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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OPERATIONAL AMPLIFICATORS
Dr. Ume ME 6405 Introduction to mechatronics
Introduction
A. Definition and presentation
B. Linear Mode
C. Non Linear Mode
Conclusion
References
ME 6405 Introduction to Mechatronics
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
Op Amp components:
Theory
ME 6405 Introduction to Mechatronics
ME 6405 Introduction to Mechatronics
Behavior assumptions for Op Amp circuit analysis :
Theory
ME 6405 Introduction to Mechatronics
Input impedance (Ri) is large
ME 6405 Introduction to Mechatronics
Modes
+ saturation ( )
 saturation ( )
linear ( )
ME 6405 Introduction to Mechatronics
ME 6405 Introduction to Mechatronics
Analysis
( for e.g. 10V <eo< 10V )
i2
e0
i1
ei
ME 6405 Introduction to Mechatronics
Analysis
i2
e0
i1
e'
ei
e+
ME 6405 Introduction to Mechatronics
Analysis
and K = 105 then
e+  e’ =10/105 = 100 V
e+ is grounded.
Hence e+ 0 and e’ 0
i2
e0
i1
e'
ei
e+
ME 6405 Introduction to Mechatronics
e0
i1
e'
ei
e+
Inverting Op Amp
ME 6405 Introduction to Mechatronics
i2
e0
i1
e'
ei
e+
Since K (0  e’) = e0 and K >>>1,
then e’ 0 since
ME 6405 Introduction to Mechatronics
i2
e0
i1
e'
ei
e+
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
ei
e0
(GROUND)
the noninverting input.
the Inverting Op Amp
ME 6405 Introduction to Mechatronics
ei
e0
(GROUND)
For this circuit we have ,
where K is the differential gain of the amplifier.
ME 6405 Introduction to Mechatronics
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
produce a weighted sum
At X,
I = IA + IB + IC
and we can see that:
ME 6405 Introduction to Mechatronics
between two voltages
ME 6405 Introduction to Mechatronics
equal to that from V1 through R1
ME 6405 Introduction to Mechatronics
Vout
Vin
x
q = CV
ME 6405 Introduction to Mechatronics
Vout
Vin
x
Rearranging this gives
Integrating both sides gives
ME 6405 Introduction to Mechatronics
Vs1
output
input
Vs2
The op amp is only used in saturation
mode:
Theory
ME 6405 Introduction to Mechatronics
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
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
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
R2
5V
+
R1
U1

U3
U2
0V
Two offsets comparator:
If
U3 = 0V
If
U3 = 5V
Theory
ME 6405 Introduction to Mechatronics
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
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
output
T
time
T
The square wave supplier or clock (cont):
Theory
ME 6405 Introduction to Mechatronics
DifferentialPart
Gain Part
Push/Pull
Output
Real OperationalAmplificators
ME 6405 Introduction to Mechatronics
Real OperationalAmplificators
ME 6405 Introduction to Mechatronics
Real OperationalAmplificators
ME 6405 Introduction to Mechatronics
Real OperationalAmplificators
ME 6405 Introduction to Mechatronics
Real OperationalAmplificators
ME 6405 Introduction to Mechatronics
Real OperationalAmplificators
ME 6405 Introduction to Mechatronics
StaticEquivalentschema
Real OperationalAmplificators
DynamicEquivalentschema
ME 6405 Introduction to Mechatronics
Real OperationalAmplificators
ME 6405 Introduction to Mechatronics
Real OperationalAmplificators
ME 6405 Introduction to Mechatronics
Applications:
Uses
ME 6405 Introduction to Mechatronics
ME 6405 Introduction to Mechatronics
Cogdell, J.R. Foundations of Electrical Engineering. Pg 489506, 1996
Thomas, Ronald E. The Analysis and Design of Linear Circuits. pg 186221, 1998
Walter G. Jung, IC OpAmp 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://courelectr.free.fr/AOP/AOP.HTM
ME 6405 Introduction to Mechatronics