lecture151 rc op-amp circuits (5.4) prof. phillips march 14, 2003
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lecture15 1
RC Op-Amp Circuits (5.4)
Prof. Phillips
March 14, 2003
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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.
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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.
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A Generic Digital Meter
Input Switchingand Ranging
Amplifier
A/D Converter
ProcessorDisplay
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Voltage Measurements
Hi Com
10V
1V
100V
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Model for Meter
The ideal meter measures the voltage across its inputs. No current flows into it; it has infinite input resistance.
10M Ideal MeterHi
Com
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10M Ideal MeterHi
ComR
Meter Loading
The 10M meter resistance in parallel with R may change the voltage that you measure.
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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.
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Loading Example
• Without Meter: voltage is 100V
• With Meter: measured voltage is 83.3V
10M Ideal MeterHi
Com2M50A
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Current Measurements
AmpCom
10V
1V
100V
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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.
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RsIdeal Meter
Amp
ComR
Meter Loading
The Rs shunt resistance in series with R may change the current that you measure.
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The Voltage Follower
vin
+
–
vout
+
–
+–
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Without a Voltage Follower
vA/D is not equal to vs
vs
Rs
RA/D
+
–
vA/DSensor A/D
Converter+–
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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.
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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.
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With a Voltage Follower
vA/D is equal to vs
vsRs
Sensor
RA/D
+
–
vA/D
A/D Converter
+
–+–
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An Integrator
–
+Vin+
–Vout
R
C
+–
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KCL at the Inverting Input
–
+vin(t)+
–
R
C
vout(t)
iR(t)
iC(t)
i-
+–
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KCL
0i
R
tv
R
vtvti inin
R
)()()(
dt
tdvC
dt
vtvdCti outout
C
)()()(
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Solve for vout(t)
0)()(
dt
tdvC
R
tv outin
RC
tv
dt
tdv inout )()(
dxRC
xvtv
tin
out
)(
)(
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Class Example
• Learning Extension E5.9