1. STUDENT LECTURE 1 OPERATIONAL AMPLIFIERS ME 6405 Introduction to Mechatronics Andrew Gibson Konstantin Froelich Benjamin Haefner Roshan Kalghatgi September 24, 2009 + -

2. 2 ME 6405 | Student Lecture 1 | Operational Amplifiers Outline  What is an Operational Amplifier?  Characteristics of Ideal and Real Op-Amps  Common Op-Amp Circuits  Applications of Op-Amps  References

3. 3 ME 6405 | Student Lecture 1 | Operational Amplifiers What is an Op-Amp?  An Operational Amplifier is an electronic device used to perform mathematical operations in a circuit – they are generally abbreviated as “Op-Amps”  Op-Amps are high gain devices that amplify a signal using an external power supply  They are composed of multiple transistors, resistors, and capacitors  Common types of op-amps:  Inverting  Non-Inverting  Integrating  Differential  Summing

4. 4 ME 6405 | Student Lecture 1 | Operational Amplifiers What is an Op-Amp?  All op-amps use a voltage supply (V cc ) to amplify the signal  The supply voltages can either have equal value but opposite signs, or the low side is grounded and the high side has a value of twice the voltage input  Some common applications of op-amps:  Low Pass Filters  Strain Gauges  PID Controllers V - Inverting Input V + Non-Inverting Input V-V- V+V+ V out V+V+ V-V- +V cc -V cc

5. 5 ME 6405 | Student Lecture 1 | Operational Amplifiers The History of Op-Amps  First invented in 1941 using vacuum tubes  In 1947, the term “Operation Amplifier” is first used and defined  First IC op-amps invented in 1961  Replacing vacuum tubes with transistors greatly reduces size  The μA741 Op-Amp is released in 1968, this becomes the standard for op-amps Vacuum Tube Op-Amp (1941) Discrete IC Op-Amp (1961)

6. 6 ME 6405 | Student Lecture 1 | Operational Amplifiers Features of Modern Op-Amps  Integrated Circuit  Multiple op-amps on a single chip  Easy to manufacture  Very inexpensive

7. 7 ME 6405 | Student Lecture 1 | Operational Amplifiers Typical 8 Pin Op-Amp

8. 8 ME 6405 | Student Lecture 1 | Operational Amplifiers The Internal Circuit (ex. 741 Op-Amp) It is important to note that it is not necessary to model the internal behavior of the op- amp in order to calculate its effect on the circuit

9. 9 ME 6405 | Student Lecture 1 | Operational Amplifiers Amplifier Gain  All op-amps can be represented by the formula:  Where K is the gain, and is a property of the individual op-amp  This gain should be distinguished from the gain of the op-amp circuit which is generally denoted by A v  A potential source of confusion comes from failing to properly distinguish between the op-amp and the op-amp circuit V out = K (V + - V - ) A v = V out / V in V-V- V+V+ V out Op-Amp Op-Amp Circuit

10. 10 ME 6405 | Student Lecture 1 | Operational Amplifiers Outline  What is an Operational Amplifier?  Characteristics of Ideal and Real Op-Amps  Common Op-Amp Circuits  Applications of Op-Amps  References

11. 11 ME 6405 | Student Lecture 1 | Operational Amplifiers Characteristics of an Ideal Op-Amp  Amplification (gain) K = V out / (V + -V - ) = ∞  Input impedance Z in = ∞  Input currents I + = I - = 0  Output impedance Z out = 0  Unlimited bandwidth  Temperature-independent V out + - Z out V-V- V+V+ Z in i - = 0 i + = 0 K

12. 12 ME 6405 | Student Lecture 1 | Operational Amplifiers Ideal v. Real Op-Amps Ideal Op-AmpTypical Op-Amp Operational Gaininfinity10 5 - 10 9 Input Resistanceinfinity 10 6  (BJT) 10 9  - 10 12  (FET) Input Current010 -12 – 10 -8 A Output Resistance0 0 – 1000  BandwidthunlimitedAttenuates and phases at high frequencies (depends on slew rate) => 1-20 MHz TemperatureindependentInfluence on Bandwidth and gain http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/opampcon.html#c1

13. 13 ME 6405 | Student Lecture 1 | Operational Amplifiers Saturation + Saturation: V out = V sat+ ≈ V vcc+ Linear Mode: V out = K (V + - V - ) V in V out V sat+ V sat- - Saturation: V out = V sat- ≈ V vcc-

14. 14 ME 6405 | Student Lecture 1 | Operational Amplifiers Outline  What is an Operational Amplifier?  Characteristics of Ideal and Real Op-Amps  Common Op-Amp Circuits  Applications of Op-Amps  References

15. 15 ME 6405 | Student Lecture 1 | Operational Amplifiers Open-Loop vs. Closed-Loop V out V in + - R1R1 R2R2 + - V-V- V+V+ V out V in + - R1R1 + - V-V- V+V+  In contrast to open-loops, closed-loop op-amps have feedback

16. 16 ME 6405 | Student Lecture 1 | Operational Amplifiers Negative vs. Positive Feedback V out + - R1R1 R2R2 V in V-V- V+V+ V out V in + - R1R1 R2R2 + - V-V- V+V+  Closed loops either have negative or positive feedback  Negative feedback leads to the inverting input, positive to the non-inverting input

17. 17 ME 6405 | Student Lecture 1 | Operational Amplifiers Basic Circuits Review  Kirchhoff’s Current Law (KCL) The sum of all currents flowing into a node equals the sum of all currents flowing out. ∑ i in = ∑ i out  Kirchhoff’s Voltage Law (KVL) The sum of all the voltage drops around a loop equals the sum of the input voltages. ∑ V k = 0 -V in + V 1 + V 2 + V 3 = 0 i1i1 i4i4 i2i2 i3i3 i 1 + i 2 = i 3 + i 4 V 1 + V 2 + V 3 = V in V in V1V1 V3V3 V2V2

18. 18 ME 6405 | Student Lecture 1 | Operational Amplifiers Basic Circuits Review  Resistance (R) Series addition Parallel addition  Capacitance (C)  Inductance (L) R = V / I R 1 R 2 R n R 1 R 2 R n

19. 19 ME 6405 | Student Lecture 1 | Operational Amplifiers Comparator  A comparator is an example of an open-loop op-amp If V + > V - V out = V sat ≈ V cc If V + < V - V out = -V sat ≈ - V cc i - = 0A i + = 0A +V cc -V cc V out + - V-V- V+V+ V in- V in+ V out V in+ - V in- + V sat - V sat

20. 20 ME 6405 | Student Lecture 1 | Operational Amplifiers Comparator

21. 21 ME 6405 | Student Lecture 1 | Operational Amplifiers Calculation Rules for Op-Amps  Assumptions:  Calculation based on the models of an ideal op-amp (Z in = ∞, Z out = 0, K = ∞)  Op-Amp operates in its linear amplifying mode (V out between saturation borders) Calculation Rules (1)i + = i - = 0 (2)V + = V - V out + - Z out V-V- V+V+ Z in i - = 0 i + = 0 K

22. 22 ME 6405 | Student Lecture 1 | Operational Amplifiers Inverting Op-Amp Circuit Characteristics  Output connected to inverting input (V - )  Non-inverting input leading to ground  Input voltage connected to inverting input (V - )  Input voltage is amplified with a negative gain V out V in V out + - R1R1 R2R2 + - R1R1 R2R2 V-V- V+V+

23. 23 ME 6405 | Student Lecture 1 | Operational Amplifiers Inverting Op-Amp (1)V in + (V + - V - ) = R 1 i 1 → i 1 = V in / R 1 (2) V out + (V + - V - ) = R 2 i 2 → V out = R 2 i 2 (3) i 2 + i 1 + i - = 0 → i 2 = - i 1 V out = - R 2 /R 1 x V in V out V in V out + - R1R1 R2R2 + - R1R1 R2R2 V-V- V+V+ (1) (2) i1i1 i2i2 i-i- (3)

24. 24 ME 6405 | Student Lecture 1 | Operational Amplifiers Inverting Op-Amp - Example  Let‘s assume we need to create an output signal of 10 V. V cc+ = 30 V, R 1 = 10 kΩ, V in = - 5 V. How do we have to choose R 2 ? V out = - (R 2 /R 1 ) x V in = (-20 kΩ / 5 kΩ) x (-10V) = 40 V ??? No! Since V out > V cc+ → V out = V cc+  What would be V out, if V cc+ = 30 V, R 1 = 5 kΩ, R 2 = 20 kΩ and V in = -10 V? V out = - (R 2 /R 1 ) x V in → R 2 = -V out x R 1 /V in = (-10 V x 10 kΩ) / (-5 V) = 20 kΩ

25. 25 ME 6405 | Student Lecture 1 | Operational Amplifiers Non-inverting Op-Amp Circuit Characteristics  Input voltage is amplified with a positive gain  Output connected to inverting input (V - )  Inverting input leading to ground  Input voltage connected to non- inverting input (V + ) V in V out + - R1R1 R2R2 + - V-V- V+V+ R2R2

26. 26 ME 6405 | Student Lecture 1 | Operational Amplifiers Non-inverting Op-Amp V in V out + - R1R1 R2R2 + - V-V- V+V+ R2R2 (3) (3)V in = i 1 R 1 + (V + - V - ) KVL V + - V - = 0 op-amp rule (2) → V in = i 1 R 1 i1i1 i2i2 i-i- (1) (1) i 2 + i - = i 1 KCL i - = 0 op-amp rule (1) → i 2 = i 1 V out /V in = (i 1 R 1 + i 2 R 2 ) / (i 1 R 1 ) = (i 1 R 1 + i 1 R 2 ) / (i 1 R 1 ) = (R 1 + R 2 ) / R 1 = 1 + (R 2 / R 1 ) (2) V out = i 1 R 1 + i 2 R 2 KVL (2)

27. 27 ME 6405 | Student Lecture 1 | Operational Amplifiers Non-inverting Op-Amp - Example  A non-inverting op-amp has an input voltage of 2 V. R 1 = 6 kΩ, R 2 = 30 kΩ. What is the output voltage?  The saturation output voltage of an non-inverting op-amp is V sat =13 V. R 1 = 10 kΩ, R 2 = 10 kΩ. Determine the maximum input voltage so that the output voltage does not saturate.

28. 28 ME 6405 | Student Lecture 1 | Operational Amplifiers Op-Amps for Math Closed-loop operational amplifiers with negative feedback can be used to fulfil various mathematic operations:  Integrating V in V out  Subtracting V in1 V out V in2 + - V in1 V out V in2 + +  Summing V in V out  Derivative

29. 29 ME 6405 | Student Lecture 1 | Operational Amplifiers Summing Op-Amp  Application of a non-inverting op-amp and Millman‘s theorem V out = V inA + V inB + V inC V inA V out + - RARA R2R2 V-V- V+V+ V inB V inC RBRB RCRC R1R1 (1)Millman’s theorem: if R A = R B = R C = R (1) (2)Non-inverting Op-Amp: (2) V’

30. 30 ME 6405 | Student Lecture 1 | Operational Amplifiers Substraction (Differential) Op-Amp V out = V inA - V inB  Applying Kirchhoff’s Rules and Op-Amp Calculation Rules yields: V inB V out + - R4R4 V-V- V+V+ V inA R1R1 R2R2 R3R3 if R 1 = R 2 = R 3 = R 4 Note: if R 1 = R 3 = R and R 2 = R 4 = a R

31. 31 ME 6405 | Student Lecture 1 | Operational Amplifiers Derivative Op-Amp  Applying Kirchhoff’s Rules and Op-Amp Calculation Rules yields: V in V out + - R V-V- V+V+ R C V in V out

32. 32 ME 6405 | Student Lecture 1 | Operational Amplifiers Integrating Op-Amp V in V out + - R V-V- V+V+ R C V in V out  Applying Kirchhoff’s Rules and Op-Amp Calculation Rules yields:

33. 33 ME 6405 | Student Lecture 1 | Operational Amplifiers Op-Amps for Math - Examples  We want to design a summing op-amp circuit to add 4 input voltages. Tsun-Yen insists that R 2 = 12 kΩ. What should be the resistance of R 1 ?  Consider an op-amp circuit to obtain the following input- output voltage relationship: V out = V A - 2 V B Calculate a possible combination of the resistor values. (example + solution on page 196 in Cetinkunt, Mechatronics) V out = V 1 + V 2 + V 3 + V 4

34. 34 ME 6405 | Student Lecture 1 | Operational Amplifiers Outline  What is an Operational Amplifier?  Characteristics of Ideal and Real Op-Amps  Common Op-Amp Circuits  Applications of Op-Amps  References

35. 35 ME 6405 | Student Lecture 1 | Operational Amplifiers Filters R 2 + - + V 0 __ + V cc - V cc - + Types: Low pass filter High pass filter Band pass filter Cascading (2 or more filters connected together) R1 R1 C Low pass filter Low pass filter Cutoff frequency  Low pass filter transfer function 

36. 36 ME 6405 | Student Lecture 1 | Operational Amplifiers Strain Gauge Use a Wheatstone bridge to determine the strain of an element by measuring the change in resistance of a strain gauge (No strain) Balanced Bridge R #1 = R #2 (Strain) Unbalanced Bridge R #1 ≠ R #2

37. 37 ME 6405 | Student Lecture 1 | Operational Amplifiers R + ΔR Strain Gauge R f + - + V 0 __ + V cc - V cc - + RfRf V ref Half-Bridge Arrangement R R - ΔR R Using KCL at the inverting and non-inverting terminals of the op amp we find that  ε ~ V o = 2ΔR(R f /R 2 ) Op amp used to amplify output from strain gauge

38. 38 ME 6405 | Student Lecture 1 | Operational Amplifiers Goal is to have V SET = V OUT Remember that V ERROR = V SET – V SENSOR Output Process uses V ERROR from the PID controller to adjust V out such that it is ~V SET P I D Output Process Sensor V ERROR V SET V OUT V SENSOR PID Controller – System Block Diagram

39. 39 ME 6405 | Student Lecture 1 | Operational Amplifiers Applications PID Controller – System Circuit Diagram Calculates V ERROR = -(V SET + V SENSOR ) Signal conditioning allows you to introduce a time delay which could account for things like inertia System to control Source: http://www.ecircuitcenter.com/Circuits/op_pid/op_pid.htm -V SENSOR

40. 40 ME 6405 | Student Lecture 1 | Operational Amplifiers Applications PID Controller – PID Controller Circuit Diagram V ERROR AdjustChange KpKp RP1, RP2 KiKi RI, CI KdKd RD, CD V ERROR PID

41. 41 ME 6405 | Student Lecture 1 | Operational Amplifiers Buying Operational Amplifiers No money? Click on “Samples”. Go to www.national.com, click on “Order”, then click on “Samples”.www.national.com

42. 42 ME 6405 | Student Lecture 1 | Operational Amplifiers Outline  What is an Operational Amplifier?  Characteristics of Ideal and Real Op-Amps  Common Op-Amp Circuits  Applications of Op-Amps  References

43. 43 ME 6405 | Student Lecture 1 | Operational Amplifiers References  Centinkunt, Sabri. Mechatronics Hoboken, NJ: John Wiley & Sons Inc., 2007.  Hambley, Allen. Electrical Engineering. Upper Saddle River, NJ: Pearson Education Inc., 2008.  Nilsson, James W., Riedel Susan A. Electric Circuits Upper Saddle River, NJ Pearson Prentice Hall, 2005.  www.allaboutcircuits.com  www.ecircuitcenter.com  www.ti.com  hyperphysics.phy-astr.gsu.edu  en.wikipedia.org