# Module 2: Op Amps Introduction and Ideal Behavior

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1 Module 2: Op Amps Introduction and Ideal Behavior Dr. Bonnie H. Ferri Professor and Associate Chair School of Electrical and Computer Engineering Introduce Op Amps and examine ideal behavior School of Electrical and Computer Engineering

2 Lesson Objectives Introduce Operational Amplifiers Describe Ideal Op Amp Behavior Introduce Comparator and Buffer Circuits 2

3 Operational Amplifiers (Op Amps) v v - - V s Specialized circuit made up of transistors, resistors, and capacitors fabricated on an integrated chip -V s Uses: Amplifiers Active Filters Analog Computers 3

4 Op Amps in Circuits v V s v - V s v - v - -V s -V s V s = 10V, 15V Symbol: - Active Element: has its own power supply Symbol ignores the /- V s in the symbol since it does not affect circuit behavior 4

5 Open Loop Behavior V s v v - - V s -V s v - v - = A(v - v - ) -V s 5

6 Comparator Circuit v in v v - - V s V V s -V s v in V o = Vs V s if if v v in in > < 0 0 -V s 6

7 Example v V s Csin(ωt) - V s v - v - v - -V s -V s 7

8 Ideal Op Amp Behavior v in v v - i Av in V s o i i - v v - - -V s i = i - = 0 v - v - = 0 8

9 Buffer Circuit v in - v in - vo v in = 9

10 Summary Op amps are active devices that can be used to filter or amplify signals linearly Ideal op amps: i v i = i - = 0 i - v - - v - v - = 0 Circuits: comparator and buffer 10

11 emainder of Module 2: Op Amps Buffer Circuit Basic Amplifier Configurations Differentiators and Integrators Active Filters 11

12 Buffer Circuits Dr. Bonnie H. Ferri Professor and Associate Chair School of Electrical and Computer Engineering Demonstrate buffer circuit behavior School of Electrical and Computer Engineering

13 Lesson Objectives Introduce physical op amps in circuits Examine Buffer Circuit behavior 13

14 Buffer Circuit Use to boost power without changing voltage waveform v in - V S v in v in = -V S 14

15 Example: Without Buffer v in 15

16 Physical Op Amps v v - - V s V s = 15V -V s Signal PIN v - 2 v 3 -V s 4 6 V s 7 16

17 Example: With Buffer v in v in - 17

18 Example: With Buffer v in - 18

19 Summary Buffers boost the power without changing the voltage waveform Demonstrated physical op amp circuits 19

20 Dr. Bonnie H. Ferri Professor and Associate Chair School of Electrical and Computer Engineering Basic Op Amp Amplifier Configurations Introduce Inverting and Non-Inverting Amplifiers, Difference and Summing Amplifiers School of Electrical and Computer Engineering

21 Lesson Objectives Introduce Inverting and Non-Inverting Configurations Difference and Summing Configurations Introduce the Gain of a circuit 21

22 Non-Inverting Amplifiers v in V o = 2 V o = GV in 3 3 V in Gain: G =

23 Non-Inverting Amplifier Example v in If 2 = 3 = 200Ω, Since,G > 1, the input is amplified If G < 1, the input is attenuated 23

24 Inverting Amplifier f 1 - v in V o = f 1 V in V o = GV in 24

25 Inverting Amplifier Example f v in 1-1 = 1000Ω, f = 2000Ω If,G > 1, the input is amplified If G < 1, the input is attenuated 25

26 Difference Circuit f v v 2 2 V o = F 1 ( V V1) 2 26

27 Difference Circuit f v v 2 2 V o = F 1 ( V V1) 2 27

28 Summing Amplifier 1 f v 1 v G 1 V o = G = F 1 1 V 1 G G 2 2 V 2 = F 2 28

29 Summary Gain: V = o GV in Amplifier Circuit Configurations Non-Inverting Amplifier Inverting Amplifier Difference Amplifier Summing Amplifier 29

30 Differentiators and Integrators Dr. Bonnie H. Ferri Professor and Associate Chair School of Electrical and Computer Engineering Introduce Integrating and Differentiating Op Amp Circuits School of Electrical and Computer Engineering

31 Lesson Objectives Introduce Differentiators and Integrators Demonstrate the performance of both circuits on an oscilloscope 31

32 Differentiator Circuit v in C v - v - dv i = C dt c Vc V o dv = C dt in 32

33 Differentiator Circuit v in C v - v - Derivation: 1. KVL: V in = V c i V o 2. V in = V c 3. V o = -i = -C(dV in / dt) V o dv = C dt in 33

34 Differentiator Example 1000Ω v in -V S v v in 1µF v - v - v - V S = 15v V S -V S = -15v 34

35 esults V o dv = C dt in 35

36 Integrator Circuit C dv i = C dt c Vc V c = 1 C t 0 idt v in v - v - V o = 1 C t 0 V in dt 36

37 Integrator Circuit C dv i = C dt c Vc V c = 1 C t 0 idt v in v - v - Derivation: For t<0: V in = i and V o = 0 For t>0: V in = i i = V in / V o = 1 C t 0 V in dt V in = i V c V o V o = -V c = -1/C t V in / dt 0 37

38 Integrator Example 1µF v in -V v v - S v in 1000Ω v - v - V S = 15v V S -V S = -15v 38

39 esults V o = 1 C t 0 V in dt 39

40 Summary Differentiator and Integrator Op Amp circuits examined 40

41 Active Filters Dr. Bonnie H. Ferri Professor and Associate Chair School of Electrical and Computer Engineering Introduce active filters and show different types of filters School of Electrical and Computer Engineering

42 Lesson Objectives Introduce active filter circuits 42

43 Analog Filters v(t) Time (sec) V in Analog Filter H(ω) V out v(t) Time (sec) 1 H(ω) 0.8 Magnitude ω ω (rad/sec) 43

44 Quiz V in = 1 cos(10(2πt)) cos(100(2πt)) V out = 0.45cos(10(2πt)θ 1 ) 0.97cos(100(2πt) θ 2 ) 44

45 Summary of C and LC (Passive) Filters Bode Plots v in C - Magnitude (db) ω v in C - Magnitude (db) ω L C v in - Magnitude (db) ω 45

46 Limitations of LC Passive Filters Depletes power No isolation v in C - V in Analog Filter V o 46

47 Active Filters has its own power supply Most common active filters are made from op amps Provide isolation V in Op Amp Circuit V out 47

48 Summary An is a circuit that has a specific shaped frequency response A is made of op amps and has its own power supply. Advantages over LC passive filters: Provides isolation (cascade filters) Boosts the power Can provide sharper roll-off 48

49 Impedance Gain V o = Z Z in F V in Derivation: V in = iz 1 V o = -iz f = -(Z f /Z 1 )V in 49

50 First-Order Lowpass Filters Dr. Bonnie H. Ferri Professor and Associate Chair School of Electrical and Computer Engineering Introduce lowpass filters School of Electrical and Computer Engineering

51 Lesson Objectives Introduce active lowpass filters 51

52 Lowpass Filters K DC Magnitude Lowpass filters pass low frequency components and attenuate high frequency components Transfer Function H(ω) Linear Plot ω B 0.707K DC ω ω 20log 10 (K DC ) Magnitude (db) Bode Plot 3dB 52

53 First-Order Filter K DC Linear Plot H(ω) = K DC 1 τjω 1 Magnitude 0.707K DC Bandwidth, ω B = 1/τ DC Gain = H(0) = K DC 0 ω B ω 53

54 From Passive to Active Lowpass Filters V in Circuit V V in V o o C - v in C V in V o C - 54

55 First-Order Inverting Lowpass Filter f C v in 1 - V o = f 1 1 V Cjω 1 f in 55

56 Frequency Characteristics of LP Filter H( ω) = f 1 ( f 1 Cjω 1) H(ω) H(ω) = f ( C ω) 1 H(ω) = 180 arctan( f DC Gain = 1 Bandwidth, ω = f f b f C 1 C f f f ω) f / f / 1 ω b H(ω) ω ω 56

57 Derivation: Lowpass Filter f C v in 1 - Z f v in Z 1-57

58 Example Design an inverting lowpass filter to have a DC gain of -2 and a bandwidth of 500 rad/s: f C v in 1 - H(ω) = f 1 1 Cjω 1 f 58

59 Summary A passes low frequency signals and attenuates high frequency signals Three first-order lowpass configurations: Noninverting, isolation at the input v - in C V o Noninverting, isolation at the output V in C - Inverting, isolation at input and output f C v in 1-59

60 First-Order Highpass Filters Dr. Bonnie H. Ferri Professor and Associate Chair School of Electrical and Computer Engineering Introduce highpass filters School of Electrical and Computer Engineering

61 Lesson Objectives Introduce active highpass filters 61

62 Highpass Filter Passes high frequency components and attenuates low frequency components Linear Plot Magnitude ω 62

63 First-Order Filter Linear Plot K PB Magnitude 0.707K PB H(ω) = Kjω τjω 1 Corner Frequency, ω c = 1/τ Passband Gain= K PB = K/τ 0 ω c ω 63

64 Inverting Highpass Filter Configuration v in C 1 f - v in Z 1 Z f - V o = fcjω V ( Cjω 1) 1 in 64

65 Frequency Characteristics of HP Filter H( ω) = H( ω) = fcjω ( Cjω 1) ( ω) = 90 arctan( Cω) H 1 Passband Gain(ω ) = 1 Corner Freq., ω c = C 1 ( Cω 1 f Cω) f 1 H(ω) f / K PB 0 ω c = 1/ 1 C ω H(ω) ω

66 Example Design a highpass filter to have a passband gain of 2 and a corner frequency of 1k rad/s: f v in C 1-66

67 Summary A passes high frequency components in signals and attenuates low frequency components First-order highpass filter f Cjω v C 1 in - v f o H( ω) = ( 1Cjω 1) Design based on Corner frequency of the passband, ω c Passband gain, K PB 67

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