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INTRODUCTION TO MECHATRONICS :

INTRODUCTION TO MECHATRONICS :. OPERATIONAL AMPLIFICATORS. Introduction to mechatronics. Contents. Introduction Theory A. Definition and presentation B. Linear Mode C. Non Linear Mode Real Operational Amplificators Uses Conclusion References. Definition and presentation.

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INTRODUCTION TO MECHATRONICS :

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  1. INTRODUCTION TO MECHATRONICS: OPERATIONAL AMPLIFICATORS Introduction to mechatronics

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

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

  11. 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. 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. 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

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

  15. 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

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

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

  29. 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

  30. 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

  31. 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

  32. 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

  33. 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

  34. 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

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

  36. Internal electrical schema DifferentialPart Gain Part Push/Pull Output Real OperationalAmplificators ME 6405 Introduction to Mechatronics

  37. 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

  38. 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

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

  40. 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

  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 OperationalAmplificators ME 6405 Introduction to Mechatronics

  42. Summary StaticEquivalentschema Real OperationalAmplificators DynamicEquivalentschema ME 6405 Introduction to Mechatronics

  43. Summary Real OperationalAmplificators ME 6405 Introduction to Mechatronics

  44. Summary Real OperationalAmplificators ME 6405 Introduction to Mechatronics

  45. 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

  46. 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

  47. 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

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

  49. 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. 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 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

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