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 NonInverting Amplifiers, Difference and Summing Amplifiers School of Electrical and Computer Engineering
21 Lesson Objectives Introduce Inverting and NonInverting Configurations Difference and Summing Configurations Introduce the Gain of a circuit 21
22 NonInverting Amplifiers v in V o = 2 V o = GV in 3 3 V in Gain: G =
23 NonInverting 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 11 = 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 NonInverting 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 rolloff 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 FirstOrder 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 FirstOrder 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 FirstOrder 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 157
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 firstorder 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 159
60 FirstOrder 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 FirstOrder 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 166
67 Summary A passes high frequency components in signals and attenuates low frequency components Firstorder 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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