Download Op Amp Circuits - Keith E. Holbert

Op Amp Circuits
Dr. Holbert
February 13, 2008
Lect9
EEE 202
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
Lect9
EEE 202
2
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
Lect9
EEE 202
3
A Generic Digital Meter
Input Switching
and Ranging
A/D Converter
Amplifier
Display
Lect9
Processor
EEE 202
4
Voltage Measurements
100V
10V
1V
Hi
Lect9
EEE 202
Com
5
Model for Meter
Hi
10MW
Ideal Meter
Com
The ideal meter measures the voltage
across its inputs. No current flows into the
ideal meter; it has infinite input resistance
Lect9
EEE 202
6
Meter Loading
Hi
R
10MW
Ideal Meter
Com
The 10MW meter resistance in parallel with
R may change the voltage that you measure
Lect9
EEE 202
7
Loading
• When measuring the voltage across R, we
need to make sure that R is much less
than 10 MW
• If R is close to 10 MW, significant current
flows through the meter, changing the
voltage across R
Lect9
EEE 202
8
Loading Example
Hi
50mA
2MW
10MW
Ideal Meter
Com
• Without Meter: voltage is 100 V
• With Meter: measured voltage is 83.3 V
Lect9
EEE 202
9
Current Measurements
100V
10V
1V
Com Amp
Lect9
EEE 202
10
Measuring 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
computed
Lect9
EEE 202
11
Meter Loading
Amp
R
Rs
Ideal Meter
Com
The Rs shunt resistance in series with R
may change the current that you measure
Lect9
EEE 202
12
The Voltage Follower
+
–
vin
+
–
+
vout
–
Lect9
EEE 202
13
Without a Voltage Follower
Rs
Sensor
vs
+
–
+
vA/D
RA/D
A/D
Converter
–
vA/D is not equal to vs
Lect9
EEE 202
14
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
Lect9
EEE 202
15
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
Lect9
EEE 202
16
With a Voltage Follower
+
vs
+
–
Rs
–
+
vA/D
RA/D
–
Sensor
vA/D is equal to vs
Lect9
EEE 202
A/D
Converter
17
An Integrator
C
R
–
Vin
Lect9
+
–
+
EEE 202
+
Vout
–
18
KCL at the Inverting Input
vin (t )  v vin (t )
iR (t ) 

R
R
C
iC(t)
R
i  0
iR(t) i–
vin(t)
+
–
–
+
+
vout(t)
–
d vout (t )  v 
dvout (t )
iC (t )  C
C
dt
dt
Lect9
EEE 202
19
Solve for vout(t)
• From the KCL:
iR (t )  iC (t )  i  0
vin (t )
dvout (t )
C
0
R
dt
dvout (t )
vin (t )

dt
RC
t
vin ( x)
vout (t )   
dx
RC

Lect9
• 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 differentiator
EEE 202
20