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ME 6405 INTRODUCTION TO MECHATRONICS :. OPERATIONAL AMPLIFICATORS. Dr. Ume ME 6405 Introduction to mechatronics. Contents. Introduction Theory A. Definition and presentation B. Linear Mode C. Non Linear Mode Real Operational Amplificators Uses Conclusion References. - PowerPoint PPT Presentation
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OPERATIONAL OPERATIONAL AMPLIFICATORSAMPLIFICATORS
Dr. UmeDr. Ume ME 6405 Introduction to mechatronicsME 6405 Introduction to mechatronics
ME 6405ME 6405INTRODUCTION TO INTRODUCTION TO MECHATRONICSMECHATRONICS::
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
ContentsContentsIntroductionIntroduction
I.I. TheoryTheory
A. Definition and presentationA. Definition and presentation
B. Linear ModeB. Linear Mode
C. Non Linear Mode C. Non Linear Mode
II.II. Real Operational AmplificatorsReal Operational Amplificators
III.III. Uses Uses
ConclusionConclusion
ReferencesReferences
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
Definition and presentationDefinition and presentationT
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Operational Amplifier (Op Amp)Operational Amplifier (Op Amp)
DefinitionDefinition: a high gain electronic : a high gain electronic amplifying circuit element in a amplifying circuit element in a feedback amplifier, that feedback amplifier, that accomplishes many functions or accomplishes many functions or mathematical “operations” inmathematical “operations” inanalog circuits.analog circuits.
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
Definition and presentationDefinition and presentationT
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Op Amp components:Op Amp components:
transistorstransistors
resistorsresistors
diodesdiodes
capacitorscapacitors
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
Definition and presentationDefinition and presentationT
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Op Amp Circuit ModelOp Amp Circuit Model
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
Op Amp Circuit Chip
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
Definition and presentationDefinition and presentationT
heo
ryT
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circuit analysis :circuit analysis :
Amplifier operates in its linear Amplifier operates in its linear amplifying regionamplifying region
Large voltage gain (A) Large voltage gain (A)
VVAVout
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
Difference between input voltages Difference between input voltages to Op Amp is very small because to Op Amp is very small because voltage gain (A) is very largevoltage gain (A) is very large
Input impedance (RInput impedance (Rii) is large ) is large 0
iR
VVii
VVA
VVV out
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
Transfer Characteristic:Transfer Characteristic:
ModesModes + saturation ( )+ saturation ( )
- saturation ( )- saturation ( )
linear ( )linear ( )
ccout VV
ccout VV
VVAVout
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
Op Amp transfer characteristic relation
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
ei
e0
i2
i1
AnalysisAnalysis• 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 < eo < 10V )
Inverting Op AmpInverting Op Amp
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
ei
e0
i2
i1
AnalysisAnalysis• The difference between input
voltages to the op amp is very small, essentially 0.
• The input impedance to the op-amp is extremely large.
e+
e'
Inverting OpInverting Op Amp Amp
0'0
Ke
ee
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
AnalysisAnalysis• For e.g. if |eo | < 10V
and K = 105 then
|e+ - e’| =10/105 = 100 V
• For the inverting amplifier,
e+ is grounded.
Hence e+ 0 and e’ 0
ei
i2
i1
e+
e'e0
Inverting OpInverting Op Amp Amp
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
• The equation for this circuit can be obtained as follows:
ei
i2
i1e+
e' e0
Inverting OpInverting Op Amp Amp
2
02
1
i1 R
ee'i,
R
e'ei
21ii
2
0
1
i
R
ee'
R
e'e
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
Since K (0 - e’) = e0 and K >>>1,
then e’ 0 since
ei
i2
i1e+
e' e0
Inverting OpInverting Op Amp Amp
Ke
e' 0
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
• Hence we have
or
ei
i2
i1e+
e' e0
Notice that the sign of
the output voltage, e0
is the negative of that
of the input voltage, ei.
Inverting OpInverting Op Amp Amp
2
0
1
i
R
e
R
e
i1
20
.eRR
e
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
• 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
(GROUND)
ei e0
Non - Inverting OpNon - Inverting Op Amp Amp
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
For this circuit we have ,
where K is the differential gain of the amplifier.
(GROUND)
ei e0
Non - Inverting OpNon - Inverting Op Amp Amp
021
1i0
.eRR
ReKe
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
• 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.
(GROUND)
ei e0
Non - Inverting OpNon - Inverting Op Amp Amp
i1
20
.eRR
1e
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
• An inverting amplifier can accept two or more inputs and
produce a weighted sumAt X,
I = IA + IB + IC
and we can see that:
SummingSumming Amplifier Amplifier
C
CC
B
BB
A
AA R
VIand,
RV
I,RV
I
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
• By utilizing the usual assumptions, we obtain:
SummingSumming Amplifier Amplifier
CC
2B
B
2A
A
2out
.VRR
.VRR
.VRR
V
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
• A differential amplifier is one that amplifies the difference
between two voltages
DifferenDifferencing Amplifiercing Amplifier
21
2
2
X
RRR
VV
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
• The current through the feedback resistance must be equal to that from V1 through R1
DifferenDifferencing Amplifiercing Amplifier
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
• Hence
• which can be rearranged to give,
DifferenDifferencing Amplifiercing Amplifier
2
outX
1
X1
R
VV
R
VV
121
2out
VVR
RV
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
• Potential Difference across capacitor = VX - Vout
q = CV
Integrating AmplifierIntegrating Amplifier
2
1
t
t
Vout
x
Vin
dt
dVC.i
dt
dq
dt
dVC.i out
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
2
1
t
tRearranging this gives
Integrating both sides gives
Vout
x
Vin
Integrating AmplifierIntegrating Amplifier
.dtVRC
1dV
inout
2
1
t
tin1out2out.dtV
RC
1tVtV
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
Non Linear ModeNon Linear Mode T
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input
outputVs1
Vs2
General use of op amp:General use of op amp:
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
Non Linear ModeNon Linear Mode T
heo
ryT
heo
ryThe op amp is only used in saturationThe op amp is only used in saturation
mode:mode:
input
outputVs1
Vs2
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
Non Linear ModeNon Linear Mode T
heo
ryT
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ryHow to find the output:How to find the output:
+
-
U1
U2
U3
Vs1
Vs2
If U1 > U2,
U3 = Vs1
If U2 > U1,
U3 = Vs2
In each case, i3 is unknown and i1 and i2 are null.
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
Non Linear ModeNon Linear Mode T
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ryT
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ryGate operator: ORGate operator: OR
1V
+
-
U1
U2 U3
5V
0V
If U1 or/and U2 = 5V,
U3 = 5V
If U2 and U1 = 0V,
U3 = 0V
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
Non Linear ModeNon Linear Mode T
heo
ryT
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ryOther gate: NON OROther gate: NON OR
+
-U3
5V
0V
1V
U1
U2
If U1 or/and U2 = 5V,
U3 = 0V
If U2 and U1 = 0V,
U3 = 5V
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
Non Linear ModeNon Linear Mode T
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ryTwo offsets comparator:Two offsets comparator:
If
U3 = 0V
If
U3 = 5V
+
-
U1
U2
U3
5V
0V
R1
R2
1
21
22
.URR
RU
21
2112
RR
.RU5.RU
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
Non Linear ModeNon Linear Mode T
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ryTwo offsets comparator (cont):Two offsets comparator (cont):
input
outputVs1
Vs2
Uup
Udown
If U2 ≤ Udown ,
U3 = 0V
If U2 ≥ Uup,
U3 = 5V
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
Non Linear ModeNon Linear Mode T
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ry U3 will alternativelly be equal to 5V for T second and to -5V for T seconds.
In this case
The square wave supplier or clock:The square wave supplier or clock:
+
-U3
5V
-5V
R1
R1
C
R2
0V
2C.R
1T
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
Non Linear ModeNon Linear Mode T
heo
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heo
ryThe square wave supplier or clock (cont):The square wave supplier or clock (cont):
T
output
time
T
2C.R
1T
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
InternInternalal electrical schema electrical schemaR
eal O
per
atio
nal
Rea
l Op
erat
ion
alA
mp
lific
ato
rsA
mp
lific
ato
rsDifferentialPart
Gain Part
Push/PullOutput
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
Input CharacteristicsInput CharacteristicsR
eal O
per
atio
nal
Rea
l Op
erat
ion
alA
mp
lific
ato
rsA
mp
lific
ato
rs Input Impedance: 1M to more than 20 MInput Impedance: 1M to more than 20 M
and notand not infinite infinite
Input Offset (most important default):Input Offset (most important default):when V+ or V- are low or G is highwhen V+ or V- are low or G is high
some 10 some 10 VV
because T1 and T2 are notbecause T1 and T2 are notexactly the sameexactly the same
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
Input CharacteristicsInput CharacteristicsR
eal O
per
atio
nal
Rea
l Op
erat
ion
alA
mp
lific
ato
rsA
mp
lific
ato
rs PPolarization olarization currents:currents:
to polarize T1 and T2to polarize T1 and T2
Offset currentsOffset currents1/201/20thth to 1/5 to 1/5thth of I+ and I- of I+ and I-due to resistors and polarization currentsdue to resistors and polarization currents
Limited Input VoltageLimited Input Voltage
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
Transfer CharacteristicsTransfer CharacteristicsR
eal O
per
atio
nal
Rea
l Op
erat
ion
alA
mp
lific
ato
rsA
mp
lific
ato
rs The output is proportional to the The output is proportional to the
input:input:
It is limited by VIt is limited by Vsat+sat+ and V and Vsat-sat-
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
OutOutput Characteristicsput CharacteristicsR
eal O
per
atio
nal
Rea
l Op
erat
ion
alA
mp
lific
ato
rsA
mp
lific
ato
rs Output Impedance not null:Output Impedance not null:
around 100 around 100
Slew rateSlew rate 0,5V/µs0,5V/µs up to up to 150V/µs150V/µs
capacitor needs to be chargedcapacitor needs to be charged
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
OutOutput Characteristicsput CharacteristicsR
eal O
per
atio
nal
Rea
l Op
erat
ion
alA
mp
lific
ato
rsA
mp
lific
ato
rs Vs limited by VVs limited by Vsat+ sat+ and Vand Vsat-sat-
Output currents limited (some mA) Output currents limited (some mA) to protect op-ampsto protect op-amps
high impedances needed high impedances needed
High Power userHigh Power user 250mW250mW to several Watts to several Watts
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
SummarySummaryR
eal O
per
atio
nal
Rea
l Op
erat
ion
alA
mp
lific
ato
rsA
mp
lific
ato
rs
StaticEquivalentschema
DynamicEquivalentschema
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
SummarySummaryR
eal O
per
atio
nal
Rea
l Op
erat
ion
alA
mp
lific
ato
rsA
mp
lific
ato
rs
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
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
SummarySummaryR
eal O
per
atio
nal
Rea
l Op
erat
ion
alA
mp
lific
ato
rsA
mp
lific
ato
rs
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
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
SolutionsSolutionsR
eal O
per
atio
nal
Rea
l Op
erat
ion
alA
mp
lific
ato
rsA
mp
lific
ato
rs Be careful because VBe careful because Vsat+ sat+ and Vand Vsat-sat- are are
different different trigger… trigger…
Be careful with high frequency Be careful with high frequency integratorsintegrators Input Impedance may be too low Input Impedance may be too low
Offset can be Offset can be compensatedcompensated(already exists (already exists or special or special schema)schema)
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
SolutionsSolutionsR
eal O
per
atio
nal
Rea
l Op
erat
ion
alA
mp
lific
ato
rsA
mp
lific
ato
rs Need to have sameNeed to have same
polarization currentspolarization currents
Need to use lowNeed to use lowresistors at inputresistors at inputto limit offset currentto limit offset current
Do not overpass VDo not overpass Vinin maxi maxi
Chose fast op-amps (10V/µs) for Chose fast op-amps (10V/µs) for high frequency requirements or use high frequency requirements or use a differencing comparatora differencing comparator
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
Practical ApplicationsPractical ApplicationsU
ses
Use
s Applications:Applications:
Perform math operationsPerform math operations
inexpensive and lead to easy inexpensive and lead to easy designs that are easy to constructdesigns that are easy to construct
Power Source Power Source
PID ControlPID Control
FilterFilter
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
Characteristics / NumbersCharacteristics / Numbers U
ses
Use
s Op Amp Examples:Op Amp Examples:
Type Price($)
OutputCurrent(mA)
MinsupplyV (volt)
VoltageNoise(nV/Hz)
CLC452
1.24 130 5 2.80
LF 147 4.50 30 5 20
CLC400
17.80 70 10 2.60
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
CONCLUSIONCONCLUSION IntroductionIntroduction
Theory of Op Amp’sTheory of Op Amp’s
Definition and AnalysisDefinition and Analysis
Linear ModeLinear Mode
Non Linear ModeNon Linear Mode
Real Operational AmplifiersReal Operational Amplifiers
UsesUses In practice, do not hesitate to make the In practice, do not hesitate to make the
assemblies more abracadabrantsassemblies more abracadabrants Have Fun Have Fun
ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics
REFERENCESREFERENCES Cogdell, J.R. Cogdell, J.R. Foundations of Electrical Foundations of Electrical
EngineeringEngineering. Pg 489-506, 1996. Pg 489-506, 1996
Thomas, Ronald E. Thomas, Ronald E. The Analysis and Design The Analysis and Design of Linear Circuitsof Linear Circuits. pg 186-221, 1998. pg 186-221, 1998
Walter G. Jung, Walter G. Jung, IC Op-Amp Cook BookIC Op-Amp Cook Book
Michel GirardMichel Girard, , Amplificateurs opérationnels 1Amplificateurs opérationnels 1 & 2 & 2
www.uoguelph.ca/~antoon/gadgets/T41.htmwww.uoguelph.ca/~antoon/gadgets/T41.htm
www.national.com/appinfo/amps/ www.national.com/appinfo/amps/
http://c3iwww.epfl.ch/teaching/physiciens/lecon07/http://c3iwww.epfl.ch/teaching/physiciens/lecon07/lecoleconn7.html7.html
http://courelectr.free.fr/AOP/AOP.HTMhttp://courelectr.free.fr/AOP/AOP.HTM