lecture151 RC Op-Amp Circuits (5.4) Prof. Phillips March 14, 2003

lecture152 Digital 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 processors.

lecture153 Data 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 data.

lecture154 A Generic Digital Meter Input Switching and Ranging Amplifier A/D Converter ProcessorDisplay

lecture155 Voltage Measurements HiCom 10V 1V 100V

lecture156 Model for Meter The ideal meter measures the voltage across its inputs. No current flows into it; it has infinite input resistance. 10M  Ideal Meter Hi Com

lecture157 10M  Ideal Meter Hi Com R Meter Loading The 10M  meter resistance in parallel with R may change the voltage that you measure.

lecture158 Loading When measuring the voltage across R, we need to make sure that R is much less than 10M  If R is close to 10M , significant current flows through the meter, changing the voltage across R.

lecture159 Loading Example Without Meter: voltage is 100V With Meter: measured voltage is 83.3V 10M  Ideal Meter Hi Com 2M  50  A

lecture1510 Current Measurements AmpCom 10V 1V 100V

lecture1511 Measuring Large Currents (> 100mA) 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 computed.

lecture1512 RsRs Ideal Meter Amp Com R Meter Loading The R s shunt resistance in series with R may change the current that you measure.

lecture1513 The Voltage Follower v in + – v out + – +–+–

lecture1514 Without a Voltage Follower v A/D is not equal to v s vsvs RsRs R A/D + – v A/D Sensor A/D Converter +–+–

lecture1515 Op-Amp Review The ideal op-amp model leads to the following conditions: i + = i - = 0 v + = v - The op amp will set the output voltage to whatever value results in the same voltages at the inputs.

lecture1516 Op-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 voltage.

lecture1517 With a Voltage Follower v A/D is equal to v s vsvs RsRs Sensor R A/D + – v A/D A/D Converter + – +–+–

lecture1518 An Integrator – + V in + – V out R C +–+–

lecture1519 KCL at the Inverting Input – + v in (t) + – R C v out (t) iR(t)iR(t) iC(t)iC(t) i-i- +–+–

lecture1520 KCL

lecture1521 Solve for v out (t)

lecture1522 Class Example Learning Extension E5.9