energy

Biosenors -Photodiode

119862119889119881

119889119905+119881

119877= 119868119871119894119892ℎ119905 minus 119868119863119894119900119889119890

119868119863119894119900119889119890 = 119868119889119886119903119896(119890 119902119881 119870119879 minus 1)

Low pass filter

Light increases the

dark current

119877 =119889119881

119889119868=

119870119879

119902 ∙ 119868

C is the junction capacitance

Biosensor converts one type of energy to electrical energy

Piezoelectricity convert mechanical energy to electrical energyMeasure pressure and ultrasound waves

Biosenors - Piezoelectricity

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 deflectiondisplacement to charge generator

Kxq K is a constant depends on the material

X is a deflection

R Sensor leakage resistance

C Sensor capacitance

Piezoelectric crystal (quartz)

x

AC r0

Biosenors - Piezoelectricity

Changes in x cause to change in the charge and producing a current

Convert charge generator to current generator

119868119861 =119889119902

119889119905= 119870

119889119909

119889119905

119862119889119881

119889119905+119881

119877= 119870

119889119909

119889119905

119889119881

119889119905= 119870119878

119889119909

119889119905minus119881

120591

Ks = KC sensitivity Vm

= RC time constant

Fourier transform

119895120596119907 = 119870119878 ∙ 119895120596119909(120596) minus119907

120591

119907(120596) =119870119878119895120596120591

1 + 119895120596120591∙ 119909(120596)

Biosenors - Piezoelectricity

Ks = KC sensitivity Vm

= RC time constant

119907(120596) =119870119878 ∙ 120596 120596119888

120596 1205961198882 + 1

∙ 119909(120596)

ωb lt ωc V=0

ωb gt ωc V ~ x

High Pass filter (HPF)

Electrochemical Biosenors

Electrochemistry interfacing electrode with electrolyte Oxidation Ions that lose their electronsReduction Ions that gain new electrons

Convert biochemical reactions to electrical signal

Electrochemical Biosenors

Equivalent electrical circuit of electrochemical cells

Rct Charge transfer resistance due to transfer of electrons from ions to electrodeCdl Double layer capacitor ndashaccumulation of charge in the interface between the electrolyte and electrodeRS series resistance ndash electrolyte solution resistance

119885119890119902 = 119877119904 +119877119888119905

1 + 119895 ∙ 120596 ∙ 119877119888119905 ∙ 119862119889119897

LPF

Amplifier

An input signals (currentvoltage) is amplified to a larger output signals (currentvoltage)

Features1 Linearity (wide linear range)2 High Gain3 Vin=0 Vout=04 High signal to noise ratio5 Stability at time (One dominant half time)6 Stable gain (not depend on circuit parameters VDD temperature hellip)

Amplifier

Amplifier

bull Voltage amplifier

119907119900119906119905 = 119860119907 ∙ 119907119894119899

Vin ndashinputVout ndashoutputAv ndash voltage gain [db]Ri is input resistanceRo output resistanceRS source resistanceRL Load Resistance

119907119894119899 = 119907119904 ∙119877119894

119877119894 + 119877119878 119907119900119906119905 = 119860119907119907119894119899 ∙119877119871

119877119871+119877119874

119907119900119906119905 = 119860119907119907119904 ∙119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

119860119907119890119891119891 =119907119900119906119905

119907119904= 119860119907 ∙

119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

20 log 119860119907 [119889119861] decibels

Amplifier

Differential amplifier

Reject common noise

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992 = 1198811198941198991 + ∆ minus 1198811198941198992 minus ∆

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

Negative feedbackNegative feedback loop when the output of the system feed it back to control and reduce his activity

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

1198811198941198992 = 120573 ∙ 119881119900119906119905

Open loop equation

Negative feedback loop equation

rArr 119881119900119906119905= 119860 ∙ 1198811198941198991 minus 120573 ∙ 119881119900119906119905

119933119952119958119957 = 119933119946119951120783 ∙119912

120783 + 120631 ∙ 119912Blackrsquos Formula

β∙Agtgt1 Vout=Vin1βNegative feedback can increase the stability

Analog-to-digital converts

Noise accumulated in analog circuits

Solution Digital circuit

noise hampers our ability to distinguish between small differences in value mdasheg between 31V and 32V

Digital circuits1 Device of two states (OFFON) or (01)

119881119900119906119905 = 119881119874119873 119881119894119899gt 119881119905ℎ119881119900119891119891 119881119894119899 lt 119881119905ℎ

2 Computation arises from logic functions (Boolean algebra) using basic logic gates

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 ldquo0rdquo ON State ldquo0rdquo

Analog and DigitalBiological Signals are often analog continues in time

Every signal can be represented as a Sum of periodic signals with different frequency and amplitude (linear operation) The amplitude value is Fourier Transform

Frequency Response

Analog and DigitalSampling the analog signal (fs geBW)

Digitized signal sequence of numbers that represents the magnitudes of signal samples

Computation and signal processing in computers are often digital discrete in time

Converts Biological signal to electrical signal Requirements1 Specificity 2 Can track the changes in the biological signals faster than the biological

signal (BWBiosen gtBWSignal)3 Sensitivity4 linearity5 Noise

Biosenors

Transfer function of sensor

Linearization - Small Signal Analysis

Biosenors

119881 = 119891 119909

∆119907 =119889119891

119889119909119883119863

∙ ∆119883

119881 = 11988101198901199091198830

∆119881 =1

11988301198810119890

1198831198631198830 ∙ ∆119883

For example

119878119897119900119901119890 =∆119881

∆119883=

119881119863

1198830

First Order Biosensor

R and C are patristic

Biosenors

119868119861 = 119868119877 + 119868119862

119868119861 = 119891 119909

119868119877 =119881

119877 119868119862 = 119862

119889119881

119889119905

119862119889119881

119889119905+119881

119877= 119891 119909

119889119881

119889119905=

119891(119909)

119862minus

119881

119877119862

120591 = 119877119862

For constant IB

119881 119905 = 119868119861 ∙ 119877(1 minus 119890minus119905

120591)

119881 119905 = 120591 = 119868119861 ∙ 119877 1 minus 119890minus1 = 063119868119861 ∙ 119877

First Order Biosensor Frequency response

Biosenors

For constant IB

119889119881

119889119905=

119868119861119862minus119881

120591

119895120596119907 =119894119861119862minus119907

120591

119907 119895120596120591 + 1 = 119877 ∙ 119894119861

119907(120596) =119877 ∙ 119894119861(120596)

(119895120596120591 + 1)

120596119888 = 1120591

Fourier transform

119907(120596 = 0) = 119877 ∙ 119868119861

119907(120596 rarr infin) = 0

119907(120596) =119877 ∙ 119868119861

120596 1205961198882 + 1

119907(120596 = 120596119888) =119877 ∙ 119868119861

2

First Order Biosensor Frequency response

Biosenors

119907(120596) =119877 ∙ 119868119861

120596 1205961198882 + 1

120596119888 = 1119877119862

119907(120596 = 0) = 119877 ∙ 119868119861

119907(120596 rarr infin) = 0

Low pass filter every input signal with frequency higher ωC

will be cut-off

119907(120596 = 120596119888) =119877 ∙ 119868119861

2

log 1 2 asymp minus015

Low pass filter

Biosenors

ωb gt ωc V=0

sin 120596119887119905

Fourier transform

120575(120596 minus 120596119887)

ωb lt ωc V=Biological Signal

Therefore it is important to design the biosensor physical parameters to set the value of RC (eg dimensions )

119907(120596) =119877 ∙ 119894119861(120596)

(119895120596120591 + 1)

119907 120596 = 119894119861(120596) ∙ 119867119871119875119865(120596)

First Order Biosensor Frequency response

Biosenors

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=1jωC)

119881 = 119868119861 ∙ (119885119877||119885119862)

119881 = 119868119861119885119877 ∙ 119885119862119885119877 + 119885119862

119881 = 119868119861

119877 ∙1

119895120596119862

119877 +1

119895120596119862

119881 = 119868119861

119877 ∙1

119895120596119862119895120596119862119877 + 1

119895120596119862

119881 = 119868119861119877

119895120596119877119862 + 1

119881 = 119868119861119877

(120596119877119862)2+1

Biosensor converts one type of energy to electrical energyPhotodiode is pn junction that converts light to electrical energy

Biosenors -Photodiode

119862119889119881

119889119905+119881

119877= 119868119871119894119892ℎ119905 minus 119868119863119894119900119889119890

119868119863119894119900119889119890 = 119868119889119886119903119896(119890 119902119881 119870119879 minus 1)

Low pass filter

Light increases the

dark current

119877 =119889119881

119889119868=

119870119879

119902 ∙ 119868

C is the junction capacitance

Biosensor converts one type of energy to electrical energy

Piezoelectricity convert mechanical energy to electrical energyMeasure pressure and ultrasound waves

Biosenors - Piezoelectricity

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 deflectiondisplacement to charge generator

Kxq K is a constant depends on the material

X is a deflection

R Sensor leakage resistance

C Sensor capacitance

Piezoelectric crystal (quartz)

x

AC r0

Biosenors - Piezoelectricity

Changes in x cause to change in the charge and producing a current

Convert charge generator to current generator

119868119861 =119889119902

119889119905= 119870

119889119909

119889119905

119862119889119881

119889119905+119881

119877= 119870

119889119909

119889119905

119889119881

119889119905= 119870119878

119889119909

119889119905minus119881

120591

Ks = KC sensitivity Vm

= RC time constant

Fourier transform

119895120596119907 = 119870119878 ∙ 119895120596119909(120596) minus119907

120591

119907(120596) =119870119878119895120596120591

1 + 119895120596120591∙ 119909(120596)

Biosenors - Piezoelectricity

Ks = KC sensitivity Vm

= RC time constant

119907(120596) =119870119878 ∙ 120596 120596119888

120596 1205961198882 + 1

∙ 119909(120596)

ωb lt ωc V=0

ωb gt ωc V ~ x

High Pass filter (HPF)

Electrochemical Biosenors

Electrochemistry interfacing electrode with electrolyte Oxidation Ions that lose their electronsReduction Ions that gain new electrons

Convert biochemical reactions to electrical signal

Electrochemical Biosenors

Equivalent electrical circuit of electrochemical cells

Rct Charge transfer resistance due to transfer of electrons from ions to electrodeCdl Double layer capacitor ndashaccumulation of charge in the interface between the electrolyte and electrodeRS series resistance ndash electrolyte solution resistance

119885119890119902 = 119877119904 +119877119888119905

1 + 119895 ∙ 120596 ∙ 119877119888119905 ∙ 119862119889119897

LPF

Amplifier

An input signals (currentvoltage) is amplified to a larger output signals (currentvoltage)

Features1 Linearity (wide linear range)2 High Gain3 Vin=0 Vout=04 High signal to noise ratio5 Stability at time (One dominant half time)6 Stable gain (not depend on circuit parameters VDD temperature hellip)

Amplifier

Amplifier

bull Voltage amplifier

119907119900119906119905 = 119860119907 ∙ 119907119894119899

Vin ndashinputVout ndashoutputAv ndash voltage gain [db]Ri is input resistanceRo output resistanceRS source resistanceRL Load Resistance

119907119894119899 = 119907119904 ∙119877119894

119877119894 + 119877119878 119907119900119906119905 = 119860119907119907119894119899 ∙119877119871

119877119871+119877119874

119907119900119906119905 = 119860119907119907119904 ∙119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

119860119907119890119891119891 =119907119900119906119905

119907119904= 119860119907 ∙

119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

20 log 119860119907 [119889119861] decibels

Amplifier

Differential amplifier

Reject common noise

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992 = 1198811198941198991 + ∆ minus 1198811198941198992 minus ∆

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

Negative feedbackNegative feedback loop when the output of the system feed it back to control and reduce his activity

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

1198811198941198992 = 120573 ∙ 119881119900119906119905

Open loop equation

Negative feedback loop equation

rArr 119881119900119906119905= 119860 ∙ 1198811198941198991 minus 120573 ∙ 119881119900119906119905

119933119952119958119957 = 119933119946119951120783 ∙119912

120783 + 120631 ∙ 119912Blackrsquos Formula

β∙Agtgt1 Vout=Vin1βNegative feedback can increase the stability

Analog-to-digital converts

Noise accumulated in analog circuits

Solution Digital circuit

noise hampers our ability to distinguish between small differences in value mdasheg between 31V and 32V

Digital circuits1 Device of two states (OFFON) or (01)

119881119900119906119905 = 119881119874119873 119881119894119899gt 119881119905ℎ119881119900119891119891 119881119894119899 lt 119881119905ℎ

2 Computation arises from logic functions (Boolean algebra) using basic logic gates

Analog and DigitalBiological Signals are often analog continues in time

Every signal can be represented as a Sum of periodic signals with different frequency and amplitude (linear operation) The amplitude value is Fourier Transform

Frequency Response

Analog and DigitalSampling the analog signal (fs geBW)

Digitized signal sequence of numbers that represents the magnitudes of signal samples

Computation and signal processing in computers are often digital discrete in time

Converts Biological signal to electrical signal Requirements1 Specificity 2 Can track the changes in the biological signals faster than the biological

signal (BWBiosen gtBWSignal)3 Sensitivity4 linearity5 Noise

Biosenors

Transfer function of sensor

Linearization - Small Signal Analysis

Biosenors

119881 = 119891 119909

∆119907 =119889119891

119889119909119883119863

∙ ∆119883

119881 = 11988101198901199091198830

∆119881 =1

11988301198810119890

1198831198631198830 ∙ ∆119883

For example

119878119897119900119901119890 =∆119881

∆119883=

119881119863

1198830

First Order Biosensor

R and C are patristic

Biosenors

119868119861 = 119868119877 + 119868119862

119868119861 = 119891 119909

119868119877 =119881

119877 119868119862 = 119862

119889119881

119889119905

119862119889119881

119889119905+119881

119877= 119891 119909

119889119881

119889119905=

119891(119909)

119862minus

119881

119877119862

120591 = 119877119862

For constant IB

119881 119905 = 119868119861 ∙ 119877(1 minus 119890minus119905

120591)

119881 119905 = 120591 = 119868119861 ∙ 119877 1 minus 119890minus1 = 063119868119861 ∙ 119877

First Order Biosensor Frequency response

Biosenors

For constant IB

119889119881

119889119905=

119868119861119862minus119881

120591

119895120596119907 =119894119861119862minus119907

120591

119907 119895120596120591 + 1 = 119877 ∙ 119894119861

119907(120596) =119877 ∙ 119894119861(120596)

(119895120596120591 + 1)

120596119888 = 1120591

Fourier transform

119907(120596 = 0) = 119877 ∙ 119868119861

119907(120596 rarr infin) = 0

119907(120596) =119877 ∙ 119868119861

120596 1205961198882 + 1

119907(120596 = 120596119888) =119877 ∙ 119868119861

2

First Order Biosensor Frequency response

Biosenors

119907(120596) =119877 ∙ 119868119861

120596 1205961198882 + 1

120596119888 = 1119877119862

119907(120596 = 0) = 119877 ∙ 119868119861

119907(120596 rarr infin) = 0

Low pass filter every input signal with frequency higher ωC

will be cut-off

119907(120596 = 120596119888) =119877 ∙ 119868119861

2

log 1 2 asymp minus015

Low pass filter

Biosenors

ωb gt ωc V=0

sin 120596119887119905

Fourier transform

120575(120596 minus 120596119887)

ωb lt ωc V=Biological Signal

Therefore it is important to design the biosensor physical parameters to set the value of RC (eg dimensions )

119907(120596) =119877 ∙ 119894119861(120596)

(119895120596120591 + 1)

119907 120596 = 119894119861(120596) ∙ 119867119871119875119865(120596)

First Order Biosensor Frequency response

Biosenors

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=1jωC)

119881 = 119868119861 ∙ (119885119877||119885119862)

119881 = 119868119861119885119877 ∙ 119885119862119885119877 + 119885119862

119881 = 119868119861

119877 ∙1

119895120596119862

119877 +1

119895120596119862

119881 = 119868119861

119877 ∙1

119895120596119862119895120596119862119877 + 1

119895120596119862

119881 = 119868119861119877

119895120596119877119862 + 1

119881 = 119868119861119877

(120596119877119862)2+1

Biosensor converts one type of energy to electrical energyPhotodiode is pn junction that converts light to electrical energy

Biosenors -Photodiode

119862119889119881

119889119905+119881

119877= 119868119871119894119892ℎ119905 minus 119868119863119894119900119889119890

119868119863119894119900119889119890 = 119868119889119886119903119896(119890 119902119881 119870119879 minus 1)

Low pass filter

Light increases the

dark current

119877 =119889119881

119889119868=

119870119879

119902 ∙ 119868

C is the junction capacitance

Biosensor converts one type of energy to electrical energy

Piezoelectricity convert mechanical energy to electrical energyMeasure pressure and ultrasound waves

Biosenors - Piezoelectricity

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 deflectiondisplacement to charge generator

Kxq K is a constant depends on the material

X is a deflection

R Sensor leakage resistance

C Sensor capacitance

Piezoelectric crystal (quartz)

x

AC r0

Biosenors - Piezoelectricity

Changes in x cause to change in the charge and producing a current

Convert charge generator to current generator

119868119861 =119889119902

119889119905= 119870

119889119909

119889119905

119862119889119881

119889119905+119881

119877= 119870

119889119909

119889119905

119889119881

119889119905= 119870119878

119889119909

119889119905minus119881

120591

Ks = KC sensitivity Vm

= RC time constant

Fourier transform

119895120596119907 = 119870119878 ∙ 119895120596119909(120596) minus119907

120591

119907(120596) =119870119878119895120596120591

1 + 119895120596120591∙ 119909(120596)

Biosenors - Piezoelectricity

Ks = KC sensitivity Vm

= RC time constant

119907(120596) =119870119878 ∙ 120596 120596119888

120596 1205961198882 + 1

∙ 119909(120596)

ωb lt ωc V=0

ωb gt ωc V ~ x

High Pass filter (HPF)

Electrochemical Biosenors

Electrochemistry interfacing electrode with electrolyte Oxidation Ions that lose their electronsReduction Ions that gain new electrons

Convert biochemical reactions to electrical signal

Electrochemical Biosenors

Equivalent electrical circuit of electrochemical cells

Rct Charge transfer resistance due to transfer of electrons from ions to electrodeCdl Double layer capacitor ndashaccumulation of charge in the interface between the electrolyte and electrodeRS series resistance ndash electrolyte solution resistance

119885119890119902 = 119877119904 +119877119888119905

1 + 119895 ∙ 120596 ∙ 119877119888119905 ∙ 119862119889119897

LPF

Amplifier

An input signals (currentvoltage) is amplified to a larger output signals (currentvoltage)

Features1 Linearity (wide linear range)2 High Gain3 Vin=0 Vout=04 High signal to noise ratio5 Stability at time (One dominant half time)6 Stable gain (not depend on circuit parameters VDD temperature hellip)

Amplifier

Amplifier

bull Voltage amplifier

119907119900119906119905 = 119860119907 ∙ 119907119894119899

Vin ndashinputVout ndashoutputAv ndash voltage gain [db]Ri is input resistanceRo output resistanceRS source resistanceRL Load Resistance

119907119894119899 = 119907119904 ∙119877119894

119877119894 + 119877119878 119907119900119906119905 = 119860119907119907119894119899 ∙119877119871

119877119871+119877119874

119907119900119906119905 = 119860119907119907119904 ∙119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

119860119907119890119891119891 =119907119900119906119905

119907119904= 119860119907 ∙

119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

20 log 119860119907 [119889119861] decibels

Amplifier

Differential amplifier

Reject common noise

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992 = 1198811198941198991 + ∆ minus 1198811198941198992 minus ∆

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

Negative feedbackNegative feedback loop when the output of the system feed it back to control and reduce his activity

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

1198811198941198992 = 120573 ∙ 119881119900119906119905

Open loop equation

Negative feedback loop equation

rArr 119881119900119906119905= 119860 ∙ 1198811198941198991 minus 120573 ∙ 119881119900119906119905

119933119952119958119957 = 119933119946119951120783 ∙119912

120783 + 120631 ∙ 119912Blackrsquos Formula

β∙Agtgt1 Vout=Vin1βNegative feedback can increase the stability

Analog-to-digital converts

Noise accumulated in analog circuits

Solution Digital circuit

noise hampers our ability to distinguish between small differences in value mdasheg between 31V and 32V

Digital circuits1 Device of two states (OFFON) or (01)

119881119900119906119905 = 119881119874119873 119881119894119899gt 119881119905ℎ119881119900119891119891 119881119894119899 lt 119881119905ℎ

2 Computation arises from logic functions (Boolean algebra) using basic logic gates

Analog and DigitalSampling the analog signal (fs geBW)

Digitized signal sequence of numbers that represents the magnitudes of signal samples

Computation and signal processing in computers are often digital discrete in time

Converts Biological signal to electrical signal Requirements1 Specificity 2 Can track the changes in the biological signals faster than the biological

signal (BWBiosen gtBWSignal)3 Sensitivity4 linearity5 Noise

Biosenors

Transfer function of sensor

Linearization - Small Signal Analysis

Biosenors

119881 = 119891 119909

∆119907 =119889119891

119889119909119883119863

∙ ∆119883

119881 = 11988101198901199091198830

∆119881 =1

11988301198810119890

1198831198631198830 ∙ ∆119883

For example

119878119897119900119901119890 =∆119881

∆119883=

119881119863

1198830

First Order Biosensor

R and C are patristic

Biosenors

119868119861 = 119868119877 + 119868119862

119868119861 = 119891 119909

119868119877 =119881

119877 119868119862 = 119862

119889119881

119889119905

119862119889119881

119889119905+119881

119877= 119891 119909

119889119881

119889119905=

119891(119909)

119862minus

119881

119877119862

120591 = 119877119862

For constant IB

119881 119905 = 119868119861 ∙ 119877(1 minus 119890minus119905

120591)

119881 119905 = 120591 = 119868119861 ∙ 119877 1 minus 119890minus1 = 063119868119861 ∙ 119877

First Order Biosensor Frequency response

Biosenors

For constant IB

119889119881

119889119905=

119868119861119862minus119881

120591

119895120596119907 =119894119861119862minus119907

120591

119907 119895120596120591 + 1 = 119877 ∙ 119894119861

119907(120596) =119877 ∙ 119894119861(120596)

(119895120596120591 + 1)

120596119888 = 1120591

Fourier transform

119907(120596 = 0) = 119877 ∙ 119868119861

119907(120596 rarr infin) = 0

119907(120596) =119877 ∙ 119868119861

120596 1205961198882 + 1

119907(120596 = 120596119888) =119877 ∙ 119868119861

2

First Order Biosensor Frequency response

Biosenors

119907(120596) =119877 ∙ 119868119861

120596 1205961198882 + 1

120596119888 = 1119877119862

119907(120596 = 0) = 119877 ∙ 119868119861

119907(120596 rarr infin) = 0

Low pass filter every input signal with frequency higher ωC

will be cut-off

119907(120596 = 120596119888) =119877 ∙ 119868119861

2

log 1 2 asymp minus015

Low pass filter

Biosenors

ωb gt ωc V=0

sin 120596119887119905

Fourier transform

120575(120596 minus 120596119887)

ωb lt ωc V=Biological Signal

Therefore it is important to design the biosensor physical parameters to set the value of RC (eg dimensions )

119907(120596) =119877 ∙ 119894119861(120596)

(119895120596120591 + 1)

119907 120596 = 119894119861(120596) ∙ 119867119871119875119865(120596)

First Order Biosensor Frequency response

Biosenors

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=1jωC)

119881 = 119868119861 ∙ (119885119877||119885119862)

119881 = 119868119861119885119877 ∙ 119885119862119885119877 + 119885119862

119881 = 119868119861

119877 ∙1

119895120596119862

119877 +1

119895120596119862

119881 = 119868119861

119877 ∙1

119895120596119862119895120596119862119877 + 1

119895120596119862

119881 = 119868119861119877

119895120596119877119862 + 1

119881 = 119868119861119877

(120596119877119862)2+1

Biosensor converts one type of energy to electrical energyPhotodiode is pn junction that converts light to electrical energy

Biosenors -Photodiode

119862119889119881

119889119905+119881

119877= 119868119871119894119892ℎ119905 minus 119868119863119894119900119889119890

119868119863119894119900119889119890 = 119868119889119886119903119896(119890 119902119881 119870119879 minus 1)

Low pass filter

Light increases the

dark current

119877 =119889119881

119889119868=

119870119879

119902 ∙ 119868

C is the junction capacitance

Biosensor converts one type of energy to electrical energy

Piezoelectricity convert mechanical energy to electrical energyMeasure pressure and ultrasound waves

Biosenors - Piezoelectricity

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 deflectiondisplacement to charge generator

Kxq K is a constant depends on the material

X is a deflection

R Sensor leakage resistance

C Sensor capacitance

Piezoelectric crystal (quartz)

x

AC r0

Biosenors - Piezoelectricity

Changes in x cause to change in the charge and producing a current

Convert charge generator to current generator

119868119861 =119889119902

119889119905= 119870

119889119909

119889119905

119862119889119881

119889119905+119881

119877= 119870

119889119909

119889119905

119889119881

119889119905= 119870119878

119889119909

119889119905minus119881

120591

Ks = KC sensitivity Vm

= RC time constant

Fourier transform

119895120596119907 = 119870119878 ∙ 119895120596119909(120596) minus119907

120591

119907(120596) =119870119878119895120596120591

1 + 119895120596120591∙ 119909(120596)

Biosenors - Piezoelectricity

Ks = KC sensitivity Vm

= RC time constant

119907(120596) =119870119878 ∙ 120596 120596119888

120596 1205961198882 + 1

∙ 119909(120596)

ωb lt ωc V=0

ωb gt ωc V ~ x

High Pass filter (HPF)

Electrochemical Biosenors

Electrochemistry interfacing electrode with electrolyte Oxidation Ions that lose their electronsReduction Ions that gain new electrons

Convert biochemical reactions to electrical signal

Electrochemical Biosenors

Equivalent electrical circuit of electrochemical cells

Rct Charge transfer resistance due to transfer of electrons from ions to electrodeCdl Double layer capacitor ndashaccumulation of charge in the interface between the electrolyte and electrodeRS series resistance ndash electrolyte solution resistance

119885119890119902 = 119877119904 +119877119888119905

1 + 119895 ∙ 120596 ∙ 119877119888119905 ∙ 119862119889119897

LPF

Amplifier

An input signals (currentvoltage) is amplified to a larger output signals (currentvoltage)

Features1 Linearity (wide linear range)2 High Gain3 Vin=0 Vout=04 High signal to noise ratio5 Stability at time (One dominant half time)6 Stable gain (not depend on circuit parameters VDD temperature hellip)

Amplifier

Amplifier

bull Voltage amplifier

119907119900119906119905 = 119860119907 ∙ 119907119894119899

Vin ndashinputVout ndashoutputAv ndash voltage gain [db]Ri is input resistanceRo output resistanceRS source resistanceRL Load Resistance

119907119894119899 = 119907119904 ∙119877119894

119877119894 + 119877119878 119907119900119906119905 = 119860119907119907119894119899 ∙119877119871

119877119871+119877119874

119907119900119906119905 = 119860119907119907119904 ∙119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

119860119907119890119891119891 =119907119900119906119905

119907119904= 119860119907 ∙

119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

20 log 119860119907 [119889119861] decibels

Amplifier

Differential amplifier

Reject common noise

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992 = 1198811198941198991 + ∆ minus 1198811198941198992 minus ∆

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

Negative feedbackNegative feedback loop when the output of the system feed it back to control and reduce his activity

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

1198811198941198992 = 120573 ∙ 119881119900119906119905

Open loop equation

Negative feedback loop equation

rArr 119881119900119906119905= 119860 ∙ 1198811198941198991 minus 120573 ∙ 119881119900119906119905

119933119952119958119957 = 119933119946119951120783 ∙119912

120783 + 120631 ∙ 119912Blackrsquos Formula

β∙Agtgt1 Vout=Vin1βNegative feedback can increase the stability

Analog-to-digital converts

Noise accumulated in analog circuits

Solution Digital circuit

noise hampers our ability to distinguish between small differences in value mdasheg between 31V and 32V

Digital circuits1 Device of two states (OFFON) or (01)

119881119900119906119905 = 119881119874119873 119881119894119899gt 119881119905ℎ119881119900119891119891 119881119894119899 lt 119881119905ℎ

2 Computation arises from logic functions (Boolean algebra) using basic logic gates

Converts Biological signal to electrical signal Requirements1 Specificity 2 Can track the changes in the biological signals faster than the biological

signal (BWBiosen gtBWSignal)3 Sensitivity4 linearity5 Noise

Biosenors

Transfer function of sensor

Linearization - Small Signal Analysis

Biosenors

119881 = 119891 119909

∆119907 =119889119891

119889119909119883119863

∙ ∆119883

119881 = 11988101198901199091198830

∆119881 =1

11988301198810119890

1198831198631198830 ∙ ∆119883

For example

119878119897119900119901119890 =∆119881

∆119883=

119881119863

1198830

First Order Biosensor

R and C are patristic

Biosenors

119868119861 = 119868119877 + 119868119862

119868119861 = 119891 119909

119868119877 =119881

119877 119868119862 = 119862

119889119881

119889119905

119862119889119881

119889119905+119881

119877= 119891 119909

119889119881

119889119905=

119891(119909)

119862minus

119881

119877119862

120591 = 119877119862

For constant IB

119881 119905 = 119868119861 ∙ 119877(1 minus 119890minus119905

120591)

119881 119905 = 120591 = 119868119861 ∙ 119877 1 minus 119890minus1 = 063119868119861 ∙ 119877

First Order Biosensor Frequency response

Biosenors

For constant IB

119889119881

119889119905=

119868119861119862minus119881

120591

119895120596119907 =119894119861119862minus119907

120591

119907 119895120596120591 + 1 = 119877 ∙ 119894119861

119907(120596) =119877 ∙ 119894119861(120596)

(119895120596120591 + 1)

120596119888 = 1120591

Fourier transform

119907(120596 = 0) = 119877 ∙ 119868119861

119907(120596 rarr infin) = 0

119907(120596) =119877 ∙ 119868119861

120596 1205961198882 + 1

119907(120596 = 120596119888) =119877 ∙ 119868119861

2

First Order Biosensor Frequency response

Biosenors

119907(120596) =119877 ∙ 119868119861

120596 1205961198882 + 1

120596119888 = 1119877119862

119907(120596 = 0) = 119877 ∙ 119868119861

119907(120596 rarr infin) = 0

Low pass filter every input signal with frequency higher ωC

will be cut-off

119907(120596 = 120596119888) =119877 ∙ 119868119861

2

log 1 2 asymp minus015

Low pass filter

Biosenors

ωb gt ωc V=0

sin 120596119887119905

Fourier transform

120575(120596 minus 120596119887)

ωb lt ωc V=Biological Signal

Therefore it is important to design the biosensor physical parameters to set the value of RC (eg dimensions )

119907(120596) =119877 ∙ 119894119861(120596)

(119895120596120591 + 1)

119907 120596 = 119894119861(120596) ∙ 119867119871119875119865(120596)

First Order Biosensor Frequency response

Biosenors

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=1jωC)

119881 = 119868119861 ∙ (119885119877||119885119862)

119881 = 119868119861119885119877 ∙ 119885119862119885119877 + 119885119862

119881 = 119868119861

119877 ∙1

119895120596119862

119877 +1

119895120596119862

119881 = 119868119861

119877 ∙1

119895120596119862119895120596119862119877 + 1

119895120596119862

119881 = 119868119861119877

119895120596119877119862 + 1

119881 = 119868119861119877

(120596119877119862)2+1

Biosensor converts one type of energy to electrical energyPhotodiode is pn junction that converts light to electrical energy

Biosenors -Photodiode

119862119889119881

119889119905+119881

119877= 119868119871119894119892ℎ119905 minus 119868119863119894119900119889119890

119868119863119894119900119889119890 = 119868119889119886119903119896(119890 119902119881 119870119879 minus 1)

Low pass filter

Light increases the

dark current

119877 =119889119881

119889119868=

119870119879

119902 ∙ 119868

C is the junction capacitance

Biosensor converts one type of energy to electrical energy

Piezoelectricity convert mechanical energy to electrical energyMeasure pressure and ultrasound waves

Biosenors - Piezoelectricity

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 deflectiondisplacement to charge generator

Kxq K is a constant depends on the material

X is a deflection

R Sensor leakage resistance

C Sensor capacitance

Piezoelectric crystal (quartz)

x

AC r0

Biosenors - Piezoelectricity

Changes in x cause to change in the charge and producing a current

Convert charge generator to current generator

119868119861 =119889119902

119889119905= 119870

119889119909

119889119905

119862119889119881

119889119905+119881

119877= 119870

119889119909

119889119905

119889119881

119889119905= 119870119878

119889119909

119889119905minus119881

120591

Ks = KC sensitivity Vm

= RC time constant

Fourier transform

119895120596119907 = 119870119878 ∙ 119895120596119909(120596) minus119907

120591

119907(120596) =119870119878119895120596120591

1 + 119895120596120591∙ 119909(120596)

Biosenors - Piezoelectricity

Ks = KC sensitivity Vm

= RC time constant

119907(120596) =119870119878 ∙ 120596 120596119888

120596 1205961198882 + 1

∙ 119909(120596)

ωb lt ωc V=0

ωb gt ωc V ~ x

High Pass filter (HPF)

Electrochemical Biosenors

Electrochemistry interfacing electrode with electrolyte Oxidation Ions that lose their electronsReduction Ions that gain new electrons

Convert biochemical reactions to electrical signal

Electrochemical Biosenors

Equivalent electrical circuit of electrochemical cells

Rct Charge transfer resistance due to transfer of electrons from ions to electrodeCdl Double layer capacitor ndashaccumulation of charge in the interface between the electrolyte and electrodeRS series resistance ndash electrolyte solution resistance

119885119890119902 = 119877119904 +119877119888119905

1 + 119895 ∙ 120596 ∙ 119877119888119905 ∙ 119862119889119897

LPF

Amplifier

An input signals (currentvoltage) is amplified to a larger output signals (currentvoltage)

Features1 Linearity (wide linear range)2 High Gain3 Vin=0 Vout=04 High signal to noise ratio5 Stability at time (One dominant half time)6 Stable gain (not depend on circuit parameters VDD temperature hellip)

Amplifier

Amplifier

bull Voltage amplifier

119907119900119906119905 = 119860119907 ∙ 119907119894119899

Vin ndashinputVout ndashoutputAv ndash voltage gain [db]Ri is input resistanceRo output resistanceRS source resistanceRL Load Resistance

119907119894119899 = 119907119904 ∙119877119894

119877119894 + 119877119878 119907119900119906119905 = 119860119907119907119894119899 ∙119877119871

119877119871+119877119874

119907119900119906119905 = 119860119907119907119904 ∙119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

119860119907119890119891119891 =119907119900119906119905

119907119904= 119860119907 ∙

119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

20 log 119860119907 [119889119861] decibels

Amplifier

Differential amplifier

Reject common noise

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992 = 1198811198941198991 + ∆ minus 1198811198941198992 minus ∆

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

Negative feedbackNegative feedback loop when the output of the system feed it back to control and reduce his activity

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

1198811198941198992 = 120573 ∙ 119881119900119906119905

Open loop equation

Negative feedback loop equation

rArr 119881119900119906119905= 119860 ∙ 1198811198941198991 minus 120573 ∙ 119881119900119906119905

119933119952119958119957 = 119933119946119951120783 ∙119912

120783 + 120631 ∙ 119912Blackrsquos Formula

β∙Agtgt1 Vout=Vin1βNegative feedback can increase the stability

Analog-to-digital converts

Noise accumulated in analog circuits

Solution Digital circuit

noise hampers our ability to distinguish between small differences in value mdasheg between 31V and 32V

Digital circuits1 Device of two states (OFFON) or (01)

119881119900119906119905 = 119881119874119873 119881119894119899gt 119881119905ℎ119881119900119891119891 119881119894119899 lt 119881119905ℎ

2 Computation arises from logic functions (Boolean algebra) using basic logic gates

Linearization - Small Signal Analysis

Biosenors

119881 = 119891 119909

∆119907 =119889119891

119889119909119883119863

∙ ∆119883

119881 = 11988101198901199091198830

∆119881 =1

11988301198810119890

1198831198631198830 ∙ ∆119883

For example

119878119897119900119901119890 =∆119881

∆119883=

119881119863

1198830

First Order Biosensor

R and C are patristic

Biosenors

119868119861 = 119868119877 + 119868119862

119868119861 = 119891 119909

119868119877 =119881

119877 119868119862 = 119862

119889119881

119889119905

119862119889119881

119889119905+119881

119877= 119891 119909

119889119881

119889119905=

119891(119909)

119862minus

119881

119877119862

120591 = 119877119862

For constant IB

119881 119905 = 119868119861 ∙ 119877(1 minus 119890minus119905

120591)

119881 119905 = 120591 = 119868119861 ∙ 119877 1 minus 119890minus1 = 063119868119861 ∙ 119877

First Order Biosensor Frequency response

Biosenors

For constant IB

119889119881

119889119905=

119868119861119862minus119881

120591

119895120596119907 =119894119861119862minus119907

120591

119907 119895120596120591 + 1 = 119877 ∙ 119894119861

119907(120596) =119877 ∙ 119894119861(120596)

(119895120596120591 + 1)

120596119888 = 1120591

Fourier transform

119907(120596 = 0) = 119877 ∙ 119868119861

119907(120596 rarr infin) = 0

119907(120596) =119877 ∙ 119868119861

120596 1205961198882 + 1

119907(120596 = 120596119888) =119877 ∙ 119868119861

2

First Order Biosensor Frequency response

Biosenors

119907(120596) =119877 ∙ 119868119861

120596 1205961198882 + 1

120596119888 = 1119877119862

119907(120596 = 0) = 119877 ∙ 119868119861

119907(120596 rarr infin) = 0

Low pass filter every input signal with frequency higher ωC

will be cut-off

119907(120596 = 120596119888) =119877 ∙ 119868119861

2

log 1 2 asymp minus015

Low pass filter

Biosenors

ωb gt ωc V=0

sin 120596119887119905

Fourier transform

120575(120596 minus 120596119887)

ωb lt ωc V=Biological Signal

Therefore it is important to design the biosensor physical parameters to set the value of RC (eg dimensions )

119907(120596) =119877 ∙ 119894119861(120596)

(119895120596120591 + 1)

119907 120596 = 119894119861(120596) ∙ 119867119871119875119865(120596)

First Order Biosensor Frequency response

Biosenors

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=1jωC)

119881 = 119868119861 ∙ (119885119877||119885119862)

119881 = 119868119861119885119877 ∙ 119885119862119885119877 + 119885119862

119881 = 119868119861

119877 ∙1

119895120596119862

119877 +1

119895120596119862

119881 = 119868119861

119877 ∙1

119895120596119862119895120596119862119877 + 1

119895120596119862

119881 = 119868119861119877

119895120596119877119862 + 1

119881 = 119868119861119877

(120596119877119862)2+1

Biosensor converts one type of energy to electrical energyPhotodiode is pn junction that converts light to electrical energy

Biosenors -Photodiode

119862119889119881

119889119905+119881

119877= 119868119871119894119892ℎ119905 minus 119868119863119894119900119889119890

119868119863119894119900119889119890 = 119868119889119886119903119896(119890 119902119881 119870119879 minus 1)

Low pass filter

Light increases the

dark current

119877 =119889119881

119889119868=

119870119879

119902 ∙ 119868

C is the junction capacitance

Biosensor converts one type of energy to electrical energy

Piezoelectricity convert mechanical energy to electrical energyMeasure pressure and ultrasound waves

Biosenors - Piezoelectricity

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 deflectiondisplacement to charge generator

Kxq K is a constant depends on the material

X is a deflection

R Sensor leakage resistance

C Sensor capacitance

Piezoelectric crystal (quartz)

x

AC r0

Biosenors - Piezoelectricity

Changes in x cause to change in the charge and producing a current

Convert charge generator to current generator

119868119861 =119889119902

119889119905= 119870

119889119909

119889119905

119862119889119881

119889119905+119881

119877= 119870

119889119909

119889119905

119889119881

119889119905= 119870119878

119889119909

119889119905minus119881

120591

Ks = KC sensitivity Vm

= RC time constant

Fourier transform

119895120596119907 = 119870119878 ∙ 119895120596119909(120596) minus119907

120591

119907(120596) =119870119878119895120596120591

1 + 119895120596120591∙ 119909(120596)

Biosenors - Piezoelectricity

Ks = KC sensitivity Vm

= RC time constant

119907(120596) =119870119878 ∙ 120596 120596119888

120596 1205961198882 + 1

∙ 119909(120596)

ωb lt ωc V=0

ωb gt ωc V ~ x

High Pass filter (HPF)

Electrochemical Biosenors

Electrochemistry interfacing electrode with electrolyte Oxidation Ions that lose their electronsReduction Ions that gain new electrons

Convert biochemical reactions to electrical signal

Electrochemical Biosenors

Equivalent electrical circuit of electrochemical cells

Rct Charge transfer resistance due to transfer of electrons from ions to electrodeCdl Double layer capacitor ndashaccumulation of charge in the interface between the electrolyte and electrodeRS series resistance ndash electrolyte solution resistance

119885119890119902 = 119877119904 +119877119888119905

1 + 119895 ∙ 120596 ∙ 119877119888119905 ∙ 119862119889119897

LPF

Amplifier

An input signals (currentvoltage) is amplified to a larger output signals (currentvoltage)

Features1 Linearity (wide linear range)2 High Gain3 Vin=0 Vout=04 High signal to noise ratio5 Stability at time (One dominant half time)6 Stable gain (not depend on circuit parameters VDD temperature hellip)

Amplifier

Amplifier

bull Voltage amplifier

119907119900119906119905 = 119860119907 ∙ 119907119894119899

Vin ndashinputVout ndashoutputAv ndash voltage gain [db]Ri is input resistanceRo output resistanceRS source resistanceRL Load Resistance

119907119894119899 = 119907119904 ∙119877119894

119877119894 + 119877119878 119907119900119906119905 = 119860119907119907119894119899 ∙119877119871

119877119871+119877119874

119907119900119906119905 = 119860119907119907119904 ∙119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

119860119907119890119891119891 =119907119900119906119905

119907119904= 119860119907 ∙

119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

20 log 119860119907 [119889119861] decibels

Amplifier

Differential amplifier

Reject common noise

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992 = 1198811198941198991 + ∆ minus 1198811198941198992 minus ∆

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

Negative feedbackNegative feedback loop when the output of the system feed it back to control and reduce his activity

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

1198811198941198992 = 120573 ∙ 119881119900119906119905

Open loop equation

Negative feedback loop equation

rArr 119881119900119906119905= 119860 ∙ 1198811198941198991 minus 120573 ∙ 119881119900119906119905

119933119952119958119957 = 119933119946119951120783 ∙119912

120783 + 120631 ∙ 119912Blackrsquos Formula

β∙Agtgt1 Vout=Vin1βNegative feedback can increase the stability

Analog-to-digital converts

Noise accumulated in analog circuits

Solution Digital circuit

noise hampers our ability to distinguish between small differences in value mdasheg between 31V and 32V

Digital circuits1 Device of two states (OFFON) or (01)

119881119900119906119905 = 119881119874119873 119881119894119899gt 119881119905ℎ119881119900119891119891 119881119894119899 lt 119881119905ℎ

2 Computation arises from logic functions (Boolean algebra) using basic logic gates

First Order Biosensor

R and C are patristic

Biosenors

119868119861 = 119868119877 + 119868119862

119868119861 = 119891 119909

119868119877 =119881

119877 119868119862 = 119862

119889119881

119889119905

119862119889119881

119889119905+119881

119877= 119891 119909

119889119881

119889119905=

119891(119909)

119862minus

119881

119877119862

120591 = 119877119862

For constant IB

119881 119905 = 119868119861 ∙ 119877(1 minus 119890minus119905

120591)

119881 119905 = 120591 = 119868119861 ∙ 119877 1 minus 119890minus1 = 063119868119861 ∙ 119877

First Order Biosensor Frequency response

Biosenors

For constant IB

119889119881

119889119905=

119868119861119862minus119881

120591

119895120596119907 =119894119861119862minus119907

120591

119907 119895120596120591 + 1 = 119877 ∙ 119894119861

119907(120596) =119877 ∙ 119894119861(120596)

(119895120596120591 + 1)

120596119888 = 1120591

Fourier transform

119907(120596 = 0) = 119877 ∙ 119868119861

119907(120596 rarr infin) = 0

119907(120596) =119877 ∙ 119868119861

120596 1205961198882 + 1

119907(120596 = 120596119888) =119877 ∙ 119868119861

2

First Order Biosensor Frequency response

Biosenors

119907(120596) =119877 ∙ 119868119861

120596 1205961198882 + 1

120596119888 = 1119877119862

119907(120596 = 0) = 119877 ∙ 119868119861

119907(120596 rarr infin) = 0

Low pass filter every input signal with frequency higher ωC

will be cut-off

119907(120596 = 120596119888) =119877 ∙ 119868119861

2

log 1 2 asymp minus015

Low pass filter

Biosenors

ωb gt ωc V=0

sin 120596119887119905

Fourier transform

120575(120596 minus 120596119887)

ωb lt ωc V=Biological Signal

Therefore it is important to design the biosensor physical parameters to set the value of RC (eg dimensions )

119907(120596) =119877 ∙ 119894119861(120596)

(119895120596120591 + 1)

119907 120596 = 119894119861(120596) ∙ 119867119871119875119865(120596)

First Order Biosensor Frequency response

Biosenors

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=1jωC)

119881 = 119868119861 ∙ (119885119877||119885119862)

119881 = 119868119861119885119877 ∙ 119885119862119885119877 + 119885119862

119881 = 119868119861

119877 ∙1

119895120596119862

119877 +1

119895120596119862

119881 = 119868119861

119877 ∙1

119895120596119862119895120596119862119877 + 1

119895120596119862

119881 = 119868119861119877

119895120596119877119862 + 1

119881 = 119868119861119877

(120596119877119862)2+1

Biosensor converts one type of energy to electrical energyPhotodiode is pn junction that converts light to electrical energy

Biosenors -Photodiode

119862119889119881

119889119905+119881

119877= 119868119871119894119892ℎ119905 minus 119868119863119894119900119889119890

119868119863119894119900119889119890 = 119868119889119886119903119896(119890 119902119881 119870119879 minus 1)

Low pass filter

Light increases the

dark current

119877 =119889119881

119889119868=

119870119879

119902 ∙ 119868

C is the junction capacitance

Biosensor converts one type of energy to electrical energy

Piezoelectricity convert mechanical energy to electrical energyMeasure pressure and ultrasound waves

Biosenors - Piezoelectricity

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 deflectiondisplacement to charge generator

Kxq K is a constant depends on the material

X is a deflection

R Sensor leakage resistance

C Sensor capacitance

Piezoelectric crystal (quartz)

x

AC r0

Biosenors - Piezoelectricity

Changes in x cause to change in the charge and producing a current

Convert charge generator to current generator

119868119861 =119889119902

119889119905= 119870

119889119909

119889119905

119862119889119881

119889119905+119881

119877= 119870

119889119909

119889119905

119889119881

119889119905= 119870119878

119889119909

119889119905minus119881

120591

Ks = KC sensitivity Vm

= RC time constant

Fourier transform

119895120596119907 = 119870119878 ∙ 119895120596119909(120596) minus119907

120591

119907(120596) =119870119878119895120596120591

1 + 119895120596120591∙ 119909(120596)

Biosenors - Piezoelectricity

Ks = KC sensitivity Vm

= RC time constant

119907(120596) =119870119878 ∙ 120596 120596119888

120596 1205961198882 + 1

∙ 119909(120596)

ωb lt ωc V=0

ωb gt ωc V ~ x

High Pass filter (HPF)

Electrochemical Biosenors

Electrochemistry interfacing electrode with electrolyte Oxidation Ions that lose their electronsReduction Ions that gain new electrons

Convert biochemical reactions to electrical signal

Electrochemical Biosenors

Equivalent electrical circuit of electrochemical cells

Rct Charge transfer resistance due to transfer of electrons from ions to electrodeCdl Double layer capacitor ndashaccumulation of charge in the interface between the electrolyte and electrodeRS series resistance ndash electrolyte solution resistance

119885119890119902 = 119877119904 +119877119888119905

1 + 119895 ∙ 120596 ∙ 119877119888119905 ∙ 119862119889119897

LPF

Amplifier

An input signals (currentvoltage) is amplified to a larger output signals (currentvoltage)

Features1 Linearity (wide linear range)2 High Gain3 Vin=0 Vout=04 High signal to noise ratio5 Stability at time (One dominant half time)6 Stable gain (not depend on circuit parameters VDD temperature hellip)

Amplifier

Amplifier

bull Voltage amplifier

119907119900119906119905 = 119860119907 ∙ 119907119894119899

Vin ndashinputVout ndashoutputAv ndash voltage gain [db]Ri is input resistanceRo output resistanceRS source resistanceRL Load Resistance

119907119894119899 = 119907119904 ∙119877119894

119877119894 + 119877119878 119907119900119906119905 = 119860119907119907119894119899 ∙119877119871

119877119871+119877119874

119907119900119906119905 = 119860119907119907119904 ∙119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

119860119907119890119891119891 =119907119900119906119905

119907119904= 119860119907 ∙

119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

20 log 119860119907 [119889119861] decibels

Amplifier

Differential amplifier

Reject common noise

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992 = 1198811198941198991 + ∆ minus 1198811198941198992 minus ∆

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

Negative feedbackNegative feedback loop when the output of the system feed it back to control and reduce his activity

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

1198811198941198992 = 120573 ∙ 119881119900119906119905

Open loop equation

Negative feedback loop equation

rArr 119881119900119906119905= 119860 ∙ 1198811198941198991 minus 120573 ∙ 119881119900119906119905

119933119952119958119957 = 119933119946119951120783 ∙119912

120783 + 120631 ∙ 119912Blackrsquos Formula

β∙Agtgt1 Vout=Vin1βNegative feedback can increase the stability

Analog-to-digital converts

Noise accumulated in analog circuits

Solution Digital circuit

noise hampers our ability to distinguish between small differences in value mdasheg between 31V and 32V

Digital circuits1 Device of two states (OFFON) or (01)

119881119900119906119905 = 119881119874119873 119881119894119899gt 119881119905ℎ119881119900119891119891 119881119894119899 lt 119881119905ℎ

2 Computation arises from logic functions (Boolean algebra) using basic logic gates

First Order Biosensor Frequency response

Biosenors

For constant IB

119889119881

119889119905=

119868119861119862minus119881

120591

119895120596119907 =119894119861119862minus119907

120591

119907 119895120596120591 + 1 = 119877 ∙ 119894119861

119907(120596) =119877 ∙ 119894119861(120596)

(119895120596120591 + 1)

120596119888 = 1120591

Fourier transform

119907(120596 = 0) = 119877 ∙ 119868119861

119907(120596 rarr infin) = 0

119907(120596) =119877 ∙ 119868119861

120596 1205961198882 + 1

119907(120596 = 120596119888) =119877 ∙ 119868119861

2

First Order Biosensor Frequency response

Biosenors

119907(120596) =119877 ∙ 119868119861

120596 1205961198882 + 1

120596119888 = 1119877119862

119907(120596 = 0) = 119877 ∙ 119868119861

119907(120596 rarr infin) = 0

Low pass filter every input signal with frequency higher ωC

will be cut-off

119907(120596 = 120596119888) =119877 ∙ 119868119861

2

log 1 2 asymp minus015

Low pass filter

Biosenors

ωb gt ωc V=0

sin 120596119887119905

Fourier transform

120575(120596 minus 120596119887)

ωb lt ωc V=Biological Signal

Therefore it is important to design the biosensor physical parameters to set the value of RC (eg dimensions )

119907(120596) =119877 ∙ 119894119861(120596)

(119895120596120591 + 1)

119907 120596 = 119894119861(120596) ∙ 119867119871119875119865(120596)

First Order Biosensor Frequency response

Biosenors

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=1jωC)

119881 = 119868119861 ∙ (119885119877||119885119862)

119881 = 119868119861119885119877 ∙ 119885119862119885119877 + 119885119862

119881 = 119868119861

119877 ∙1

119895120596119862

119877 +1

119895120596119862

119881 = 119868119861

119877 ∙1

119895120596119862119895120596119862119877 + 1

119895120596119862

119881 = 119868119861119877

119895120596119877119862 + 1

119881 = 119868119861119877

(120596119877119862)2+1

Biosensor converts one type of energy to electrical energyPhotodiode is pn junction that converts light to electrical energy

Biosenors -Photodiode

119862119889119881

119889119905+119881

119877= 119868119871119894119892ℎ119905 minus 119868119863119894119900119889119890

119868119863119894119900119889119890 = 119868119889119886119903119896(119890 119902119881 119870119879 minus 1)

Low pass filter

Light increases the

dark current

119877 =119889119881

119889119868=

119870119879

119902 ∙ 119868

C is the junction capacitance

Biosensor converts one type of energy to electrical energy

Piezoelectricity convert mechanical energy to electrical energyMeasure pressure and ultrasound waves

Biosenors - Piezoelectricity

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 deflectiondisplacement to charge generator

Kxq K is a constant depends on the material

X is a deflection

R Sensor leakage resistance

C Sensor capacitance

Piezoelectric crystal (quartz)

x

AC r0

Biosenors - Piezoelectricity

Changes in x cause to change in the charge and producing a current

Convert charge generator to current generator

119868119861 =119889119902

119889119905= 119870

119889119909

119889119905

119862119889119881

119889119905+119881

119877= 119870

119889119909

119889119905

119889119881

119889119905= 119870119878

119889119909

119889119905minus119881

120591

Ks = KC sensitivity Vm

= RC time constant

Fourier transform

119895120596119907 = 119870119878 ∙ 119895120596119909(120596) minus119907

120591

119907(120596) =119870119878119895120596120591

1 + 119895120596120591∙ 119909(120596)

Biosenors - Piezoelectricity

Ks = KC sensitivity Vm

= RC time constant

119907(120596) =119870119878 ∙ 120596 120596119888

120596 1205961198882 + 1

∙ 119909(120596)

ωb lt ωc V=0

ωb gt ωc V ~ x

High Pass filter (HPF)

Electrochemical Biosenors

Electrochemistry interfacing electrode with electrolyte Oxidation Ions that lose their electronsReduction Ions that gain new electrons

Convert biochemical reactions to electrical signal

Electrochemical Biosenors

Equivalent electrical circuit of electrochemical cells

Rct Charge transfer resistance due to transfer of electrons from ions to electrodeCdl Double layer capacitor ndashaccumulation of charge in the interface between the electrolyte and electrodeRS series resistance ndash electrolyte solution resistance

119885119890119902 = 119877119904 +119877119888119905

1 + 119895 ∙ 120596 ∙ 119877119888119905 ∙ 119862119889119897

LPF

Amplifier

An input signals (currentvoltage) is amplified to a larger output signals (currentvoltage)

Features1 Linearity (wide linear range)2 High Gain3 Vin=0 Vout=04 High signal to noise ratio5 Stability at time (One dominant half time)6 Stable gain (not depend on circuit parameters VDD temperature hellip)

Amplifier

Amplifier

bull Voltage amplifier

119907119900119906119905 = 119860119907 ∙ 119907119894119899

Vin ndashinputVout ndashoutputAv ndash voltage gain [db]Ri is input resistanceRo output resistanceRS source resistanceRL Load Resistance

119907119894119899 = 119907119904 ∙119877119894

119877119894 + 119877119878 119907119900119906119905 = 119860119907119907119894119899 ∙119877119871

119877119871+119877119874

119907119900119906119905 = 119860119907119907119904 ∙119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

119860119907119890119891119891 =119907119900119906119905

119907119904= 119860119907 ∙

119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

20 log 119860119907 [119889119861] decibels

Amplifier

Differential amplifier

Reject common noise

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992 = 1198811198941198991 + ∆ minus 1198811198941198992 minus ∆

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

Negative feedbackNegative feedback loop when the output of the system feed it back to control and reduce his activity

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

1198811198941198992 = 120573 ∙ 119881119900119906119905

Open loop equation

Negative feedback loop equation

rArr 119881119900119906119905= 119860 ∙ 1198811198941198991 minus 120573 ∙ 119881119900119906119905

119933119952119958119957 = 119933119946119951120783 ∙119912

120783 + 120631 ∙ 119912Blackrsquos Formula

β∙Agtgt1 Vout=Vin1βNegative feedback can increase the stability

Analog-to-digital converts

Noise accumulated in analog circuits

Solution Digital circuit

noise hampers our ability to distinguish between small differences in value mdasheg between 31V and 32V

Digital circuits1 Device of two states (OFFON) or (01)

119881119900119906119905 = 119881119874119873 119881119894119899gt 119881119905ℎ119881119900119891119891 119881119894119899 lt 119881119905ℎ

2 Computation arises from logic functions (Boolean algebra) using basic logic gates

First Order Biosensor Frequency response

Biosenors

119907(120596) =119877 ∙ 119868119861

120596 1205961198882 + 1

120596119888 = 1119877119862

119907(120596 = 0) = 119877 ∙ 119868119861

119907(120596 rarr infin) = 0

Low pass filter every input signal with frequency higher ωC

will be cut-off

119907(120596 = 120596119888) =119877 ∙ 119868119861

2

log 1 2 asymp minus015

Low pass filter

Biosenors

ωb gt ωc V=0

sin 120596119887119905

Fourier transform

120575(120596 minus 120596119887)

ωb lt ωc V=Biological Signal

Therefore it is important to design the biosensor physical parameters to set the value of RC (eg dimensions )

119907(120596) =119877 ∙ 119894119861(120596)

(119895120596120591 + 1)

119907 120596 = 119894119861(120596) ∙ 119867119871119875119865(120596)

First Order Biosensor Frequency response

Biosenors

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=1jωC)

119881 = 119868119861 ∙ (119885119877||119885119862)

119881 = 119868119861119885119877 ∙ 119885119862119885119877 + 119885119862

119881 = 119868119861

119877 ∙1

119895120596119862

119877 +1

119895120596119862

119881 = 119868119861

119877 ∙1

119895120596119862119895120596119862119877 + 1

119895120596119862

119881 = 119868119861119877

119895120596119877119862 + 1

119881 = 119868119861119877

(120596119877119862)2+1

Biosensor converts one type of energy to electrical energyPhotodiode is pn junction that converts light to electrical energy

Biosenors -Photodiode

119862119889119881

119889119905+119881

119877= 119868119871119894119892ℎ119905 minus 119868119863119894119900119889119890

119868119863119894119900119889119890 = 119868119889119886119903119896(119890 119902119881 119870119879 minus 1)

Low pass filter

Light increases the

dark current

119877 =119889119881

119889119868=

119870119879

119902 ∙ 119868

C is the junction capacitance

Biosensor converts one type of energy to electrical energy

Piezoelectricity convert mechanical energy to electrical energyMeasure pressure and ultrasound waves

Biosenors - Piezoelectricity

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 deflectiondisplacement to charge generator

Kxq K is a constant depends on the material

X is a deflection

R Sensor leakage resistance

C Sensor capacitance

Piezoelectric crystal (quartz)

x

AC r0

Biosenors - Piezoelectricity

Changes in x cause to change in the charge and producing a current

Convert charge generator to current generator

119868119861 =119889119902

119889119905= 119870

119889119909

119889119905

119862119889119881

119889119905+119881

119877= 119870

119889119909

119889119905

119889119881

119889119905= 119870119878

119889119909

119889119905minus119881

120591

Ks = KC sensitivity Vm

= RC time constant

Fourier transform

119895120596119907 = 119870119878 ∙ 119895120596119909(120596) minus119907

120591

119907(120596) =119870119878119895120596120591

1 + 119895120596120591∙ 119909(120596)

Biosenors - Piezoelectricity

Ks = KC sensitivity Vm

= RC time constant

119907(120596) =119870119878 ∙ 120596 120596119888

120596 1205961198882 + 1

∙ 119909(120596)

ωb lt ωc V=0

ωb gt ωc V ~ x

High Pass filter (HPF)

Electrochemical Biosenors

Electrochemistry interfacing electrode with electrolyte Oxidation Ions that lose their electronsReduction Ions that gain new electrons

Convert biochemical reactions to electrical signal

Electrochemical Biosenors

Equivalent electrical circuit of electrochemical cells

Rct Charge transfer resistance due to transfer of electrons from ions to electrodeCdl Double layer capacitor ndashaccumulation of charge in the interface between the electrolyte and electrodeRS series resistance ndash electrolyte solution resistance

119885119890119902 = 119877119904 +119877119888119905

1 + 119895 ∙ 120596 ∙ 119877119888119905 ∙ 119862119889119897

LPF

Amplifier

An input signals (currentvoltage) is amplified to a larger output signals (currentvoltage)

Features1 Linearity (wide linear range)2 High Gain3 Vin=0 Vout=04 High signal to noise ratio5 Stability at time (One dominant half time)6 Stable gain (not depend on circuit parameters VDD temperature hellip)

Amplifier

Amplifier

bull Voltage amplifier

119907119900119906119905 = 119860119907 ∙ 119907119894119899

Vin ndashinputVout ndashoutputAv ndash voltage gain [db]Ri is input resistanceRo output resistanceRS source resistanceRL Load Resistance

119907119894119899 = 119907119904 ∙119877119894

119877119894 + 119877119878 119907119900119906119905 = 119860119907119907119894119899 ∙119877119871

119877119871+119877119874

119907119900119906119905 = 119860119907119907119904 ∙119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

119860119907119890119891119891 =119907119900119906119905

119907119904= 119860119907 ∙

119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

20 log 119860119907 [119889119861] decibels

Amplifier

Differential amplifier

Reject common noise

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992 = 1198811198941198991 + ∆ minus 1198811198941198992 minus ∆

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

Negative feedbackNegative feedback loop when the output of the system feed it back to control and reduce his activity

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

1198811198941198992 = 120573 ∙ 119881119900119906119905

Open loop equation

Negative feedback loop equation

rArr 119881119900119906119905= 119860 ∙ 1198811198941198991 minus 120573 ∙ 119881119900119906119905

119933119952119958119957 = 119933119946119951120783 ∙119912

120783 + 120631 ∙ 119912Blackrsquos Formula

β∙Agtgt1 Vout=Vin1βNegative feedback can increase the stability

Analog-to-digital converts

Noise accumulated in analog circuits

Solution Digital circuit

noise hampers our ability to distinguish between small differences in value mdasheg between 31V and 32V

Digital circuits1 Device of two states (OFFON) or (01)

119881119900119906119905 = 119881119874119873 119881119894119899gt 119881119905ℎ119881119900119891119891 119881119894119899 lt 119881119905ℎ

2 Computation arises from logic functions (Boolean algebra) using basic logic gates

Low pass filter

Biosenors

ωb gt ωc V=0

sin 120596119887119905

Fourier transform

120575(120596 minus 120596119887)

ωb lt ωc V=Biological Signal

Therefore it is important to design the biosensor physical parameters to set the value of RC (eg dimensions )

119907(120596) =119877 ∙ 119894119861(120596)

(119895120596120591 + 1)

119907 120596 = 119894119861(120596) ∙ 119867119871119875119865(120596)

First Order Biosensor Frequency response

Biosenors

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=1jωC)

119881 = 119868119861 ∙ (119885119877||119885119862)

119881 = 119868119861119885119877 ∙ 119885119862119885119877 + 119885119862

119881 = 119868119861

119877 ∙1

119895120596119862

119877 +1

119895120596119862

119881 = 119868119861

119877 ∙1

119895120596119862119895120596119862119877 + 1

119895120596119862

119881 = 119868119861119877

119895120596119877119862 + 1

119881 = 119868119861119877

(120596119877119862)2+1

Biosensor converts one type of energy to electrical energyPhotodiode is pn junction that converts light to electrical energy

Biosenors -Photodiode

119862119889119881

119889119905+119881

119877= 119868119871119894119892ℎ119905 minus 119868119863119894119900119889119890

119868119863119894119900119889119890 = 119868119889119886119903119896(119890 119902119881 119870119879 minus 1)

Low pass filter

Light increases the

dark current

119877 =119889119881

119889119868=

119870119879

119902 ∙ 119868

C is the junction capacitance

Biosensor converts one type of energy to electrical energy

Piezoelectricity convert mechanical energy to electrical energyMeasure pressure and ultrasound waves

Biosenors - Piezoelectricity

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 deflectiondisplacement to charge generator

Kxq K is a constant depends on the material

X is a deflection

R Sensor leakage resistance

C Sensor capacitance

Piezoelectric crystal (quartz)

x

AC r0

Biosenors - Piezoelectricity

Changes in x cause to change in the charge and producing a current

Convert charge generator to current generator

119868119861 =119889119902

119889119905= 119870

119889119909

119889119905

119862119889119881

119889119905+119881

119877= 119870

119889119909

119889119905

119889119881

119889119905= 119870119878

119889119909

119889119905minus119881

120591

Ks = KC sensitivity Vm

= RC time constant

Fourier transform

119895120596119907 = 119870119878 ∙ 119895120596119909(120596) minus119907

120591

119907(120596) =119870119878119895120596120591

1 + 119895120596120591∙ 119909(120596)

Biosenors - Piezoelectricity

Ks = KC sensitivity Vm

= RC time constant

119907(120596) =119870119878 ∙ 120596 120596119888

120596 1205961198882 + 1

∙ 119909(120596)

ωb lt ωc V=0

ωb gt ωc V ~ x

High Pass filter (HPF)

Electrochemical Biosenors

Electrochemistry interfacing electrode with electrolyte Oxidation Ions that lose their electronsReduction Ions that gain new electrons

Convert biochemical reactions to electrical signal

Electrochemical Biosenors

Equivalent electrical circuit of electrochemical cells

Rct Charge transfer resistance due to transfer of electrons from ions to electrodeCdl Double layer capacitor ndashaccumulation of charge in the interface between the electrolyte and electrodeRS series resistance ndash electrolyte solution resistance

119885119890119902 = 119877119904 +119877119888119905

1 + 119895 ∙ 120596 ∙ 119877119888119905 ∙ 119862119889119897

LPF

Amplifier

An input signals (currentvoltage) is amplified to a larger output signals (currentvoltage)

Features1 Linearity (wide linear range)2 High Gain3 Vin=0 Vout=04 High signal to noise ratio5 Stability at time (One dominant half time)6 Stable gain (not depend on circuit parameters VDD temperature hellip)

Amplifier

Amplifier

bull Voltage amplifier

119907119900119906119905 = 119860119907 ∙ 119907119894119899

Vin ndashinputVout ndashoutputAv ndash voltage gain [db]Ri is input resistanceRo output resistanceRS source resistanceRL Load Resistance

119907119894119899 = 119907119904 ∙119877119894

119877119894 + 119877119878 119907119900119906119905 = 119860119907119907119894119899 ∙119877119871

119877119871+119877119874

119907119900119906119905 = 119860119907119907119904 ∙119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

119860119907119890119891119891 =119907119900119906119905

119907119904= 119860119907 ∙

119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

20 log 119860119907 [119889119861] decibels

Amplifier

Differential amplifier

Reject common noise

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992 = 1198811198941198991 + ∆ minus 1198811198941198992 minus ∆

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

Negative feedbackNegative feedback loop when the output of the system feed it back to control and reduce his activity

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

1198811198941198992 = 120573 ∙ 119881119900119906119905

Open loop equation

Negative feedback loop equation

rArr 119881119900119906119905= 119860 ∙ 1198811198941198991 minus 120573 ∙ 119881119900119906119905

119933119952119958119957 = 119933119946119951120783 ∙119912

120783 + 120631 ∙ 119912Blackrsquos Formula

β∙Agtgt1 Vout=Vin1βNegative feedback can increase the stability

Analog-to-digital converts

Noise accumulated in analog circuits

Solution Digital circuit

noise hampers our ability to distinguish between small differences in value mdasheg between 31V and 32V

Digital circuits1 Device of two states (OFFON) or (01)

119881119900119906119905 = 119881119874119873 119881119894119899gt 119881119905ℎ119881119900119891119891 119881119894119899 lt 119881119905ℎ

2 Computation arises from logic functions (Boolean algebra) using basic logic gates

First Order Biosensor Frequency response

Biosenors

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=1jωC)

119881 = 119868119861 ∙ (119885119877||119885119862)

119881 = 119868119861119885119877 ∙ 119885119862119885119877 + 119885119862

119881 = 119868119861

119877 ∙1

119895120596119862

119877 +1

119895120596119862

119881 = 119868119861

119877 ∙1

119895120596119862119895120596119862119877 + 1

119895120596119862

119881 = 119868119861119877

119895120596119877119862 + 1

119881 = 119868119861119877

(120596119877119862)2+1

Biosensor converts one type of energy to electrical energyPhotodiode is pn junction that converts light to electrical energy

Biosenors -Photodiode

119862119889119881

119889119905+119881

119877= 119868119871119894119892ℎ119905 minus 119868119863119894119900119889119890

119868119863119894119900119889119890 = 119868119889119886119903119896(119890 119902119881 119870119879 minus 1)

Low pass filter

Light increases the

dark current

119877 =119889119881

119889119868=

119870119879

119902 ∙ 119868

C is the junction capacitance

Biosensor converts one type of energy to electrical energy

Piezoelectricity convert mechanical energy to electrical energyMeasure pressure and ultrasound waves

Biosenors - Piezoelectricity

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 deflectiondisplacement to charge generator

Kxq K is a constant depends on the material

X is a deflection

R Sensor leakage resistance

C Sensor capacitance

Piezoelectric crystal (quartz)

x

AC r0

Biosenors - Piezoelectricity

Changes in x cause to change in the charge and producing a current

Convert charge generator to current generator

119868119861 =119889119902

119889119905= 119870

119889119909

119889119905

119862119889119881

119889119905+119881

119877= 119870

119889119909

119889119905

119889119881

119889119905= 119870119878

119889119909

119889119905minus119881

120591

Ks = KC sensitivity Vm

= RC time constant

Fourier transform

119895120596119907 = 119870119878 ∙ 119895120596119909(120596) minus119907

120591

119907(120596) =119870119878119895120596120591

1 + 119895120596120591∙ 119909(120596)

Biosenors - Piezoelectricity

Ks = KC sensitivity Vm

= RC time constant

119907(120596) =119870119878 ∙ 120596 120596119888

120596 1205961198882 + 1

∙ 119909(120596)

ωb lt ωc V=0

ωb gt ωc V ~ x

High Pass filter (HPF)

Electrochemical Biosenors

Electrochemistry interfacing electrode with electrolyte Oxidation Ions that lose their electronsReduction Ions that gain new electrons

Convert biochemical reactions to electrical signal

Electrochemical Biosenors

Equivalent electrical circuit of electrochemical cells

Rct Charge transfer resistance due to transfer of electrons from ions to electrodeCdl Double layer capacitor ndashaccumulation of charge in the interface between the electrolyte and electrodeRS series resistance ndash electrolyte solution resistance

119885119890119902 = 119877119904 +119877119888119905

1 + 119895 ∙ 120596 ∙ 119877119888119905 ∙ 119862119889119897

LPF

Amplifier

An input signals (currentvoltage) is amplified to a larger output signals (currentvoltage)

Features1 Linearity (wide linear range)2 High Gain3 Vin=0 Vout=04 High signal to noise ratio5 Stability at time (One dominant half time)6 Stable gain (not depend on circuit parameters VDD temperature hellip)

Amplifier

Amplifier

bull Voltage amplifier

119907119900119906119905 = 119860119907 ∙ 119907119894119899

Vin ndashinputVout ndashoutputAv ndash voltage gain [db]Ri is input resistanceRo output resistanceRS source resistanceRL Load Resistance

119907119894119899 = 119907119904 ∙119877119894

119877119894 + 119877119878 119907119900119906119905 = 119860119907119907119894119899 ∙119877119871

119877119871+119877119874

119907119900119906119905 = 119860119907119907119904 ∙119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

119860119907119890119891119891 =119907119900119906119905

119907119904= 119860119907 ∙

119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

20 log 119860119907 [119889119861] decibels

Amplifier

Differential amplifier

Reject common noise

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992 = 1198811198941198991 + ∆ minus 1198811198941198992 minus ∆

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

Negative feedbackNegative feedback loop when the output of the system feed it back to control and reduce his activity

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

1198811198941198992 = 120573 ∙ 119881119900119906119905

Open loop equation

Negative feedback loop equation

rArr 119881119900119906119905= 119860 ∙ 1198811198941198991 minus 120573 ∙ 119881119900119906119905

119933119952119958119957 = 119933119946119951120783 ∙119912

120783 + 120631 ∙ 119912Blackrsquos Formula

β∙Agtgt1 Vout=Vin1βNegative feedback can increase the stability

Analog-to-digital converts

Noise accumulated in analog circuits

Solution Digital circuit

noise hampers our ability to distinguish between small differences in value mdasheg between 31V and 32V

Digital circuits1 Device of two states (OFFON) or (01)

119881119900119906119905 = 119881119874119873 119881119894119899gt 119881119905ℎ119881119900119891119891 119881119894119899 lt 119881119905ℎ

2 Computation arises from logic functions (Boolean algebra) using basic logic gates

Biosensor converts one type of energy to electrical energyPhotodiode is pn junction that converts light to electrical energy

Biosenors -Photodiode

119862119889119881

119889119905+119881

119877= 119868119871119894119892ℎ119905 minus 119868119863119894119900119889119890

119868119863119894119900119889119890 = 119868119889119886119903119896(119890 119902119881 119870119879 minus 1)

Low pass filter

Light increases the

dark current

119877 =119889119881

119889119868=

119870119879

119902 ∙ 119868

C is the junction capacitance

Biosensor converts one type of energy to electrical energy

Piezoelectricity convert mechanical energy to electrical energyMeasure pressure and ultrasound waves

Biosenors - Piezoelectricity

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 deflectiondisplacement to charge generator

Kxq K is a constant depends on the material

X is a deflection

R Sensor leakage resistance

C Sensor capacitance

Piezoelectric crystal (quartz)

x

AC r0

Biosenors - Piezoelectricity

Changes in x cause to change in the charge and producing a current

Convert charge generator to current generator

119868119861 =119889119902

119889119905= 119870

119889119909

119889119905

119862119889119881

119889119905+119881

119877= 119870

119889119909

119889119905

119889119881

119889119905= 119870119878

119889119909

119889119905minus119881

120591

Ks = KC sensitivity Vm

= RC time constant

Fourier transform

119895120596119907 = 119870119878 ∙ 119895120596119909(120596) minus119907

120591

119907(120596) =119870119878119895120596120591

1 + 119895120596120591∙ 119909(120596)

Biosenors - Piezoelectricity

Ks = KC sensitivity Vm

= RC time constant

119907(120596) =119870119878 ∙ 120596 120596119888

120596 1205961198882 + 1

∙ 119909(120596)

ωb lt ωc V=0

ωb gt ωc V ~ x

High Pass filter (HPF)

Electrochemical Biosenors

Electrochemistry interfacing electrode with electrolyte Oxidation Ions that lose their electronsReduction Ions that gain new electrons

Convert biochemical reactions to electrical signal

Electrochemical Biosenors

Equivalent electrical circuit of electrochemical cells

Rct Charge transfer resistance due to transfer of electrons from ions to electrodeCdl Double layer capacitor ndashaccumulation of charge in the interface between the electrolyte and electrodeRS series resistance ndash electrolyte solution resistance

119885119890119902 = 119877119904 +119877119888119905

1 + 119895 ∙ 120596 ∙ 119877119888119905 ∙ 119862119889119897

LPF

Amplifier

An input signals (currentvoltage) is amplified to a larger output signals (currentvoltage)

Features1 Linearity (wide linear range)2 High Gain3 Vin=0 Vout=04 High signal to noise ratio5 Stability at time (One dominant half time)6 Stable gain (not depend on circuit parameters VDD temperature hellip)

Amplifier

Amplifier

bull Voltage amplifier

119907119900119906119905 = 119860119907 ∙ 119907119894119899

Vin ndashinputVout ndashoutputAv ndash voltage gain [db]Ri is input resistanceRo output resistanceRS source resistanceRL Load Resistance

119907119894119899 = 119907119904 ∙119877119894

119877119894 + 119877119878 119907119900119906119905 = 119860119907119907119894119899 ∙119877119871

119877119871+119877119874

119907119900119906119905 = 119860119907119907119904 ∙119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

119860119907119890119891119891 =119907119900119906119905

119907119904= 119860119907 ∙

119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

20 log 119860119907 [119889119861] decibels

Amplifier

Differential amplifier

Reject common noise

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992 = 1198811198941198991 + ∆ minus 1198811198941198992 minus ∆

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

Negative feedbackNegative feedback loop when the output of the system feed it back to control and reduce his activity

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

1198811198941198992 = 120573 ∙ 119881119900119906119905

Open loop equation

Negative feedback loop equation

rArr 119881119900119906119905= 119860 ∙ 1198811198941198991 minus 120573 ∙ 119881119900119906119905

119933119952119958119957 = 119933119946119951120783 ∙119912

120783 + 120631 ∙ 119912Blackrsquos Formula

β∙Agtgt1 Vout=Vin1βNegative feedback can increase the stability

Analog-to-digital converts

Noise accumulated in analog circuits

Solution Digital circuit

noise hampers our ability to distinguish between small differences in value mdasheg between 31V and 32V

Digital circuits1 Device of two states (OFFON) or (01)

119881119900119906119905 = 119881119874119873 119881119894119899gt 119881119905ℎ119881119900119891119891 119881119894119899 lt 119881119905ℎ

2 Computation arises from logic functions (Boolean algebra) using basic logic gates

Biosensor converts one type of energy to electrical energy

Piezoelectricity convert mechanical energy to electrical energyMeasure pressure and ultrasound waves

Biosenors - Piezoelectricity

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 deflectiondisplacement to charge generator

Kxq K is a constant depends on the material

X is a deflection

R Sensor leakage resistance

C Sensor capacitance

Piezoelectric crystal (quartz)

x

AC r0

Biosenors - Piezoelectricity

Changes in x cause to change in the charge and producing a current

Convert charge generator to current generator

119868119861 =119889119902

119889119905= 119870

119889119909

119889119905

119862119889119881

119889119905+119881

119877= 119870

119889119909

119889119905

119889119881

119889119905= 119870119878

119889119909

119889119905minus119881

120591

Ks = KC sensitivity Vm

= RC time constant

Fourier transform

119895120596119907 = 119870119878 ∙ 119895120596119909(120596) minus119907

120591

119907(120596) =119870119878119895120596120591

1 + 119895120596120591∙ 119909(120596)

Biosenors - Piezoelectricity

Ks = KC sensitivity Vm

= RC time constant

119907(120596) =119870119878 ∙ 120596 120596119888

120596 1205961198882 + 1

∙ 119909(120596)

ωb lt ωc V=0

ωb gt ωc V ~ x

High Pass filter (HPF)

Electrochemical Biosenors

Electrochemistry interfacing electrode with electrolyte Oxidation Ions that lose their electronsReduction Ions that gain new electrons

Convert biochemical reactions to electrical signal

Electrochemical Biosenors

Equivalent electrical circuit of electrochemical cells

Rct Charge transfer resistance due to transfer of electrons from ions to electrodeCdl Double layer capacitor ndashaccumulation of charge in the interface between the electrolyte and electrodeRS series resistance ndash electrolyte solution resistance

119885119890119902 = 119877119904 +119877119888119905

1 + 119895 ∙ 120596 ∙ 119877119888119905 ∙ 119862119889119897

LPF

Amplifier

An input signals (currentvoltage) is amplified to a larger output signals (currentvoltage)

Features1 Linearity (wide linear range)2 High Gain3 Vin=0 Vout=04 High signal to noise ratio5 Stability at time (One dominant half time)6 Stable gain (not depend on circuit parameters VDD temperature hellip)

Amplifier

Amplifier

bull Voltage amplifier

119907119900119906119905 = 119860119907 ∙ 119907119894119899

Vin ndashinputVout ndashoutputAv ndash voltage gain [db]Ri is input resistanceRo output resistanceRS source resistanceRL Load Resistance

119907119894119899 = 119907119904 ∙119877119894

119877119894 + 119877119878 119907119900119906119905 = 119860119907119907119894119899 ∙119877119871

119877119871+119877119874

119907119900119906119905 = 119860119907119907119904 ∙119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

119860119907119890119891119891 =119907119900119906119905

119907119904= 119860119907 ∙

119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

20 log 119860119907 [119889119861] decibels

Amplifier

Differential amplifier

Reject common noise

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992 = 1198811198941198991 + ∆ minus 1198811198941198992 minus ∆

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

Negative feedbackNegative feedback loop when the output of the system feed it back to control and reduce his activity

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

1198811198941198992 = 120573 ∙ 119881119900119906119905

Open loop equation

Negative feedback loop equation

rArr 119881119900119906119905= 119860 ∙ 1198811198941198991 minus 120573 ∙ 119881119900119906119905

119933119952119958119957 = 119933119946119951120783 ∙119912

120783 + 120631 ∙ 119912Blackrsquos Formula

β∙Agtgt1 Vout=Vin1βNegative feedback can increase the stability

Analog-to-digital converts

Noise accumulated in analog circuits

Solution Digital circuit

noise hampers our ability to distinguish between small differences in value mdasheg between 31V and 32V

Digital circuits1 Device of two states (OFFON) or (01)

119881119900119906119905 = 119881119874119873 119881119894119899gt 119881119905ℎ119881119900119891119891 119881119894119899 lt 119881119905ℎ

2 Computation arises from logic functions (Boolean algebra) using basic logic gates

Biosenors - Piezoelectricity

Changes in x cause to change in the charge and producing a current

Convert charge generator to current generator

119868119861 =119889119902

119889119905= 119870

119889119909

119889119905

119862119889119881

119889119905+119881

119877= 119870

119889119909

119889119905

119889119881

119889119905= 119870119878

119889119909

119889119905minus119881

120591

Ks = KC sensitivity Vm

= RC time constant

Fourier transform

119895120596119907 = 119870119878 ∙ 119895120596119909(120596) minus119907

120591

119907(120596) =119870119878119895120596120591

1 + 119895120596120591∙ 119909(120596)

Biosenors - Piezoelectricity

Ks = KC sensitivity Vm

= RC time constant

119907(120596) =119870119878 ∙ 120596 120596119888

120596 1205961198882 + 1

∙ 119909(120596)

ωb lt ωc V=0

ωb gt ωc V ~ x

High Pass filter (HPF)

Electrochemical Biosenors

Electrochemistry interfacing electrode with electrolyte Oxidation Ions that lose their electronsReduction Ions that gain new electrons

Convert biochemical reactions to electrical signal

Electrochemical Biosenors

Equivalent electrical circuit of electrochemical cells

Rct Charge transfer resistance due to transfer of electrons from ions to electrodeCdl Double layer capacitor ndashaccumulation of charge in the interface between the electrolyte and electrodeRS series resistance ndash electrolyte solution resistance

119885119890119902 = 119877119904 +119877119888119905

1 + 119895 ∙ 120596 ∙ 119877119888119905 ∙ 119862119889119897

LPF

Amplifier

An input signals (currentvoltage) is amplified to a larger output signals (currentvoltage)

Features1 Linearity (wide linear range)2 High Gain3 Vin=0 Vout=04 High signal to noise ratio5 Stability at time (One dominant half time)6 Stable gain (not depend on circuit parameters VDD temperature hellip)

Amplifier

Amplifier

bull Voltage amplifier

119907119900119906119905 = 119860119907 ∙ 119907119894119899

Vin ndashinputVout ndashoutputAv ndash voltage gain [db]Ri is input resistanceRo output resistanceRS source resistanceRL Load Resistance

119907119894119899 = 119907119904 ∙119877119894

119877119894 + 119877119878 119907119900119906119905 = 119860119907119907119894119899 ∙119877119871

119877119871+119877119874

119907119900119906119905 = 119860119907119907119904 ∙119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

119860119907119890119891119891 =119907119900119906119905

119907119904= 119860119907 ∙

119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

20 log 119860119907 [119889119861] decibels

Amplifier

Differential amplifier

Reject common noise

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992 = 1198811198941198991 + ∆ minus 1198811198941198992 minus ∆

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

Negative feedbackNegative feedback loop when the output of the system feed it back to control and reduce his activity

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

1198811198941198992 = 120573 ∙ 119881119900119906119905

Open loop equation

Negative feedback loop equation

rArr 119881119900119906119905= 119860 ∙ 1198811198941198991 minus 120573 ∙ 119881119900119906119905

119933119952119958119957 = 119933119946119951120783 ∙119912

120783 + 120631 ∙ 119912Blackrsquos Formula

β∙Agtgt1 Vout=Vin1βNegative feedback can increase the stability

Analog-to-digital converts

Noise accumulated in analog circuits

Solution Digital circuit

noise hampers our ability to distinguish between small differences in value mdasheg between 31V and 32V

Digital circuits1 Device of two states (OFFON) or (01)

119881119900119906119905 = 119881119874119873 119881119894119899gt 119881119905ℎ119881119900119891119891 119881119894119899 lt 119881119905ℎ

2 Computation arises from logic functions (Boolean algebra) using basic logic gates

Biosenors - Piezoelectricity

Ks = KC sensitivity Vm

= RC time constant

119907(120596) =119870119878 ∙ 120596 120596119888

120596 1205961198882 + 1

∙ 119909(120596)

ωb lt ωc V=0

ωb gt ωc V ~ x

High Pass filter (HPF)

Electrochemical Biosenors

Electrochemistry interfacing electrode with electrolyte Oxidation Ions that lose their electronsReduction Ions that gain new electrons

Convert biochemical reactions to electrical signal

Electrochemical Biosenors

Equivalent electrical circuit of electrochemical cells

Rct Charge transfer resistance due to transfer of electrons from ions to electrodeCdl Double layer capacitor ndashaccumulation of charge in the interface between the electrolyte and electrodeRS series resistance ndash electrolyte solution resistance

119885119890119902 = 119877119904 +119877119888119905

1 + 119895 ∙ 120596 ∙ 119877119888119905 ∙ 119862119889119897

LPF

Amplifier

An input signals (currentvoltage) is amplified to a larger output signals (currentvoltage)

Features1 Linearity (wide linear range)2 High Gain3 Vin=0 Vout=04 High signal to noise ratio5 Stability at time (One dominant half time)6 Stable gain (not depend on circuit parameters VDD temperature hellip)

Amplifier

Amplifier

bull Voltage amplifier

119907119900119906119905 = 119860119907 ∙ 119907119894119899

Vin ndashinputVout ndashoutputAv ndash voltage gain [db]Ri is input resistanceRo output resistanceRS source resistanceRL Load Resistance

119907119894119899 = 119907119904 ∙119877119894

119877119894 + 119877119878 119907119900119906119905 = 119860119907119907119894119899 ∙119877119871

119877119871+119877119874

119907119900119906119905 = 119860119907119907119904 ∙119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

119860119907119890119891119891 =119907119900119906119905

119907119904= 119860119907 ∙

119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

20 log 119860119907 [119889119861] decibels

Amplifier

Differential amplifier

Reject common noise

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992 = 1198811198941198991 + ∆ minus 1198811198941198992 minus ∆

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

Negative feedbackNegative feedback loop when the output of the system feed it back to control and reduce his activity

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

1198811198941198992 = 120573 ∙ 119881119900119906119905

Open loop equation

Negative feedback loop equation

rArr 119881119900119906119905= 119860 ∙ 1198811198941198991 minus 120573 ∙ 119881119900119906119905

119933119952119958119957 = 119933119946119951120783 ∙119912

120783 + 120631 ∙ 119912Blackrsquos Formula

β∙Agtgt1 Vout=Vin1βNegative feedback can increase the stability

Analog-to-digital converts

Noise accumulated in analog circuits

Solution Digital circuit

noise hampers our ability to distinguish between small differences in value mdasheg between 31V and 32V

Digital circuits1 Device of two states (OFFON) or (01)

119881119900119906119905 = 119881119874119873 119881119894119899gt 119881119905ℎ119881119900119891119891 119881119894119899 lt 119881119905ℎ

2 Computation arises from logic functions (Boolean algebra) using basic logic gates

Electrochemical Biosenors

Electrochemistry interfacing electrode with electrolyte Oxidation Ions that lose their electronsReduction Ions that gain new electrons

Convert biochemical reactions to electrical signal

Electrochemical Biosenors

Equivalent electrical circuit of electrochemical cells

Rct Charge transfer resistance due to transfer of electrons from ions to electrodeCdl Double layer capacitor ndashaccumulation of charge in the interface between the electrolyte and electrodeRS series resistance ndash electrolyte solution resistance

119885119890119902 = 119877119904 +119877119888119905

1 + 119895 ∙ 120596 ∙ 119877119888119905 ∙ 119862119889119897

LPF

Amplifier

An input signals (currentvoltage) is amplified to a larger output signals (currentvoltage)

Features1 Linearity (wide linear range)2 High Gain3 Vin=0 Vout=04 High signal to noise ratio5 Stability at time (One dominant half time)6 Stable gain (not depend on circuit parameters VDD temperature hellip)

Amplifier

Amplifier

bull Voltage amplifier

119907119900119906119905 = 119860119907 ∙ 119907119894119899

Vin ndashinputVout ndashoutputAv ndash voltage gain [db]Ri is input resistanceRo output resistanceRS source resistanceRL Load Resistance

119907119894119899 = 119907119904 ∙119877119894

119877119894 + 119877119878 119907119900119906119905 = 119860119907119907119894119899 ∙119877119871

119877119871+119877119874

119907119900119906119905 = 119860119907119907119904 ∙119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

119860119907119890119891119891 =119907119900119906119905

119907119904= 119860119907 ∙

119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

20 log 119860119907 [119889119861] decibels

Amplifier

Differential amplifier

Reject common noise

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992 = 1198811198941198991 + ∆ minus 1198811198941198992 minus ∆

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

Negative feedbackNegative feedback loop when the output of the system feed it back to control and reduce his activity

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

1198811198941198992 = 120573 ∙ 119881119900119906119905

Open loop equation

Negative feedback loop equation

rArr 119881119900119906119905= 119860 ∙ 1198811198941198991 minus 120573 ∙ 119881119900119906119905

119933119952119958119957 = 119933119946119951120783 ∙119912

120783 + 120631 ∙ 119912Blackrsquos Formula

β∙Agtgt1 Vout=Vin1βNegative feedback can increase the stability

Analog-to-digital converts

Noise accumulated in analog circuits

Solution Digital circuit

noise hampers our ability to distinguish between small differences in value mdasheg between 31V and 32V

Digital circuits1 Device of two states (OFFON) or (01)

119881119900119906119905 = 119881119874119873 119881119894119899gt 119881119905ℎ119881119900119891119891 119881119894119899 lt 119881119905ℎ

2 Computation arises from logic functions (Boolean algebra) using basic logic gates

Electrochemical Biosenors

Equivalent electrical circuit of electrochemical cells

Rct Charge transfer resistance due to transfer of electrons from ions to electrodeCdl Double layer capacitor ndashaccumulation of charge in the interface between the electrolyte and electrodeRS series resistance ndash electrolyte solution resistance

119885119890119902 = 119877119904 +119877119888119905

1 + 119895 ∙ 120596 ∙ 119877119888119905 ∙ 119862119889119897

LPF

Amplifier

An input signals (currentvoltage) is amplified to a larger output signals (currentvoltage)

Features1 Linearity (wide linear range)2 High Gain3 Vin=0 Vout=04 High signal to noise ratio5 Stability at time (One dominant half time)6 Stable gain (not depend on circuit parameters VDD temperature hellip)

Amplifier

Amplifier

bull Voltage amplifier

119907119900119906119905 = 119860119907 ∙ 119907119894119899

Vin ndashinputVout ndashoutputAv ndash voltage gain [db]Ri is input resistanceRo output resistanceRS source resistanceRL Load Resistance

119907119894119899 = 119907119904 ∙119877119894

119877119894 + 119877119878 119907119900119906119905 = 119860119907119907119894119899 ∙119877119871

119877119871+119877119874

119907119900119906119905 = 119860119907119907119904 ∙119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

119860119907119890119891119891 =119907119900119906119905

119907119904= 119860119907 ∙

119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

20 log 119860119907 [119889119861] decibels

Amplifier

Differential amplifier

Reject common noise

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992 = 1198811198941198991 + ∆ minus 1198811198941198992 minus ∆

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

Negative feedbackNegative feedback loop when the output of the system feed it back to control and reduce his activity

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

1198811198941198992 = 120573 ∙ 119881119900119906119905

Open loop equation

Negative feedback loop equation

rArr 119881119900119906119905= 119860 ∙ 1198811198941198991 minus 120573 ∙ 119881119900119906119905

119933119952119958119957 = 119933119946119951120783 ∙119912

120783 + 120631 ∙ 119912Blackrsquos Formula

β∙Agtgt1 Vout=Vin1βNegative feedback can increase the stability

Analog-to-digital converts

Noise accumulated in analog circuits

Solution Digital circuit

noise hampers our ability to distinguish between small differences in value mdasheg between 31V and 32V

Digital circuits1 Device of two states (OFFON) or (01)

119881119900119906119905 = 119881119874119873 119881119894119899gt 119881119905ℎ119881119900119891119891 119881119894119899 lt 119881119905ℎ

2 Computation arises from logic functions (Boolean algebra) using basic logic gates

Amplifier

An input signals (currentvoltage) is amplified to a larger output signals (currentvoltage)

Features1 Linearity (wide linear range)2 High Gain3 Vin=0 Vout=04 High signal to noise ratio5 Stability at time (One dominant half time)6 Stable gain (not depend on circuit parameters VDD temperature hellip)

Amplifier

Amplifier

bull Voltage amplifier

119907119900119906119905 = 119860119907 ∙ 119907119894119899

Vin ndashinputVout ndashoutputAv ndash voltage gain [db]Ri is input resistanceRo output resistanceRS source resistanceRL Load Resistance

119907119894119899 = 119907119904 ∙119877119894

119877119894 + 119877119878 119907119900119906119905 = 119860119907119907119894119899 ∙119877119871

119877119871+119877119874

119907119900119906119905 = 119860119907119907119904 ∙119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

119860119907119890119891119891 =119907119900119906119905

119907119904= 119860119907 ∙

119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

20 log 119860119907 [119889119861] decibels

Amplifier

Differential amplifier

Reject common noise

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992 = 1198811198941198991 + ∆ minus 1198811198941198992 minus ∆

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

Negative feedbackNegative feedback loop when the output of the system feed it back to control and reduce his activity

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

1198811198941198992 = 120573 ∙ 119881119900119906119905

Open loop equation

Negative feedback loop equation

rArr 119881119900119906119905= 119860 ∙ 1198811198941198991 minus 120573 ∙ 119881119900119906119905

119933119952119958119957 = 119933119946119951120783 ∙119912

120783 + 120631 ∙ 119912Blackrsquos Formula

β∙Agtgt1 Vout=Vin1βNegative feedback can increase the stability

Analog-to-digital converts

Noise accumulated in analog circuits

Solution Digital circuit

noise hampers our ability to distinguish between small differences in value mdasheg between 31V and 32V

Digital circuits1 Device of two states (OFFON) or (01)

119881119900119906119905 = 119881119874119873 119881119894119899gt 119881119905ℎ119881119900119891119891 119881119894119899 lt 119881119905ℎ

2 Computation arises from logic functions (Boolean algebra) using basic logic gates

Amplifier

Amplifier

bull Voltage amplifier

119907119900119906119905 = 119860119907 ∙ 119907119894119899

Vin ndashinputVout ndashoutputAv ndash voltage gain [db]Ri is input resistanceRo output resistanceRS source resistanceRL Load Resistance

119907119894119899 = 119907119904 ∙119877119894

119877119894 + 119877119878 119907119900119906119905 = 119860119907119907119894119899 ∙119877119871

119877119871+119877119874

119907119900119906119905 = 119860119907119907119904 ∙119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

119860119907119890119891119891 =119907119900119906119905

119907119904= 119860119907 ∙

119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

20 log 119860119907 [119889119861] decibels

Amplifier

Differential amplifier

Reject common noise

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992 = 1198811198941198991 + ∆ minus 1198811198941198992 minus ∆

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

Negative feedbackNegative feedback loop when the output of the system feed it back to control and reduce his activity

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

1198811198941198992 = 120573 ∙ 119881119900119906119905

Open loop equation

Negative feedback loop equation

rArr 119881119900119906119905= 119860 ∙ 1198811198941198991 minus 120573 ∙ 119881119900119906119905

119933119952119958119957 = 119933119946119951120783 ∙119912

120783 + 120631 ∙ 119912Blackrsquos Formula

β∙Agtgt1 Vout=Vin1βNegative feedback can increase the stability

Analog-to-digital converts

Noise accumulated in analog circuits

Solution Digital circuit

noise hampers our ability to distinguish between small differences in value mdasheg between 31V and 32V

Digital circuits1 Device of two states (OFFON) or (01)

119881119900119906119905 = 119881119874119873 119881119894119899gt 119881119905ℎ119881119900119891119891 119881119894119899 lt 119881119905ℎ

2 Computation arises from logic functions (Boolean algebra) using basic logic gates

Amplifier

bull Voltage amplifier

119907119900119906119905 = 119860119907 ∙ 119907119894119899

Vin ndashinputVout ndashoutputAv ndash voltage gain [db]Ri is input resistanceRo output resistanceRS source resistanceRL Load Resistance

119907119894119899 = 119907119904 ∙119877119894

119877119894 + 119877119878 119907119900119906119905 = 119860119907119907119894119899 ∙119877119871

119877119871+119877119874

119907119900119906119905 = 119860119907119907119904 ∙119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

119860119907119890119891119891 =119907119900119906119905

119907119904= 119860119907 ∙

119877119894

119877119894+119877119878∙

119877119871

119877119871+119877119874

20 log 119860119907 [119889119861] decibels

Amplifier

Differential amplifier

Reject common noise

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992 = 1198811198941198991 + ∆ minus 1198811198941198992 minus ∆

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

Negative feedbackNegative feedback loop when the output of the system feed it back to control and reduce his activity

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

1198811198941198992 = 120573 ∙ 119881119900119906119905

Open loop equation

Negative feedback loop equation

rArr 119881119900119906119905= 119860 ∙ 1198811198941198991 minus 120573 ∙ 119881119900119906119905

119933119952119958119957 = 119933119946119951120783 ∙119912

120783 + 120631 ∙ 119912Blackrsquos Formula

β∙Agtgt1 Vout=Vin1βNegative feedback can increase the stability

Analog-to-digital converts

Noise accumulated in analog circuits

Solution Digital circuit

noise hampers our ability to distinguish between small differences in value mdasheg between 31V and 32V

Digital circuits1 Device of two states (OFFON) or (01)

119881119900119906119905 = 119881119874119873 119881119894119899gt 119881119905ℎ119881119900119891119891 119881119894119899 lt 119881119905ℎ

2 Computation arises from logic functions (Boolean algebra) using basic logic gates

Amplifier

Differential amplifier

Reject common noise

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992 = 1198811198941198991 + ∆ minus 1198811198941198992 minus ∆

∆119881119894119899 = 1198811198941198991 minus 1198811198941198992

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

Negative feedbackNegative feedback loop when the output of the system feed it back to control and reduce his activity

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

1198811198941198992 = 120573 ∙ 119881119900119906119905

Open loop equation

Negative feedback loop equation

rArr 119881119900119906119905= 119860 ∙ 1198811198941198991 minus 120573 ∙ 119881119900119906119905

119933119952119958119957 = 119933119946119951120783 ∙119912

120783 + 120631 ∙ 119912Blackrsquos Formula

β∙Agtgt1 Vout=Vin1βNegative feedback can increase the stability

Analog-to-digital converts

Noise accumulated in analog circuits

Solution Digital circuit

noise hampers our ability to distinguish between small differences in value mdasheg between 31V and 32V

Digital circuits1 Device of two states (OFFON) or (01)

119881119900119906119905 = 119881119874119873 119881119894119899gt 119881119905ℎ119881119900119891119891 119881119894119899 lt 119881119905ℎ

2 Computation arises from logic functions (Boolean algebra) using basic logic gates

Negative feedbackNegative feedback loop when the output of the system feed it back to control and reduce his activity

)119881119900119906119905 = 119860 ∙ (1198811198941198991 minus 1198811198941198992

1198811198941198992 = 120573 ∙ 119881119900119906119905

Open loop equation

Negative feedback loop equation

rArr 119881119900119906119905= 119860 ∙ 1198811198941198991 minus 120573 ∙ 119881119900119906119905

119933119952119958119957 = 119933119946119951120783 ∙119912

120783 + 120631 ∙ 119912Blackrsquos Formula

β∙Agtgt1 Vout=Vin1βNegative feedback can increase the stability

Analog-to-digital converts

Noise accumulated in analog circuits

Solution Digital circuit

noise hampers our ability to distinguish between small differences in value mdasheg between 31V and 32V

Digital circuits1 Device of two states (OFFON) or (01)

119881119900119906119905 = 119881119874119873 119881119894119899gt 119881119905ℎ119881119900119891119891 119881119894119899 lt 119881119905ℎ

2 Computation arises from logic functions (Boolean algebra) using basic logic gates

Analog-to-digital converts

Noise accumulated in analog circuits

Solution Digital circuit

noise hampers our ability to distinguish between small differences in value mdasheg between 31V and 32V

Digital circuits1 Device of two states (OFFON) or (01)

119881119900119906119905 = 119881119874119873 119881119894119899gt 119881119905ℎ119881119900119891119891 119881119894119899 lt 119881119905ℎ

2 Computation arises from logic functions (Boolean algebra) using basic logic gates

Noise accumulated in analog circuits

Solution Digital circuit

noise hampers our ability to distinguish between small differences in value mdasheg between 31V and 32V

Digital circuits1 Device of two states (OFFON) or (01)

119881119900119906119905 = 119881119874119873 119881119894119899gt 119881119905ℎ119881119900119891119891 119881119894119899 lt 119881119905ℎ

2 Computation arises from logic functions (Boolean algebra) using basic logic gates

Digital circuits1 Device of two states (OFFON) or (01)

119881119900119906119905 = 119881119874119873 119881119894119899gt 119881119905ℎ119881119900119891119891 119881119894119899 lt 119881119905ℎ

2 Computation arises from logic functions (Boolean algebra) using basic logic gates