_4a3b3c2f3af76e42b511c6532a2e0cd0_week-3-slides.pdf
- 1. School of Electrical and Computer Engineering Introduction to Electronics An introduction to electronic components and a study of circuits containing such devices.
- 2. School of Electrical and Computer Engineering Week 3: Op Amps Part 2
- 3. Dr. Bonnie H. Ferri Professor and Associate Chair School of Electrical and Computer Engineering School of Electrical and Computer Engineering First-Order Lowpass Filters Introduce lowpass filters
- 4. Introduce active lowpass filters Lesson Objectives 51
- 5. Lowpass Filters ω Linear Plot Magnitude KDC ωB 0.707KDC ω Bode Plot Magnitude (dB) 20log10(KDC) 3dB Lowpass filters pass low frequency components and attenuate high frequency components Transfer Function H(ω) 52
- 6. First-Order Filter Bandwidth, ωB = 1/τ DC Gain = H(0) = KDC ω Linear Plot Magnitude KDC ωB 0.707KDC 0 1 j 1 K H DC + ω τ = ω) ( 53
- 7. From Passive to Active Lowpass Filters Circuit Vin Vo Vin Vo R C Vo R C + - vin Vin R C + - vo 54
- 8. First-Order Inverting Lowpass Filter + - vo R1 C Rf vin in f 1 f o V 1 Cj R 1 R R V + ω − = 55
- 9. Frequency Characteristics of LP Filter ω |H(ω)| Rf/R1 .707 Rf/R1 ωb 180° 90° H(ω) ω 1 f R R Gain DC − = ) ( ) ( 1 Cj R 1 R R H f 1 f + ω − = ω 1 ) ω C R ( 1 R R )| ω ( H | 2 f f f 1 + = ) ω C R arctan( 180 ) ω ( H f f − = ∠ f b C R 1 ω , Bandwidth f = 56
- 10. Derivation: Lowpass Filter + - vo Z1 vin Zf + - vo R1 C Rf vin 57
- 11. Design an inverting lowpass filter to have a DC gain of -2 and a bandwidth of 500 rad/s: Example + - vo R1 C Rf vin 1 Cj R 1 R R H f 1 f + ω − = ω) ( 58
- 12. A passes low frequency signals and attenuates high frequency signals Three first-order lowpass configurations: Noninverting, isolation at the input Noninverting, isolation at the output Inverting, isolation at input and output Summary Vo R C + - vin Vin R C + - vo + - vo R1 C Rf vin 59
- 13. Dr. Bonnie H. Ferri Professor and Associate Chair School of Electrical and Computer Engineering School of Electrical and Computer Engineering First-Order Highpass Filters Introduce highpass filters
- 14. Introduce active highpass filters Lesson Objectives 61
- 15. Passes high frequency components and attenuates low frequency components Highpass Filter Linear Plot ω Magnitude 62
- 16. First-Order Filter Corner Frequency, ωc = 1/τ Passband Gain= KPB = K/τ Linear Plot 1 j Kj H + ω τ ω = ω) ( ω Magnitude KPB ωc 0.707KPB 0 63
- 17. Inverting Highpass Filter Configuration in 1 f o V 1 Cj R Cj R V ) ( + ω ω − = + - vo R1 C Rf vin + - vo Z1 vin Zf 64
- 18. Frequency Characteristics of HP Filter C R 1 Freq Corner 1 c = ω ., 1 f R R Gain Passband − = ∞ → ω ) ( ) arctan( ) ( ω − ° − = ω ∠ C R 90 H 1 ) ( ) ( 1 Cj R Cj R H 1 f + ω ω − = ω 1 C R C R H 2 1 f + ω ω = ω ) ( | ) ( | |H(ω)| Rf/R1 ωc = 1/R1C ω 0.707KPB 0 -90° H(ω) ω 0° 65
- 19. Design a highpass filter to have a passband gain of 2 and a corner frequency of 1k rad/s: Example + - vo R1 C Rf vin 66
- 20. A passes high frequency components in signals and attenuates low frequency components First-order highpass filter Design based on Corner frequency of the passband, ωc Passband gain, KPB Summary + - vo R1 C Rf vin ) ( ) ( 1 Cj R Cj R H 1 f + ω ω − = ω 67
- 21. Dr. Allen Robinson Academic Professional School of Electrical and Computer Engineering School of Electrical and Computer Engineering Introduction to Electronics An introduction to electronic components and a study of circuits containing such devices.
- 22. Dr. Allen Robinson Academic Professional School of Electrical and Computer Engineering School of Electrical and Computer Engineering Cascaded First- Order Filters Introduce cascaded first-order op-amp filters
- 23. Introduced op-amp first-order highpass filters Previous Lesson 3
- 24. Introduce cascaded filters Introduce bandpass filter characteristics Lesson Objectives 4
- 25. Transfer Functions in Hertz f 5 1 j Kj H + ω τ ω = ω) ( 1 j 1 K H DC + ω τ = ω) ( Lowpass Highpass
- 26. First-Order LPF and HPF 6
- 27. Cascaded Filter 7 Input Output First-Order LPF Input Output First-Order HPF
- 30. Cascaded Filter Transfer Function 10
- 31. Cascaded Lowpass and Highpass Filters Bandpass Filter Characteristics Summary 11
- 32. Second-Order Transfer Functions Next Lesson 12
- 33. Dr. Allen Robinson Academic Professional School of Electrical and Computer Engineering School of Electrical and Computer Engineering Introduction to Electronics An introduction to electronic components and a study of circuits containing such devices.
- 34. Dr. Allen Robinson Academic Professional School of Electrical and Computer Engineering School of Electrical and Computer Engineering Second-Order Transfer Functions Introduce second-order filter transfer functions
- 35. Introduced cascaded first-order op-amp filters Previous Lesson 3
- 36. Introduce second-order filter transfer functions Examine features of transfer functions Lesson Objectives 4
- 37. Ratio of output voltage to input voltage as a function of frequency For any frequency, the transfer function is a complex number that indicates how the filter modifies the magnitude and phase of the input to produce the output Filter Transfer Function 5
- 40. Effect of Quality Factor (Q) 8
- 43. Butterworth and Chebyshev 11 Types of transfer functions For second-order filters, the type is determined by the Q value Butterworth (Maximally Flat) Chebyshev
- 46. Fourth-Order Butterworth vs. Chebyshev 14
- 47. Introduced second-order transfer functions Examined features of transfer functions Summary 15
- 48. Op-Amp Second-Order Filter Circuits Next Lesson 16
- 49. Dr. Allen Robinson Academic Professional School of Electrical and Computer Engineering School of Electrical and Computer Engineering Introduction to Electronics An introduction to electronic components and a study of circuits containing such devices.
- 50. Dr. Allen Robinson Academic Professional School of Electrical and Computer Engineering School of Electrical and Computer Engineering Second-Order Filter Circuits Introduce second-order Sallen-Key filter circuits
- 51. Introduced second-order transfer functions Previous Lesson 3
- 52. Introduce second-order filter circuits Design second-order filters Lesson Objectives 4
- 54. Lowpass Design Equations 6 Special Case 2 (K = 1, Solve for R’s) Special Case 1 (K = 1, Solve for C’s) Special Case 3 (R’s equal and C’s equal) Can simplify with R1 and R2 are interchangeable
- 56. Highpass Design Equations 8 Special Case 2 (R’s equal and C’s equal) Special Case 1 (K = 1, C1 = C2 = C)
- 58. Bandpass Design Equations 10 Special Case (R’s equal and C’s equal)
- 59. Notch Filters 11
- 60. Introduced second-order filter circuits Summary 12
- 61. Next Lesson 13 Filter Design Example
- 62. Dr. Allen Robinson Academic Professional School of Electrical and Computer Engineering School of Electrical and Computer Engineering Introduction to Electronics An introduction to electronic components and a study of circuits containing such devices.
- 63. Dr. Allen Robinson Academic Professional School of Electrical and Computer Engineering School of Electrical and Computer Engineering Lowpass Filter Design Example Design a second-order Sallen-Key lowpass filter circuit
- 64. Butterworth 2nd Order LPF Example Design 3 Special Case 1 (K = 1, Solve for C’s) Can simplify with
- 65. Example Design 4
- 66. Designed a second-order lowpass filter Summary 5
- 67. Next Lesson 6 Filter Demonstration
- 68. Dr. Allen Robinson Academic Professional School of Electrical and Computer Engineering School of Electrical and Computer Engineering Introduction to Electronics An introduction to electronic components and a study of circuits containing such devices.
- 69. Dr. Allen Robinson Academic Professional School of Electrical and Computer Engineering School of Electrical and Computer Engineering Filtering Demonstration Demonstrate filtering of signals
- 70. Introduced second-order filter circuits Previous Lesson 3
- 71. Examine frequency spectra of signals Demonstrate filtering by a second-order filter circuit Lesson Objectives 4
- 72. Spectrum of Sine Wave 5
- 73. Spectrum of Sum of Two Sine Waves 6
- 74. Spectrum of Square Wave 7
- 75. Spectrum of Square Wave 8
- 77. Measurements 10 f0 = 1kHz Q=5 Sallen-Key BPF Vo Relaxation Oscillator 1kHz Square Wave
- 78. Total Harmonic Distortion (THD) 11
- 79. Introduced frequency spectra Examined physical circuit filtering performance Summary 12