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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.

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ME 6405INTRODUCTION 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

ME 6405 Introduction to Mechatronics

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

ME 6405 Introduction to Mechatronics

Definition and presentation

Op Amp components:

• transistors
• resistors
• diodes
• capacitors

Theory

ME 6405 Introduction to Mechatronics

Definition and presentation

Op Amp Circuit Model

Theory

ME 6405 Introduction to Mechatronics

Op Amp Circuit Chip

ME 6405 Introduction to Mechatronics

Definition and presentation

Behavior assumptions for Op Amp circuit analysis :

• Amplifier operates in its linear amplifying region
• Large voltage gain (A)

Theory

ME 6405 Introduction to Mechatronics

Difference between input voltages to Op Amp is very small because voltage gain (A) is very large

Input impedance (Ri) is large

ME 6405 Introduction to Mechatronics

Transfer Characteristic:

Modes

+ saturation ( )

- saturation ( )

linear ( )

ME 6405 Introduction to Mechatronics

Op Amp transfer characteristic relation

ME 6405 Introduction to Mechatronics

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 <eo< 10V )

i2

e0

i1

ei

ME 6405 Introduction to Mechatronics

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+

ME 6405 Introduction to Mechatronics

Inverting Op Amp

Analysis

• 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

i2

e0

i1

e'

ei

e+

ME 6405 Introduction to Mechatronics

i2

e0

i1

e'

ei

e+

Inverting Op Amp

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

ME 6405 Introduction to Mechatronics

Inverting Op Amp

i2

e0

i1

e'

ei

e+

Since K (0 - e’) = e0 and K >>>1,

then e’ 0 since

ME 6405 Introduction to Mechatronics

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.

ME 6405 Introduction to Mechatronics

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

ME 6405 Introduction to Mechatronics

Non - Inverting Op Amp

ei

e0

(GROUND)

For this circuit we have ,

where K is the differential gain of the amplifier.

ME 6405 Introduction to Mechatronics

Non - Inverting Op Amp

ei

e0

(GROUND)

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.

ME 6405 Introduction to Mechatronics

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:

ME 6405 Introduction to Mechatronics

Summing Amplifier

• By utilizing the usual assumptions, we obtain:

ME 6405 Introduction to Mechatronics

Differencing Amplifier

• A differential amplifier is one that amplifies the difference

between two voltages

ME 6405 Introduction to Mechatronics

Differencing Amplifier

• The current through the feedback resistance must be

equal to that from V1 through R1

ME 6405 Introduction to Mechatronics

Differencing Amplifier

• Hence
• which can be rearranged to give,

ME 6405 Introduction to Mechatronics

Integrating Amplifier

Vout

Vin

x

• Potential Difference across capacitor = VX - Vout

q = CV

ME 6405 Introduction to Mechatronics

Integrating Amplifier

Vout

Vin

x

Rearranging this gives

Integrating both sides gives

ME 6405 Introduction to Mechatronics

Non Linear Mode

Vs1

output

input

Vs2

General use of op amp:

Theory

ME 6405 Introduction to Mechatronics

Non Linear Mode

Vs1

output

input

Vs2

The op amp is only used in saturation

mode:

Theory

ME 6405 Introduction to Mechatronics

Non Linear Mode

Vs1

+

U1

U3

U2

-

Vs2

How to find the output:

If U1 > U2,

U3 = Vs1

If U2 > U1,

U3 = Vs2

Theory

In each case, i3 is unknown and i1 and i2 are null.

ME 6405 Introduction to Mechatronics

Non Linear Mode

5V

U1

+

U2

U3

-

1V

0V

Gate operator: OR

If U1 or/and U2 = 5V,

U3 = 5V

If U2 and U1 = 0V,

U3 = 0V

Theory

ME 6405 Introduction to Mechatronics

Non Linear Mode

5V

U1

1V

+

U2

U3

-

0V

Other gate: NON OR

If U1 or/and U2 = 5V,

U3 = 0V

If U2 and U1 = 0V,

U3 = 5V

Theory

ME 6405 Introduction to Mechatronics

Non Linear Mode

R2

5V

+

R1

U1

-

U3

U2

0V

Two offsets comparator:

If

U3 = 0V

If

U3 = 5V

Theory

ME 6405 Introduction to Mechatronics

Non Linear Mode

output

Vs1

input

Udown

Uup

Vs2

Two offsets comparator (cont):

If U2 ≤ Udown ,

U3 = 0V

If U2 ≥ Uup,

U3 = 5V

Theory

ME 6405 Introduction to Mechatronics

Non Linear Mode

R1

5V

R1

+

U3

-

C

-5V

R2

0V

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

ME 6405 Introduction to Mechatronics

Non Linear Mode

output

T

time

T

The square wave supplier or clock (cont):

Theory

ME 6405 Introduction to Mechatronics

Internal electrical schema

DifferentialPart

Gain Part

Push/Pull

Output

Real OperationalAmplificators

ME 6405 Introduction to Mechatronics

Input Characteristics
• Input Impedance: 1M to more than 20 Mand notinfinite
• Input Offset (most important default):when V+ or V- are low or G is high some 10 Vbecause T1 and T2 are notexactly the same

Real OperationalAmplificators

ME 6405 Introduction to Mechatronics

Input Characteristics
• Polarization currents:to 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

ME 6405 Introduction to Mechatronics

Transfer Characteristics
• The output is proportional to the input:
• It is limited by Vsat+ and Vsat-

Real OperationalAmplificators

ME 6405 Introduction to Mechatronics

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

Real OperationalAmplificators

ME 6405 Introduction to Mechatronics

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

ME 6405 Introduction to Mechatronics

Summary

StaticEquivalentschema

Real OperationalAmplificators

DynamicEquivalentschema

ME 6405 Introduction to Mechatronics

Summary

Real OperationalAmplificators

ME 6405 Introduction to Mechatronics

Summary

Real OperationalAmplificators

ME 6405 Introduction to Mechatronics

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

ME 6405 Introduction to Mechatronics

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

ME 6405 Introduction to Mechatronics

Practical Applications

Applications:

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

Uses

ME 6405 Introduction to Mechatronics

Characteristics / Numbers

Op Amp Examples:

Uses

ME 6405 Introduction to Mechatronics

CONCLUSION
• Introduction
• Theory of Op Amp’s
• 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

ME 6405 Introduction to Mechatronics

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