Module 2 handouts part 2
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Transcript of Module 2 handouts part 2
Dr. Allen RobinsonAcademic ProfessionalSchool of Electrical and Computer Engineering
School of Electrical and Computer Engineering
Cascaded First-Order Filters
Introduce cascaded first-order op-amp filters
Introduce cascaded filters Introduce bandpass filter characteristics Introduce second-order transfer functions
Lesson Objectives
2
First-Order LPF and HPF
3
Cascaded Filter
Input OutputFirst-OrderLPF
Input OutputFirst-OrderHPF
4
Cascaded Filter
5
Bandpass Filter Characteristics
6
Transfer Function
Second-Order Filter Standard Form:
7
Cascaded Bandpass Filters
8
Is it possible to form a cascaded band-reject filter?
Question
9
Cascaded Filters Bandpass Transfer Functions
Summary
10
Dr. Allen RobinsonAcademic ProfessionalSchool of Electrical and Computer Engineering
School of Electrical and Computer Engineering
Second-Order Transfer Functions
Introduce second-order filter transfer functions
Introduce second-order filter transfer functions Examine features of transfer functions
Lesson Objectives
12
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
13
First-Order Low-Pass Filter
14
Second-Order Low-Pass Filter
15
Effect of Quality Factor (Q)
16
High-Pass Filters
17
Band-Pass Filters
18
Butterworth and Chebyshev
Types of transfer functions For second-order filters, the type is
determined by the Q value Butterworth (Maximally Flat) Chebyshev
19
Chebyshev Filters
20
Butterworth Filters
21
Fourth-Order Butterworth vs. Chebyshev
22
Introduced second-order transfer functions Examined features of transfer functions
Summary
23
Dr. Allen RobinsonAcademic ProfessionalSchool of Electrical and Computer Engineering
School of Electrical and Computer Engineering
Second-Order Transfer Functions
Introduce second-order filter transfer functions
Introduce second-order filter transfer functions Examine features of transfer functions
Lesson Objectives
25
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
26
First-Order Low-Pass Filter
27
Second-Order Low-Pass Filter
28
Effect of Quality Factor (Q)
29
High-Pass Filters
30
Band-Pass Filters
31
Butterworth and Chebyshev
Types of transfer functions For second-order filters, the type is
determined by the Q value Butterworth (Maximally Flat) Chebyshev
32
Chebyshev Filters
33
Butterworth Filters
34
Fourth-Order Butterworth vs. Chebyshev
35
Introduced second-order transfer functions Examined features of transfer functions
Summary
36
Dr. Allen RobinsonAcademic ProfessionalSchool of Electrical and Computer Engineering
School of Electrical and Computer Engineering
Second-Order Filter Circuits
Introduce second-order Sallen-Key filter circuits
Introduce second-order filter circuits Design second-order filters
Lesson Objectives
38
Sallen-Key Low-Pass Filter
VoVi
39
Lowpass Design Equations
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
40
Sallen-Key Highpass Filter
Vi Vo
41
Highpass Design Equations
Special Case 2 (R’s equal and C’s equal)
Special Case 1(K = 1, C1 = C2 = C)
42
Sallen-Key Bandpass Filter
Vi Vo
43
Bandpass Design Equations
Special Case(R’s equal and C’s equal)
44
Notch Filters
45
Butterworth 2nd Order LPF
Example Design
Special Case 1(K = 1, Solve for C’s)
Can simplify with
46
Example Design
47
Introduced second-order filter circuits Designed a second-order lowpass filter
Summary
48
Dr. Allen RobinsonAcademic ProfessionalSchool of Electrical and Computer Engineering
School of Electrical and Computer Engineering
Filtering Demonstration
Demonstrate filtering of signals
Examine frequency spectra of signals Demonstrate filtering by a second-order filter circuit
Lesson Objectives
50
Spectrum of Sine Wave
51
Spectrum of Sum of Two Sine Waves
52
Spectrum of Square Wave
53
Spectrum of Square Wave
54
Relaxation Oscillator
55
Measurements
f0 = 1kHz Q=5 Sallen-Key BPF
Vo
Relaxation Oscillator
1kHz Square Wave
56
Total Harmonic Distortion (THD)
57
Introduced frequency spectra Examined physical circuit filtering performance
Summary
58