Op Amp CircuitsDigital Meters and OscilloscopesData Acquisition SystemsA Generic Digital MeterVoltage MeasurementsModel for MeterMeter LoadingLoadingLoading ExampleCurrent MeasurementsMeasuring Large Currents (> 100 mA)Slide 12The Voltage FollowerWithout a Voltage FollowerOp-Amp ReviewSlide 16With a Voltage FollowerAn IntegratorKCL at the Inverting InputSolve for vout(t)Lect9 EEE 202 1Op Amp CircuitsDr. HolbertFebruary 13, 2008Lect9 EEE 202 2Digital Meters and Oscilloscopes•Most multimeters and oscilloscopes are now digital•A digital multimeter or a digital oscilloscope has an analog-to-digital (A/D) converter•Most digital meters and all digital oscilloscopes have one or more processorsLect9 EEE 202 3Data Acquisition Systems•In many applications, digital meters and scopes are being replaced by data acquisition cards that fit into a computer•The data acquisition cards have A/D converters•The computer provides processing and storage for the dataLect9 EEE 202 4A Generic Digital MeterInput Switchingand RangingAmplifierA/D ConverterProcessorDisplayLect9 EEE 202 5Voltage MeasurementsHi Com10V1V100VLect9 EEE 202 6Model for MeterThe ideal meter measures the voltage across its inputs. No current flows into the ideal meter; it has infinite input resistance10MIdeal MeterHiComLect9 EEE 202 710MIdeal MeterHiComR Meter LoadingThe 10M meter resistance in parallel with R may change the voltage that you measureLect9 EEE 202 8Loading•When measuring the voltage across R, we need to make sure that R is much less than 10 M•If R is close to 10 M, significant current flows through the meter, changing the voltage across RLect9 EEE 202 9Loading Example•Without Meter: voltage is 100 V•With Meter: measured voltage is 83.3 V10MIdeal MeterHiCom2M50ALect9 EEE 202 10Current MeasurementsAmpCom10V1V100VLect9 EEE 202 11Measuring Large Currents (> 100 mA)•The current to be measured is passed through a small resistor (called a shunt resistor) and the resulting voltage across the shunt resistor is measured•From the voltage, the current can be computedLect9 EEE 202 12RsIdeal MeterAmpComR Meter LoadingThe Rs shunt resistance in series with R may change the current that you measureLect9 EEE 202 13The Voltage Followervin+–vout+–+–Lect9 EEE 202 14Without a Voltage FollowervA/D is not equal to vsvsRsRA/D+–vA/DSensorA/D Converter+–Lect9 EEE 202 15Op-Amp Review•The ideal op-amp model leads to the following conditions:i+ = i– = 0v+ = v–•The op amp will set the output voltage to whatever value results in the same voltages at the inputsLect9 EEE 202 16Op-Amp Review•To solve an op-amp circuit, we usually apply KCL (nodal analysis) at one or both of the inputs•We then invoke the consequences of the ideal model•We solve for the op-amp output voltageLect9 EEE 202 17With a Voltage FollowervA/D is equal to vsvsRsSensorRA/D+–vA/DA/D Converter+–+–Lect9 EEE 202 18An Integrator–+Vin+–VoutRC+–Lect9 EEE 202 19KCL at the Inverting Input–+vin(t)+–RCvout(t)iR(t)iC(t)i–+–0iRtvRvtvtiininR)()()( dttdvCdtvtvdCtioutoutC)()()( Lect9 EEE 202 20Solve for vout(t)•From the KCL:•Hence, the output voltage is equal to the time integration of the input voltage—an electronic method of integrating•Now, if we could only make a
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