Electrical Engineering
Electrical Engineering
Chapter: Operational Amplifiers / Operationsverstärker
Michael E. Auer
Source of figures:
Alexander/Sadiku: Fundamentals of Electric Circuits,
McGraw-Hill
Michael E.Auer
20.09.2013
EE05
Electrical Engineering
Chapter Content
Basics of Op Amps / OV Grundlagen
Ideal Op Amp / Idealer OV
Inverting Amplifier / Invertierender Verstärker
Noninverting Amplifier / Nichtinvertierender Verstärker
Summing Amplifier / Summierer Verstärker
Difference Amplifier / Differenzverstärker
Cascaded Op Amp Circuits / Zusammenschaltung von OVs
Summary / Zusammenfassung
Michael E.Auer
20.09.2013
EE05
Electrical Engineering
Chapter Content
Basics of Op Amps / OV Grundlagen
Ideal Op Amp / Idealer OV
Inverting Amplifier / Invertierender Verstärker
Noninverting Amplifier / Nichtinvertierender Verstärker
Summing Amplifier / Summierer Verstärker
Difference Amplifier / Differenzverstärker
Cascaded Op Amp Circuits / Zusammenschaltung von OVs
Summary / Zusammenfassung
Michael E.Auer
20.09.2013
EE05
Electrical Engineering
OpAmp Basics (1)


Michael E.Auer
It is an electronic unit that behaves like a
voltage-controlled voltage source.
It is an active circuit element designed to
perform amplification and mathematical
operations of addition, subtraction,
multiplication, division, differentiation and
integration.
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EE05
Electrical Engineering
OpAmp Basics (2)
A typical op amp: (a) pin configuration, (b) circuit symbol , (b) device
(c)
Michael E.Auer
20.09.2013
EE05
Electrical Engineering
OpAmp Basics (3)
The equivalent circuit
Of the non-ideal op amp
Op Amp output:
vo as a function of Vd
A – Open Loop Voltage Gain
vd = v2 – v1
Michael E.Auer
vo = A·vd = A(v2 –v1)
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EE05
Electrical Engineering
OpAmp Basics (4)
Typical ranges for op amp parameters
Michael E.Auer
Parameter
Typical range
Ideal values
Open-loop gain, A
105 to 108
∞
Input resistance, Ri
105 to 1013 Ω
∞Ω
Output resistance, Ro
1 to 50 Ω
0Ω
Supply voltage, VCC
5 to 15 V
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EE05
Electrical Engineering
OpAmp Example
Circuit
Michael E.Auer
Simulation model
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EE05
Electrical Engineering
Chapter Content
Basics of Op Amps / OV Grundlagen
Ideal Op Amp / Idealer OV
Inverting Amplifier / Invertierender Verstärker
Noninverting Amplifier / Nichtinvertierender Verstärker
Summing Amplifier / Summierer Verstärker
Difference Amplifier / Differenzverstärker
Cascaded Op Amp Circuits / Zusammenschaltung von OVs
Summary / Zusammenfassung
Michael E.Auer
20.09.2013
EE05
Electrical Engineering
Definition of the Ideal OpAmp
An ideal op amp has the following characteristics:
•
Infinite open-loop gain, A ≈ ∞
Vd = 0
•
Infinite input resistance, Ri ≈ ∞
i1 = i2 = 0
•
Zero output resistance, Ro ≈ 0
Ideal Voltage source
Michael E.Auer
20.09.2013
EE05
Electrical Engineering
Chapter Content
Basics of Op Amps / OV Grundlagen
Ideal Op Amp / Idealer OV
Inverting Amplifier / Invertierender Verstärker
Noninverting Amplifier / Nichtinvertierender Verstärker
Summing Amplifier / Summierer Verstärker
Difference Amplifier / Differenzverstärker
Cascaded Op Amp Circuits / Zusammenschaltung von OVs
Summary / Zusammenfassung
Michael E.Auer
20.09.2013
EE05
Electrical Engineering
Inverting Amplifier Basic Circuit

Inverting amplifier reverses the polarity of the
input signal while amplifying it
vo = −
AV = −
Rf
R1
vi
Rf
R1
Voltage gain
Rin = R1
Rout = 0
Michael E.Auer
20.09.2013
EE05
Electrical Engineering
Inverting Amplifier Equivalent Circuit
Polarity !
Michael E.Auer
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EE05
Electrical Engineering
Inverting Amplifier Example (1)
Refer to the op amp below. If vi = 0.5V, calculate:
(a) The voltage gain,
(b) the output voltage, vo and
(c) the current in the 10kΩ resistor.
Answer:
(a) – 2.5; (b) -1.25V; (c)
50μA
Michael E.Auer
20.09.2013
EE05
Electrical Engineering
Inverting Amplifier Example (2)
Determine the voltage vo in the circuit below.
Answer:
vo = 3∙va – 12 = -6V
Michael E.Auer
20.09.2013
EE05
Electrical Engineering
Chapter Content
Basics of Op Amps / OV Grundlagen
Ideal Op Amp / Idealer OV
Inverting Amplifier / Invertierender Verstärker
Noninverting Amplifier / Nichtinv. Verstärker
Summing Amplifier / Summierer Verstärker
Difference Amplifier / Differenzverstärker
Cascaded Op Amp Circuits / Zusammenschaltung von OVs
Summary / Zusammenfassung
Michael E.Auer
20.09.2013
EE05
Electrical Engineering
Noninverting Amplifier Basic Circuit

Non-inverting amplifier is designed to produce positive
voltage gain
 Rf 
 ⋅ vi
vo = 1 +
R1 

AV = 1 +
Rf
R1
positive !
Rin = ∞
Rout = 0
Michael E.Auer
20.09.2013
EE05
Electrical Engineering
Noninverting Amplifier Example
Calculate the voltage vo in the circuit below.
Answer:
vo = 7V
Michael E.Auer
20.09.2013
EE05
Electrical Engineering
Unity Gain Amplifier (Voltage Follower)
Special noninverting amplifier with: Rf = 0 ; R1 = ∞
Application as buffer amplifier to isolate
one circuit from another
Voltage follower
Michael E.Auer
20.09.2013
EE05
Electrical Engineering
Chapter Content
Basics of Op Amps / OV Grundlagen
Ideal Op Amp / Idealer OV
Inverting Amplifier / Invertierender Verstärker
Noninverting Amplifier / Nichtinvertierender Verstärker
Summing Amplifier / Summierer Verstärker
Difference Amplifier / Differenzverstärker
Cascaded Op Amp Circuits / Zusammenschaltung von OVs
Summary / Zusammenfassung
Michael E.Auer
20.09.2013
EE05
Electrical Engineering
Summing Amplifier Basic Circuit

Summing Amplifier is an op amp circuit that combines
several inputs and produces an output that is the
weighted sum of the inputs.
Rf
Rf 
 Rf
vo = − 
v1 +
v2 +
v3 
R2
R3 
 R1
if R1 = R2 = R3 :
Rf
Rf 
 Rf
vo = − 
v1 +
v2 +
v3 
R1
R1 
 R1
Rf
vo = −
⋅ (v1 + v2 + v3 )
R1
Michael E.Auer
20.09.2013
EE05
Electrical Engineering
Summing Amplifier Example
Calculate the voltage vo and the current io.
Answer:
vo = -8V; io = - 4.8mA
Michael E.Auer
20.09.2013
EE05
Electrical Engineering
Chapter Content
Basics of Op Amps / OV Grundlagen
Ideal Op Amp / Idealer OV
Inverting Amplifier / Invertierender Verstärker
Noninverting Amplifier / Nichtinvertierender Verstärker
Summing Amplifier / Summierer Verstärker
Difference Amplifier / Differenzverstärker
Cascaded Op Amp Circuits / Zusammenschaltung von OVs
Summary / Zusammenfassung
Michael E.Auer
20.09.2013
EE05
Electrical Engineering
Difference Amplifier Basic Circuit

Difference amplifier is a device that amplifies the
difference between two inputs but rejects any signals
common to the two inputs.
vo =
R2 (1 + R1 / R2 )
R
v2 − 2 v1
R1 (1 + R3 / R4 )
R1
vo = v2 − v1
if
Michael E.Auer
20.09.2013
R2 R3
=
=1
R1 R4
EE05
Electrical Engineering
Instrumentation Amplifier
Michael E.Auer
20.09.2013
EE05
Electrical Engineering
Chapter Content
Basics of Op Amps / OV Grundlagen
Ideal Op Amp / Idealer OV
Inverting Amplifier / Invertierender Verstärker
Noninverting Amplifier / Nichtinvertierender Verstärker
Summing Amplifier / Summierer Verstärker
Difference Amplifier / Differenzverstärker
Cascaded Op Amp Circuits / Zusammenschaltung
von OVs
Summary / Zusammenfassung
Michael E.Auer
20.09.2013
EE05
Electrical Engineering
Cascaded OpAmps

It is an arrangement of two or more op amp circuits such
that the output to one is the input of the next.
vo = A ⋅ v1
Michael E.Auer
with
20.09.2013
A = A1 ⋅ A2 ⋅ A3
EE05
Electrical Engineering
Two-stage Amplifier Example
Determine R1 to R5 so that vo = -5v1+3v2 and Rin = 10kΩ.
R4
R5
R2
Answer:
R1 = R3 = 10kΩ
R4 = 30kΩ
R2 = R5 = 50kΩ
Michael E.Auer
20.09.2013
EE05
Electrical Engineering
Cascaded OpAmps Example
Find vo and io in the circuit shown below.
Answer:
350mV, 25μA
Michael E.Auer
20.09.2013
EE05
Electrical Engineering
Application: DAC

Digital-to Analog Converter (DAC) : it is a device which
transforms digital signals into analog form.
Four-bit DCA: (a) block diagram (b) binary weighted ladder type
− V0 =
Rf
R1
V1 +
Rf
R2
V2 +
Rf
R3
V3 +
Rf
R4
V4
where
V1 – MSB, V4 – LSB
V1 to V4 are either 0 or 1 V
Michael E.Auer
20.09.2013
EE05
Electrical Engineering
Chapter Content
Basics of Op Amps / OV Grundlagen
Ideal Op Amp / Idealer OV
Inverting Amplifier / Invertierender Verstärker
Noninverting Amplifier / Nichtinvertierender Verstärker
Summing Amplifier / Summierer Verstärker
Difference Amplifier / Differenzverstärker
Cascaded Op Amp Circuits / Zusammenschaltung von OVs
Summary / Zusammenfassung
Michael E.Auer
20.09.2013
EE05
Electrical Engineering
Summary
•
•
•
•
•
•
•
•
•
•
The OpAmp is a high gain amplifier that has high input resistance and low output resistance.
An ideal OpAmp has an infinite input resistance, a zero output resistance, and an infinite
gain.
For an ideal OpAmp, the current into each of its two input terminals is zero, and the voltage
across its input terminals is negligibly small.
In an inverting amplifier, the output is a negative multiple of the input.
In a noninverting amplifier, the output is a positive multiple of the input.
In a voltage follower, the output follows the input.
In a summing amplifier, the output is the weighted sum of the inputs.
In a difference amplifier, the output is proportional to the difference of the two inputs.
OpAmp circuits may be cascaded without changing their input-output relationships.
Typical applications of the OpAmp considered in this chapter include the DAC and the
instrumentation amplifier.
Michael E.Auer
20.09.2013
EE05