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