This document discusses cascaded first-order filters and second-order transfer functions for filters. It introduces cascaded filters and their characteristics. It then discusses second-order transfer functions, examining features like low-pass, high-pass, and band-pass filters. Finally, it introduces second-order Sallen-Key filter circuits and shows examples of designing low-pass, high-pass, and band-pass filters using these circuits.

1. 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

2.  Introduce cascaded filters
 Introduce bandpass filter characteristics
 Introduce second-order transfer functions
Lesson Objectives
2

3. First-Order LPF and HPF
3

4. Cascaded Filter
Input OutputFirst-Order
LPF
Input OutputFirst-Order
HPF
4

5. Cascaded Filter
5

6. Bandpass Filter Characteristics
6

7. Transfer Function
Second-Order Filter
Standard Form:
7

8. Cascaded Bandpass Filters
8

9.  Is it possible to form a cascaded band-reject
filter?
Question
9

10.  Cascaded Filters
 Bandpass Transfer Functions
Summary
10

11. 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

12.  Introduce second-order filter transfer functions
 Examine features of transfer functions
Lesson Objectives
12

13.  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

14. First-Order Low-Pass Filter
14

15. Second-Order Low-Pass Filter
15

16. Effect of Quality Factor (Q)
16

17. High-Pass Filters
17

18. Band-Pass Filters
18

19. Butterworth and Chebyshev
 Types of transfer functions
 For second-order filters, the type is
determined by the Q value
 Butterworth (Maximally Flat)
 Chebyshev
19

20. Chebyshev Filters
20

21. Butterworth Filters
21

22. Fourth-Order Butterworth vs. Chebyshev
22

23.  Introduced second-order transfer functions
 Examined features of transfer functions
Summary
23

24. 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

25.  Introduce second-order filter transfer functions
 Examine features of transfer functions
Lesson Objectives
25

26.  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

27. First-Order Low-Pass Filter
27

28. Second-Order Low-Pass Filter
28

29. Effect of Quality Factor (Q)
29

30. High-Pass Filters
30

31. Band-Pass Filters
31

32. Butterworth and Chebyshev
 Types of transfer functions
 For second-order filters, the type is
determined by the Q value
 Butterworth (Maximally Flat)
 Chebyshev
32

33. Chebyshev Filters
33

34. Butterworth Filters
34

35. Fourth-Order Butterworth vs. Chebyshev
35

36.  Introduced second-order transfer functions
 Examined features of transfer functions
Summary
36

37. 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

38.  Introduce second-order filter circuits
 Design second-order filters
Lesson Objectives
38

39. Sallen-Key Low-Pass Filter
Vo
Vi
39

40. 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

41. Sallen-Key Highpass Filter
Vi
Vo
41

42. Highpass Design Equations
Special Case 2
(R’s equal and C’s equal)
Special Case 1
(K = 1, C1 = C2 = C)
42

43. Sallen-Key Bandpass Filter
Vi Vo
43

44. Bandpass Design Equations
Special Case
(R’s equal and C’s equal)
44

45. Notch Filters
45

46.  Butterworth 2nd Order LPF
Example Design
Special Case 1
(K = 1, Solve for C’s)
Can simplify with
46

47. Example Design
47

48.  Introduced second-order filter circuits
 Designed a second-order lowpass filter
Summary
48

49. Dr. Allen Robinson
Academic Professional
School of Electrical and
Computer Engineering
School of Electrical and Computer Engineering
Filtering
Demonstration
Demonstrate filtering of signals

50.  Examine frequency spectra of signals
 Demonstrate filtering by a second-order filter circuit
Lesson Objectives
50

51. Spectrum of Sine Wave
51

52. Spectrum of Sum of Two Sine Waves
52

53. Spectrum of Square Wave
53

54. Spectrum of Square Wave
54

55. Relaxation Oscillator
55

56. Measurements
f0 = 1kHz Q=5 Sallen-Key BPF
Vo
Relaxation Oscillator
1kHz Square
Wave
56

57. Total Harmonic Distortion (THD)
57

58.  Introduced frequency spectra
 Examined physical circuit filtering performance
Summary
58