1Copyright 2003, Regents of University of CaliforniaLecture 14: 10/16/03 A.R. NeureutherVersion Date 10/29//03EECS 42 Intro. Digital Electronics Fall 2003EECS 42 Introduction Digital ElectronicsAndrew R. NeureutherLecture # 15 Op-Amp Circuits and Comparators 4.3-4.4 (light on non-ideal) A) Cascade Op-AmpsB) Integration/Differentiation Op-Amps C) I vs. V of Op-Amps – Source LimitsD) Comparator CircuitsE) D to A Convertershttp://inst.EECS.Berkeley.EDU/~ee42/Copyright 2003, Regents of University of CaliforniaLecture 14: 10/16/03 A.R. NeureutherVersion Date 10/29//03EECS 42 Intro. Digital Electronics Fall 2003NEGATIVE FEEDBACKFamiliar examples of negative feedback:Thermostat controlling room temperatureDriver controlling direction of automobilePhotochromic lenses in eyeglassesFamiliar examples of positive feedback:Microphone “squawk” in room sound systemMechanical bi-stability in light switchesThermonuclear reaction in H-bombFundamentally pushes toward stabilityFundamentally pushes toward instability or bi-stabilityCopyright 2003, Regents of University of CaliforniaLecture 14: 10/16/03 A.R. NeureutherVersion Date 10/29//03EECS 42 Intro. Digital Electronics Fall 2003CASCADE OP-AMP CIRCUITSV1+−V3V2RFR1R2R3V0+−1K9KIINHow do you get started on finding VO?Hint: IINdoes not affect VO1See the further examples of op-amp circuits in the readerHint: Identify StagesCopyright 2003, Regents of University of CaliforniaLecture 14: 10/16/03 A.R. NeureutherVersion Date 10/29//03EECS 42 Intro. Digital Electronics Fall 2003CASCADE OP-AMP SOLUTIONFIRST STAGE IS “SUMMING JUNCTION” AMPLIFIERSolution:F32103210RVRVRVRV:KCL=+++V1V01+−V3V2RFR1R2R333F22F11F01VRR VRR VRRV −−−=⇒)(IN0VVand0i=≅≅+−V02+−1K9KVIN2IINSECOND STAGE IS “INVERTING” AMPLIFIER≅R1-R2VIN2V02Copyright 2003, Regents of University of CaliforniaLecture 14: 10/16/03 A.R. NeureutherVersion Date 10/29//03EECS 42 Intro. Digital Electronics Fall 2003INTEGRATING OP-AMPHow do you get started on finding VO?Hint: )(IN0VVand0i=≅≅+−)(IN0VVand0i=≅≅+−Hint: KCL at V-node with IIN-= 0V0+−R1CVINCopyright 2003, Regents of University of CaliforniaLecture 14: 10/16/03 A.R. NeureutherVersion Date 10/29//03EECS 42 Intro. Digital Electronics Fall 2003INTEGRATING OP-AMPV0+−R1CVIN()0001=∂−∂+−tVCRVOINIntegrate from t0to t to get VO(t)() ()'101dttVCRtVttINO∫−=2Copyright 2003, Regents of University of CaliforniaLecture 14: 10/16/03 A.R. NeureutherVersion Date 10/29//03EECS 42 Intro. Digital Electronics Fall 2003Example: Amplifier with gain of 105, with max V0of 3V and min V0of −3V.VIN(µV)123V0 (V)0.10.2−3 −2−1−.2(a)I-V near origin−3(b)I-V over wider rangeVIN(µV)10 2030V0 (V)1−30 −20−10−2−123upper “rail”lower “rail”+−V0+−VIN• Circuit model (ideal op-amp) gives the essential linear part•But V0cannot rise above some physical voltage related to the positive power supply VCC(“ upper rail”) V0 < V+RAIL• And V0cannot go below most negative power supply, VEEi.e., limited by lower “rail” V0> V-RAILOP-AMP I-V CHARACTERISTICS WITH RAILSCopyright 2003, Regents of University of CaliforniaLecture 14: 10/16/03 A.R. NeureutherVersion Date 10/29//03EECS 42 Intro. Digital Electronics Fall 2003OP-AMP I-V CHARACTERISTICS WITH RAILS (cont.)VIN(V)123V0 (V)12−3 −2−1−2−3−13(c)Same V0vs VINover even wider range−3(b)I-V over wide rangeVIN(µV)10 2030V0 (V)1−30 −20−10−2−123upper “rail”lower “rail”Example: Amplifier with gain of 105, with upper rail of 3V and lower rail of −3V. We plot the V0vs VINcharacteristics on two different scalesCopyright 2003, Regents of University of CaliforniaLecture 14: 10/16/03 A.R. NeureutherVersion Date 10/29//03EECS 42 Intro. Digital Electronics Fall 2003I-V with equal X and Y axesVIN(V)123V0 (V)12−3 −2−1−2−3−13Note:• (a) displays linear amplifier behavior (|VIN| < 30 µV) and stops at rails• (b) shows comparator decision function (1 bit A/D converter centered at VIN= 0) where lower rail = logic “0” and upper rail = logic “1”SIMPLE A/D CONVERTER+−V0+−VINCopyright 2003, Regents of University of CaliforniaLecture 14: 10/16/03 A.R. NeureutherVersion Date 10/29//03EECS 42 Intro. Digital Electronics Fall 2003OP-AMP USE AS COMPARATOR (A/D) MODESimple comparator with threshold at 1V. Design lower rail at 0V and upper rail at 2V (logic “1”). A = large (e.g. 102to105 )NOTE: The actual diagram of a comparator would not show an amplifier with “offset” power supply as above. It would be a simple triangle, perhaps with the threshold level (here 1V) specified.If VIN> 1.010 V,V0= 2V = Logic “1”If VIN< 0.99 V,V0= 0V = Logic “0”V0VIN12012+−V0VIN+−1VV0VINComparatorCopyright 2003, Regents of University of CaliforniaLecture 14: 10/16/03 A.R. NeureutherVersion Date 10/29//03EECS 42 Intro. Digital Electronics Fall 2003ONE-BIT A/D CONVERSIONREQUIREDIN DIGITAL SYSTEMS≈pulses intransmission line→comparator regenerated pulsespulses outAs we saw, we set comparator threshold at a suitable value (e.g., halfway between rails) and comparator output goes to +rail if VIN> VTHRESHOLDand to −rail if VIN< VTHRESHOLD.The inverse pulse shaped function is generated by applying the input voltage to V- and setting V+ to the threshold voltage. +−V0VIN1V−+What would this circuit do?Copyright 2003, Regents of University of CaliforniaLecture 14: 10/16/03 A.R. NeureutherVersion Date 10/29//03EECS 42 Intro. Digital Electronics Fall 2003D/A CONVERSIONExample: Digital representation of sound to analog (so you can hear it!) → D/A conversionThe summing junction op-amp provides a simple means of D/A conversion via weighted-adder D/A converter0 0 1 0 10 0 1 10 1 0 01.520 1 0 10 1 1 00 1 1 11 0 0 02.533.541 0 0 11 0 1 01 0 1 11 1 0 01 1 0 11 1 1 01 1 1 14.555.566.577.5BinarynumberAnalogoutput(volts)0 0 0 00 0 0 10.5MSB LSBS1 closed if LSB =1S2 " if next bit = 1S3 " if " " = 1S4 " if MSB = 1Another way (not shown) is to sum charges instead of current with capacitor networks4-Bit D/A8V−+V05K80K40K20K10KS1+-S3S2S4−+3Copyright 2003, Regents of University of CaliforniaLecture 14: 10/16/03 A.R. NeureutherVersion Date 10/29//03EECS 42 Intro. Digital Electronics Fall 2003CHARACTERISTIC OF A 4-BIT DACDigital Input 0123456780 2 4 6 8 10121416Analog Output
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