1. INTRODUCTION TO MECHATRONICS:
OPERATIONAL AMPLIFICATORS
Introduction to mechatronics

2. 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

3. 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” in analog circuits.
Theory
ME 6405 Introduction to Mechatronics

4. Definition and presentation
Op Amp components:
transistors
resistors
diodes
capacitors
Theory
ME 6405 Introduction to Mechatronics

5. Definition and presentation
Op Amp Circuit Model
Theory
ME 6405 Introduction to Mechatronics

6. ME 6405 Introduction to Mechatronics
Op Amp Circuit Chip
ME 6405 Introduction to Mechatronics

7. 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

8. 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

9. ME 6405 Introduction to Mechatronics
Transfer Characteristic:
Modes
+ saturation ( )
- saturation ( )
linear ( )
ME 6405 Introduction to Mechatronics

10. ME 6405 Introduction to Mechatronics
Op Amp transfer characteristic relation
ME 6405 Introduction to Mechatronics

11. 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

12. 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

13. 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 and e’ 0 i2 e0 i1 e' ei e+
ME 6405 Introduction to Mechatronics

14. Inverting Op Amp e0 ei i2 i1 e+ e'
The equation for this circuit can be obtained as follows:
ME 6405 Introduction to Mechatronics

15. Inverting Op Amp e0 ei Since K (0 - e’) = e0 and K >>>1,
then e’ since
ME 6405 Introduction to Mechatronics

16. 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

17. 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

18. Non - Inverting Op Amp ei e0 For this circuit we have ,
(GROUND)
For this circuit we have ,
where K is the differential gain of the amplifier.
ME 6405 Introduction to Mechatronics

19. Non - Inverting Op Amp ei e0 This leads to
(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.
ME 6405 Introduction to Mechatronics

20. 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

21. Summing Amplifier By utilizing the usual assumptions, we obtain:
ME 6405 Introduction to Mechatronics

22. Differencing Amplifier
A differential amplifier is one that amplifies the difference
between two voltages
ME 6405 Introduction to Mechatronics

23. Differencing Amplifier
The current through the feedback resistance must be
equal to that from V1 through R1
ME 6405 Introduction to Mechatronics

24. Differencing Amplifier
Hence
which can be rearranged to give,
ME 6405 Introduction to Mechatronics

25. Integrating Amplifier
Vout
Vin x
Potential Difference across capacitor = VX - Vout
q = CV
ME 6405 Introduction to Mechatronics

26. Integrating Amplifier
Vout
Vin x
Rearranging this gives
Integrating both sides gives
ME 6405 Introduction to Mechatronics

27. ME 6405 Introduction to Mechatronics
Non Linear Mode
General use of op amp:
input
output
Vs1
Vs2
Theory
ME 6405 Introduction to Mechatronics

28. ME 6405 Introduction to Mechatronics
Non Linear Mode
The op amp is only used in saturation
mode:
input
output
Vs1
Vs2
Theory
ME 6405 Introduction to Mechatronics

29. Non Linear Mode Theory How to find the output: + - Vs1 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

30. ME 6405 Introduction to Mechatronics
Non Linear Mode
Gate operator: OR
If U1 or/and U2 = 5V,
U3 = 5V
If U2 and U1 = 0V,
U3 = 0V 1V + - U1 U2 U3 5V 0V
Theory
ME 6405 Introduction to Mechatronics

31. ME 6405 Introduction to Mechatronics
Non Linear Mode
Other gate: NON OR + - U3 5V 0V 1V U1 U2
If U1 or/and U2 = 5V,
U3 = 0V
If U2 and U1 = 0V,
U3 = 5V
Theory
ME 6405 Introduction to Mechatronics

32. ME 6405 Introduction to Mechatronics
Non Linear Mode
Two offsets comparator: + - U1 U2 U3 5V 0V R1 R2 If
U3 = 0V
U3 = 5V
Theory
ME 6405 Introduction to Mechatronics

33. ME 6405 Introduction to Mechatronics
Non Linear Mode
Two offsets comparator (cont):
input
output
Vs1
Vs2
Uup
Udown
If U2 ≤ Udown ,
U3 = 0V
If U2 ≥ Uup,
U3 = 5V
Theory
ME 6405 Introduction to Mechatronics

34. ME 6405 Introduction to Mechatronics
Non Linear Mode
The square wave supplier or clock: + - U3 5V
-5V R1 C R2 0V
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

35. ME 6405 Introduction to Mechatronics
Non Linear Mode
The square wave supplier or clock (cont): T
output
time
Theory
ME 6405 Introduction to Mechatronics

36. Internal electrical schema
Differential Part
Gain Part
Real Operational Amplificators
Push/Pull
Output
ME 6405 Introduction to Mechatronics

37. Input Characteristics
Input Impedance: 1M to more than 20 M and 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 not exactly the same
Real Operational Amplificators
ME 6405 Introduction to Mechatronics

38. Input Characteristics
Polarization currents: to polarize T1 and T2
Offset currents 1/20th to 1/5th of I+ and I- due to resistors and polarization currents
Limited Input Voltage
Real Operational Amplificators
ME 6405 Introduction to Mechatronics

39. Transfer Characteristics
The output is proportional to the input:
It is limited by Vsat+ and Vsat-
Real Operational Amplificators
ME 6405 Introduction to Mechatronics

40. Output Characteristics
Output Impedance not null:  around 100 
Slew rate  0,5V/µs up to 150V/µs capacitor needs to be charged
Real Operational Amplificators
ME 6405 Introduction to Mechatronics

41. 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 Operational Amplificators
ME 6405 Introduction to Mechatronics

42. ME 6405 Introduction to Mechatronics
Summary
Static Equivalent schema
Real Operational Amplificators
Dynamic Equivalent schema
ME 6405 Introduction to Mechatronics

43. ME 6405 Introduction to Mechatronics
Summary
Characteristics
Ideal
Real
Input Impedance Ze 
1M up to 20 M 
Output Impedance Zs
0 
Some 10th 
Gain
up to
Offset 0V
25 µV up to 15 mV
Real Operational Amplificators
ME 6405 Introduction to Mechatronics

44. ME 6405 Introduction to Mechatronics
Summary
Characteristics
Ideal
Real
Polarization Current
0 mA
20 pA up to 500 pA
Offset Current
10 pA up to 200 mA
Slow rate
 V/µS
0,5 V/µS up to 100 V/µS
Real Operational Amplificators
ME 6405 Introduction to Mechatronics

45. 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 Operational Amplificators
ME 6405 Introduction to Mechatronics

46. ME 6405 Introduction to Mechatronics
Solutions
Need to have same polarization currents
Need to use low resistors at input to limit offset current
Do not overpass Vin maxi
Chose fast op-amps (10V/µs) for high frequency requirements or use a differencing comparator
Real Operational Amplificators
ME 6405 Introduction to Mechatronics

47. Practical 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

48. Characteristics / Numbers
Op Amp Examples:
Uses
ME 6405 Introduction to Mechatronics

49. 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

50. ME 6405 Introduction to Mechatronics
REFERENCES
Cogdell, J.R. Foundations of Electrical Engineering. Pg , 1996
Thomas, Ronald E. The Analysis and Design of Linear Circuits. pg , 1998
Walter G. Jung, IC Op-Amp Cook Book
Michel Girard, Amplificateurs opérationnels 1 & 2
lecon7.html
ME 6405 Introduction to Mechatronics