Transcript RC Op-Amp Circuits (6.4)

RC Op-Amp Circuits (6.4)
Dr. Holbert
April 10, 2006
ECE201 Lect-18
1
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.
ECE201 Lect-18
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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 Switching
and Ranging
A/D Converter
Amplifier
Display
Processor
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Voltage Measurements
100V
10V
1V
Hi
ECE201 Lect-18
Com
5
Model for Meter
Hi
10MW
Ideal Meter
Com
The ideal meter measures the voltage across
its inputs. No current flows into it; it has
infinite input resistance.
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Meter Loading
Hi
R
10MW
Ideal Meter
Com
The 10MW 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
10MW.
• If R is close to 10MW, significant current
flows through the meter, changing the
voltage across R.
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Loading Example
Hi
50mA
2MW
10MW
Ideal Meter
Com
• Without Meter: voltage is 100V
• With Meter: measured voltage is 83.3V
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Current Measurements
100V
10V
1V
Com Amp
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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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Meter Loading
Amp
R
Rs
Ideal Meter
Com
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
Rs
Sensor
vs
+
–
+
vA/D
RA/D
A/D
Converter
–
vA/D is not equal to vs
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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
+
vs
+
–
Rs
–
+
vA/D
RA/D
–
Sensor
vA/D is equal to vs
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A/D
Converter
17
An Integrator
C
R
–
Vin
+
–
+
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Vout
–
18
KCL at the Inverting Input
C
iC(t)
R
iR(t) ivin(t)
+
–
–
+
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vout(t)
–
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KCL
i  0
iR (t ) 
iC (t )  C
v in ( t )  v 

R
d  v out ( t )  v  
dt
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v in ( t )
R
C
dv out ( t )
dt
20
Solve for vout(t)
v in ( t )
C
dv out ( t )
R
 0
dt
dv out ( t )
 
v in ( t )
dt
RC
t
v out ( t )  


v in ( x )
dx
RC
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Class Example
• Learning Extension E6.9
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