INTRODUCTION TO MECHATRONICS:

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INTRODUCTION TO MECHATRONICS
OPERATIONAL AMPLIFICATORS
Introduction to mechatronics
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Contents

• Introduction
• Theory
• A. Definition and presentation
• B. Linear Mode
• C. Non Linear Mode
• Real Operational Amplificators
• Uses
• Conclusion
• References

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Definition and presentation
Operational Amplifier (Op Amp) Definition a
high gain electronic amplifying circuit element
in a feedback amplifier, that accomplishes many
functions or mathematical operations inanalog
circuits.
Theory
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Definition and presentation

• Op Amp components
• transistors
• resistors
• diodes
• capacitors

Theory
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Definition and presentation
Op Amp Circuit Model
Theory
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Op Amp Circuit Chip
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Definition and presentation

• Behavior assumptions for Op Amp circuit analysis
  
• Amplifier operates in its linear amplifying
  region
• Large voltage gain (A)

Theory
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• Difference between input voltages to Op Amp is
  very small because voltage gain (A) is very
  large
• Input impedance (Ri) is large

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• Transfer Characteristic
• Modes
• saturation ( )
• - saturation ( )
• linear ( )

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• Op Amp transfer characteristic relation

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Inverting Op Amp

• Analysis
• We assume that the Op-Amp gain is very high,
  effectively infinity.
• It is assumed that the amplifier operates in its
  linear amplifying region.
• ( for e.g. -10V lt eo lt 10V )

i2
e0
i1
ei
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Inverting Op Amp

• Analysis
• The difference between input voltages to the op
  amp is very small, essentially 0.
• The input impedance to the op-amp is extremely
  large.

i2
e0
i1
e'
ei
e
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Inverting Op Amp

• Analysis
• For e.g. if eo lt 10V
• and K 105 then
• e - e 10/105 100 ?V
• For the inverting amplifier,
• e is grounded.
• Hence e 0 and e 0

i2
e0
i1
e'
ei
e
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Inverting Op Amp

• The equation for this circuit can be obtained as
  follows

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Inverting Op Amp
i2
e0
i1
e'
ei
e

• Since K (0 - e) e0 and K gtgtgt1,
• then e 0 since

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Inverting Op Amp
i2
e0
i1
e'
ei
e

• Hence we have
• or

Notice that the sign of the output voltage, e0
is the negative of that of the input voltage,
ei.
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Non - Inverting Op Amp
ei
e0
(GROUND)

• For the non-inverting amplifier the input is
  connected to
• the non-inverting input.
• The same assumptions have been made as in the
  case of
• the Inverting Op Amp

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Non - Inverting Op Amp
ei
e0
(GROUND)

• For this circuit we have ,
• where K is the differential gain of the
  amplifier.

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Non - Inverting Op Amp
ei
e0
(GROUND)

• This leads to
• A particular form of this amplifier is when the
  feedback
• loop is a short circuit, I.e. R2 0. Then the
• voltage gain is 1, such an amplifier is called a
  
• Voltage Follower.

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Summing Amplifier

• An inverting amplifier can accept two or more
  inputs and
• produce a weighted sum
• At X,
• I IA IB IC
• and we can see that
  

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Summing Amplifier

• By utilizing the usual assumptions, we obtain

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Differencing Amplifier

• A differential amplifier is one that amplifies
  the difference
• between two voltages

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Differencing Amplifier

• The current through the feedback resistance must
  be
• equal to that from V1 through R1

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Differencing Amplifier

• Hence
• which can be rearranged to give,

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Integrating Amplifier
Vout
Vin
x

• Potential Difference across capacitor VX -
  Vout
• q CV

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Integrating Amplifier
Vout
Vin
x

• Rearranging this gives
• Integrating both sides gives

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Non Linear Mode
General use of op amp
Theory
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Non Linear Mode
The op amp is only used in saturation mode
Theory
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Non Linear Mode
How to find the output
If U1 gt U2, U3 Vs1 If U2 gt U1, U3 Vs2
Theory
In each case, i3 is unknown and i1 and i2 are
null.
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Non Linear Mode
Gate operator OR
If U1 or/and U2 5V, U3 5V If U2 and U1
0V, U3 0V
Theory
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Non Linear Mode
Other gate NON OR
If U1 or/and U2 5V, U3 0V If U2 and U1
0V, U3 5V
Theory
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Non Linear Mode
Two offsets comparator
If U3 0V If U3 5V
Theory
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Non Linear Mode
Two offsets comparator (cont)
If U2 Udown , U3 0V If U2 Uup, U3 5V
Theory
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Non Linear Mode
The square wave supplier or clock
U3 will alternativelly be equal to 5V for T
second and to -5V for T seconds. In this case
Theory
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Non Linear Mode
The square wave supplier or clock (cont)
Theory
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Internal electrical schema
Real OperationalAmplificators
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Input Characteristics

• Input Impedance 1M to more than 20 Mand not
  infinite
• Input Offset (most important default)when V
  or V- are low or G is high ? some 10
  ?V because T1 and T2 are notexactly the same

Real OperationalAmplificators
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Input Characteristics

• Polarization currentsto polarize T1 and T2
• Offset currents1/20th to 1/5th of I and I-due
  to resistors and polarization currents
• Limited Input Voltage

Real OperationalAmplificators
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Transfer Characteristics

• The output is proportional to the input
• It is limited by Vsat and Vsat-

Real OperationalAmplificators
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Output Characteristics

• Output Impedance not null ? around 100 ?
• Slew rate ? 0,5V/µs up to 150V/µscapacitor
  needs to be charged

Real OperationalAmplificators
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Output Characteristics

• Vs limited by Vsat and Vsat-
• Output currents limited (some mA) to protect
  op-amps? high impedances needed
• High Power user? 250mW to several Watts

Real OperationalAmplificators
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Summary
StaticEquivalentschema
Real OperationalAmplificators
DynamicEquivalentschema
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Summary
Characteristics Ideal Real
Input Impedance Ze ? 1M? up to 20 M ?
Output Impedance Zs 0 ? Some10th ?
Gain ? 20.104 up to 20.1012
Offset 0V 25 µV up to 15 mV
Real OperationalAmplificators
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Summary
Characteristics Ideal Real
Polarization Current 0 mA 20 pA up to 500 pA
Offset Current 0 mA 10 pA up to 200 mA
Slow rate ? V/µS 0,5 V/µS up to 100 V/µS
Real OperationalAmplificators
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Solutions

• Be careful because Vsat and Vsat- are different
  ? trigger
• Be careful with high frequency integrators ?
  Input Impedance may be too low
• Offset can be compensated(already exists or
  special schema)

Real OperationalAmplificators
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Solutions

• Need to have samepolarization currents
• Need to use lowresistors at inputto limit
  offset current
• Do not overpass Vin maxi
• Chose fast op-amps (10V/µs) for high frequency
  requirements or use a differencing comparator

Real OperationalAmplificators
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Practical Applications

• Applications
• Perform math operations
• inexpensive and lead to easy designs that are
  easy to construct
• Power Source
• PID Control
• Filter

Uses
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Characteristics / Numbers
Op Amp Examples
Uses
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CONCLUSION

• Introduction
• Theory of Op Amps
• Definition and Analysis
• Linear Mode
• Non Linear Mode
• Real Operational Amplifiers
• Uses
• In practice, do not hesitate to make the
  assemblies more abracadabrants ? Have Fun

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REFERENCES
Cogdell, J.R. Foundations of Electrical
Engineering. Pg 489-506, 1996 Thomas, Ronald E.
The Analysis and Design of Linear Circuits. pg
186-221, 1998 Walter G. Jung, IC Op-Amp Cook
Book Michel Girard, Amplificateurs opérationnels
1 2 www.uoguelph.ca/antoon/gadgets/T41.htm www
.national.com/appinfo/amps/ http//c3iwww.epfl.ch
/teaching/physiciens/lecon07/lecon7.html http//c
ourelectr.free.fr/AOP/AOP.HTM