INTRODUCTION TO MECHATRONICS :

OPERATIONAL OPERATIONAL AMPLIFICATORSAMPLIFICATORS

Introduction to mechatronicsIntroduction to mechatronics

INTRODUCTION TO INTRODUCTION TO MECHATRONICSMECHATRONICS::

ME 6405 ME 6405 Introduction to MechatronicsIntroduction to Mechatronics

ContentsContentsIntroductionIntroductionI.I. TheoryTheory

A. Definition and presentationA. Definition and presentationB. Linear ModeB. Linear ModeC. Non Linear Mode C. Non Linear Mode

II.II. Real Operational AmplificatorsReal Operational AmplificatorsIII.III. Uses Uses ConclusionConclusionReferencesReferences


Definition and presentationDefinition and presentationTh

eory

Theo

ryOperational 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.



eory

Theo

ryOp Amp components:Op Amp components:

transistorstransistors resistorsresistors diodesdiodes capacitorscapacitors



eory

Theo

ry

Op Amp Circuit ModelOp Amp Circuit Model


Op Amp Circuit Chip



eory

Theo

ry Behavior assumptions for Op Amp Behavior assumptions for Op Amp

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


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

iRVV

ii

VVA

VVV out


Transfer Characteristic:Transfer Characteristic:ModesModes + saturation ( )+ saturation ( )

- saturation ( )- saturation ( )

linear ( )linear ( )

ccout VV

ccout VV

VVAVout


Op Amp transfer characteristic relation


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


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


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



• The equation for this circuit can be obtained as follows:

ei

i2

i1e+

e' e0


2

02

1

i1 R

ee'i,

Re'e

i

21ii

2

0

1

i

Ree'

Re'e


Since K (0 - e’) = e0 and K >>>1,

then e’ 0 since

ei

i2

i1e+

e' e0


Ke

e' 0


• 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.


2

0

1

i

Re

Re

i1

20

.eRR

e


• 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


For this circuit we have ,

where K is the differential gain of the amplifier.

(GROUND)

ei e0


021

1i0

.eRRR

eKe


• 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


i1

20

.eRR

1e


• 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:

SummingSumming Amplifier Amplifier

C

CC

B

BB

A

AA R

VIand,R

VI,R

VI


• By utilizing the usual assumptions, we obtain:

SummingSumming Amplifier Amplifier

CC

2B

B

2A

A

2out

.VRR

.VRR

.VRR

V


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

DifferenDifferencing Amplifiercing Amplifier

21

2

2

X

RRR

VV


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



• Hence

• which can be rearranged to give,


2

outX

1

X1

R

VV

R

VV

121

2out

VVR

RV


• 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


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


Non Linear ModeNon Linear Mode Th

eory

Theo

ry

input

outputVs1

Vs2

General use of op amp:General use of op amp:



eory

Theo

ryThe op amp is only used in saturationThe op amp is only used in saturationmode:mode:

input

outputVs1

Vs2



eory

Theo

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.



eory

Theo

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



eory

Theo

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



eory

Theo

ryTwo offsets comparator:Two offsets comparator:

If

U3 = 0V

If

U3 = 5V

+

-

U1

U2U3

5V

0V

R1

R2

1

21

22

.URR

RU

21

2112

RR

.RU5.RU



eory

Theo

ryTwo offsets comparator (cont):Two offsets comparator (cont):

input

outputVs1

Vs2

Uup

Udown

If U2 ≤ Udown ,

U3 = 0V

If U2 ≥ Uup,

U3 = 5V



eory

Theo

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



eory

Theo

ryThe square wave supplier or clock (cont):The square wave supplier or clock (cont):

T

output

time

T

2C.R

1T


InternInternalal electrical schema electrical schemaR

eal O

pera

tiona

lR

eal O

pera

tiona

lA

mpl

ifica

tors

Am

plifi

cato

rsDifferentialPart

Gain Part

Push/PullOutput


Input CharacteristicsInput CharacteristicsR

eal O

pera

tiona

lR

eal O

pera

tiona

lA

mpl

ifica

tors

Am

plifi

cato

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


Input CharacteristicsInput CharacteristicsR

eal O

pera

tiona

lR

eal O

pera

tiona

lA

mpl

ifica

tors

Am

plifi

cato

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


Transfer CharacteristicsTransfer CharacteristicsR

eal O

pera

tiona

lR

eal O

pera

tiona

lA

mpl

ifica

tors

Am

plifi

cato

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-


OutOutput Characteristicsput CharacteristicsR

eal O

pera

tiona

lR

eal O

pera

tiona

lA

mpl

ifica

tors

Am

plifi

cato

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/µscapacitor needs to be chargedcapacitor needs to be charged


OutOutput Characteristicsput CharacteristicsR

eal O

pera

tiona

lR

eal O

pera

tiona

lA

mpl

ifica

tors

Am

plifi

cato

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


SummarySummaryR

eal O

pera

tiona

lR

eal O

pera

tiona

lA

mpl

ifica

tors

Am

plifi

cato

rs

StaticEquivalentschema

DynamicEquivalentschema


SummarySummaryR

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tiona

lR

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ifica

tors

Am

plifi

cato

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


SummarySummaryR

eal O

pera

tiona

lR

eal O

pera

tiona

lA

mpl

ifica

tors

Am

plifi

cato

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


SolutionsSolutionsR

eal O

pera

tiona

lR

eal O

pera

tiona

lA

mpl

ifica

tors

Am

plifi

cato

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)


SolutionsSolutionsR

eal O

pera

tiona

lR

eal O

pera

tiona

lA

mpl

ifica

tors

Am

plifi

cato

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


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


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


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


REFERENCESREFERENCES Cogdell, J.R. Cogdell, J.R. Foundations of Electrical Foundations of Electrical

EngineeringEngineering. Pg 489-506, 1996. Pg 489-506, 1996Thomas, 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, 1998Walter G. Jung, Walter G. Jung, IC Op-Amp Cook BookIC Op-Amp Cook BookMichel GirardMichel Girard, , Amplificateurs opérationnels 1Amplificateurs opérationnels 1 & 2 & 2

www.uoguelph.ca/~antoon/gadgets/T41.htmwww.uoguelph.ca/~antoon/gadgets/T41.htmwww.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.htmlhttp://courelectr.free.fr/AOP/AOP.HTMhttp://courelectr.free.fr/AOP/AOP.HTM

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