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Ideal Operational Amplifiers
and Op-Amp Circuits
Chapter 2
In this lesson, we will:
 Develop the parameters and characteristics of
the ideal operational amplifier, and determine
the analysis method of ideal op-amp circuits.
 inverting operational amplifier
 summing operational amplifier
 noninverting operational amplifier
 Analyze several ideal op-amp circuits including
the voltage follower, difference amplifier, and the
instrumentation amplifier.
 Design several ideal op-amp circuits with given
design specifications.
Ideal Op-Amp Characteristics
1. Internal differential gain Aod is infinite.
2. Differential input voltage (v2-v1) is zero.
3. Effective input resistance is infinite.
4. Output resistance is zero so output voltage is
connected directly to dependent voltage
source.
Equivalent Circuit of Op-Amp
Non-Ideal Effect – Output Saturation
Non-Ideal Effect - Offset Voltage
Non-Ideal Effect – Slew Rate
Inverting Op-Amp
Problem-Solving Technique:
Ideal Op-Amp Circuits
1. If noninverting terminal is grounded, then
inverting terminal is virtual ground.
a. Sum currents at node assuming no current
enters Op Amp.
2. If noninverting terminal is not grounded, then
inverting terminal voltage is equal to that of
the noninverting terminal.
a. Sum currents at node assuming no current
enters Op Amp.
3. Output voltage is determined from either
Step 1 or 2.
Inverting Op-Amp with Finite
Differential-Mode Gain
R2
Av  
R1
1
R2
1
[1 
(1  )]
Aod
R1
Example Problem
Example Problem
Av=vO/vI=?
Example Problem
RI=vI/iI=?
Example Problem
Av=vO/vI=?
Example Problem
RI=vI/iI=?
Summing Op-Amp
RF
RF
RF
vO   (
vI1 
vI 2 
vI 3 )
R1
R2
R3
Example Problem
Example Problem
Example Problem
RF
RF
RF
vO   (
vI1 
vI 2 
vI 3 )
R1
R2
R3
Available Resistor Values in the Lab
1/4 Watt, 5% Tolerance
10
22
47
68
100 120 150 220 270 330 390 470 560 680 820
1K 1.2K 1.5K 2.2K 2.7K 3.3K 3.9K 4.7K 5.6K 6.8K 8.2K
10K 12K 15K 22K 27K 33K 39K 47K 56K 68K 82K
100K 120K 150K 220K 270K 330K 390K 470K 560K 680K 820K
1M
10M
1/2 Watt, 5% Tolerance
20
100
150 200
47
Example Problem
Noninverting Op-Amp
Noninverting Op-Amp
Example Problem
Example Problem
Example Problem
Example Problem
Op-Amp Voltage Reference Circuit
Voltage Follower
vO  vI
Voltage Follower
vO
RL

v I R L  RS
Op-Amp Difference Amplifier
Op-Amp Difference Amplifier
Instrumentation Amplifier
Instrumentation Amplifier
Instrumentation Amplifier