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