Practical Analog Filters Overview Types of practical filters Filter - - PowerPoint PPT Presentation

▶
practical analog filters overview types of practical
SMART_READER_LITE
LIVE PREVIEW

Practical Analog Filters Overview Types of practical filters Filter - - PowerPoint PPT Presentation

Jun 17, 2023 144 likes •648 views

Practical Analog Filters Overview Types of practical filters Filter specifications Tradeoffs Many examples J. McNames Portland State University ECE 222 Practical Analog Filters Ver. 1.04 1 Ideal Filters Lowpass Highpass

slide-1
SLIDE 1

Practical Analog Filters Overview

  • Types of practical filters
  • Filter specifications
  • Tradeoffs
  • Many examples
  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

1

slide-2
SLIDE 2

Ideal Filters

1 Lowpass 1 Highpass 1 Bandpass 1 Bandstop 1 Notch

ω ω ω ω ω ωc ωc ωc ωc1 ωc1 ωc2 ωc2

  • There are five ideal filters
  • Lowpass filters pass low frequencies: ω < ωc
  • Highpass filters pass high frequencies: ω > ωc
  • Bandpass filters pass a range of frequencies: ωc1 < ω < ωc2
  • Bandstop filters pass two ranges: ω < ωc1 and ω > ωc2
  • Notch filters pass all frequencies except ω ∼

= ωc

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

2

slide-3
SLIDE 3

Ideal Filters Comments

1 Lowpass 1 Highpass 1 Bandpass 1 Bandstop 1 Notch

ω ω ω ω ω ωc ωc ωc ωc1 ωc1 ωc2 ωc2

  • Phase is not shown
  • ωc is called the cutoff frequency
  • Generally, the ideal phase is 0◦ for all frequencies
  • Can not build ideal filters in practice
  • Real filters appear as rounded versions of ideal filters
  • Most LTI systems can be thought of as non-ideal filters
  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

3

slide-4
SLIDE 4

Practical Filters

  • Practical filters are usually designed to meet a set of specifications
  • Lowpass and highpass filters usually have the following

requirements – Passband range – Stopband range – Maximum ripple in the passband – Minimum attenuation in the stopband

  • If we know the specifications, we can ask MATLAB to generate

the filter for us

  • There are four popular types of standard filters

– Butterworth – Chebyshev Type I – Chebyshev Type II – Elliptic

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

4

slide-5
SLIDE 5

Practical Filter Tradeoffs

  • Butterworth
  • Highest order H(s)

+ No passband or stopband ripple

  • Chebyshev Type I

+ No stopband ripple

  • Chebyshev Type II

+ No passband ripple

  • Elliptic

+ Lowest order H(s)

  • Passband and stopband ripple
  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

5

slide-6
SLIDE 6

Example 1: Lowpass Filter Specifications Design a lowpass filter that meets the following specifications:

  • The passband ripple is no more than 0.4455 dB

(0.95 ≤ |H(jω)| ≤ 1)

  • The stopband attenuation is at least 26.02 dB (|H(jω)| ≤ 0.05)
  • The passband ranges from 0–450 rad/s
  • The stopband ranges from 550–∞ rad/s

Plot the magnitude of the resulting transfer function on a linear-linear plot, the Bode magnitude plot, the pole-zero plot, the impulse response, and the step response. Try the Butterworth, Chebyshev I, Chebyshev II, and elliptic filters. The MATLAB code is posted on the course web site.

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

6

slide-7
SLIDE 7

Example 2: Butterworth Lowpass

100 200 300 400 500 600 700 800 900 1000 0.2 0.4 0.6 0.8 1 |H(jω)| Butterworth Lowpass Filter Transfer Function Order: 21 Frequency (rad/sec)

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

7

slide-8
SLIDE 8

Example 2: Butterworth Lowpass

10

2

10

3

−30 −25 −20 −15 −10 −5 |H(jω)| (dB) Butterworth Lowpass Filter Transfer Function Order:21

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

8

slide-9
SLIDE 9

Example 2: Butterworth Lowpass

−1000 −500 500 −400 −300 −200 −100 100 200 300 400 Imaginary Axis Real Axis Butterworth Lowpass Filter Pole−Zero Plot Order:21 Poles

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

9

slide-10
SLIDE 10

Example 2: Butterworth Lowpass

0.05 0.1 0.15 0.2 0.25 −100 −50 50 100 150 h(t) Time (s) Butterworth Lowpass Filter Impulse Response Order:21

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

10

slide-11
SLIDE 11

Example 2: Butterworth Lowpass

0.05 0.1 0.15 0.2 0.25 0.2 0.4 0.6 0.8 1 1.2 1.4 h(t) Time (s) Butterworth Lowpass Filter Step Response Order:21

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

11

slide-12
SLIDE 12

Example 2: Chebyshev-I Lowpass

100 200 300 400 500 600 700 800 900 1000 0.2 0.4 0.6 0.8 1 |H(jω)| Chebyshev−I Lowpass Filter Transfer Function Order: 8 Frequency (rad/sec)

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

12

slide-13
SLIDE 13

Example 2: Chebyshev-I Lowpass

10

2

10

3

−30 −25 −20 −15 −10 −5 |H(jω)| (dB) Chebyshev−I Lowpass Filter Transfer Function Order:8

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

13

slide-14
SLIDE 14

Example 2: Chebyshev-I Lowpass

−800 −600 −400 −200 200 400 600 −400 −300 −200 −100 100 200 300 400 Imaginary Axis Real Axis Chebyshev−I Lowpass Filter Pole−Zero Plot Order:8 Poles

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

14

slide-15
SLIDE 15

Example 2: Chebyshev-I Lowpass

0.05 0.1 0.15 0.2 0.25 −100 −50 50 100 150 h(t) Time (s) Chebyshev−I Lowpass Filter Impulse Response Order:8

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

15

slide-16
SLIDE 16

Example 2: Chebyshev-I Lowpass

0.05 0.1 0.15 0.2 0.25 0.2 0.4 0.6 0.8 1 1.2 1.4 h(t) Time (s) Chebyshev−I Lowpass Filter Step Response Order:8

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

16

slide-17
SLIDE 17

Example 2: Chebyshev-II Lowpass

100 200 300 400 500 600 700 800 900 1000 0.2 0.4 0.6 0.8 1 |H(jω)| Chebyshev−II Lowpass Filter Transfer Function Order: 8 Frequency (rad/sec)

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

17

slide-18
SLIDE 18

Example 2: Chebyshev-II Lowpass

10

2

10

3

−30 −25 −20 −15 −10 −5 |H(jω)| (dB) Chebyshev−II Lowpass Filter Transfer Function Order:8

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

18

slide-19
SLIDE 19

Example 2: Chebyshev-II Lowpass

−4000 −3000 −2000 −1000 1000 2000 3000 4000 −2000 −1000 1000 2000 Imaginary Axis Real Axis Chebyshev−II Lowpass Filter Pole−Zero Plot Order:8 Poles Zeros

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

19

slide-20
SLIDE 20

Example 2: Chebyshev-II Lowpass

0.05 0.1 0.15 0.2 0.25 −200 −150 −100 −50 50 100 150 h(t) Time (s) Chebyshev−II Lowpass Filter Impulse Response Order:8

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

20

slide-21
SLIDE 21

Example 2: Chebyshev-II Lowpass

0.05 0.1 0.15 0.2 0.25 0.2 0.4 0.6 0.8 1 1.2 1.4 h(t) Time (s) Chebyshev−II Lowpass Filter Step Response Order:8

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

21

slide-22
SLIDE 22

Example 2: Elliptic Lowpass

100 200 300 400 500 600 700 800 900 1000 0.2 0.4 0.6 0.8 1 |H(jω)| Elliptic Lowpass Filter Transfer Function Order: 5 Frequency (rad/sec)

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

22

slide-23
SLIDE 23

Example 2: Elliptic Lowpass

10

2

10

3

−30 −25 −20 −15 −10 −5 |H(jω)| (dB) Elliptic Lowpass Filter Transfer Function Order:5

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

23

slide-24
SLIDE 24

Example 2: Elliptic Lowpass

−1200 −1000 −800 −600 −400 −200 200 400 600 800 −600 −400 −200 200 400 600 Imaginary Axis Real Axis Elliptic Lowpass Filter Pole−Zero Plot Order:5 Poles Zeros

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

24

slide-25
SLIDE 25

Example 2: Elliptic Lowpass

0.05 0.1 0.15 0.2 0.25 −100 −50 50 100 150 h(t) Time (s) Elliptic Lowpass Filter Impulse Response Order:5

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

25

slide-26
SLIDE 26

Example 2: Elliptic Lowpass

0.05 0.1 0.15 0.2 0.25 0.2 0.4 0.6 0.8 1 1.2 1.4 h(t) Time (s) Elliptic Lowpass Filter Step Response Order:5

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

26

slide-27
SLIDE 27

Example 3: Highpass Filter Specifications Design an elliptic highpass filter that meets the following specifications:

  • The passband ripple is no more than 0.4455 dB

(0.95 ≤ |H(jω)| ≤ 1)

  • The stopband attenuation is at least 26.02 dB (|H(jω)| ≤ 0.05)
  • The passband ranges from 550–∞ rad/s
  • The stopband ranges from 0–450 rad/s

Plot the magnitude of the resulting transfer function on a linear-linear plot, the Bode magnitude plot, the pole-zero plot, the impulse response, and the step response.

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

27

slide-28
SLIDE 28

Example 3: Elliptic Highpass

100 200 300 400 500 600 700 800 900 1000 0.2 0.4 0.6 0.8 1 |H(jω)| Elliptic Highpass Filter Transfer Function Order: 5 Frequency (rad/sec)

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

28

slide-29
SLIDE 29

Example 3: Elliptic Highpass

10

2

10

3

−30 −25 −20 −15 −10 −5 |H(jω)| (dB) Elliptic Highpass Filter Transfer Function Order:5

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

29

slide-30
SLIDE 30

Example 3: Elliptic Highpass

−1400 −1200 −1000 −800 −600 −400 −200 200 400 −500 500 Imaginary Axis Real Axis Elliptic Highpass Filter Pole−Zero Plot Order:5 Poles Zeros

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

30

slide-31
SLIDE 31

Example 3: Elliptic Highpass

0.05 0.1 0.15 −1400 −1200 −1000 −800 −600 −400 −200 200 h(t) Time (s) Elliptic Highpass Filter Impulse Response Order:5

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

31

slide-32
SLIDE 32

Example 3: Elliptic Highpass

0.05 0.1 0.15 −0.4 −0.2 0.2 0.4 0.6 0.8 1 h(t) Time (s) Elliptic Highpass Filter Step Response Order:5

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

32

slide-33
SLIDE 33

Example 3: Relevant MATLAB Code

Wp = 550; % Passband ends Ws = 450; % Stopband begins Rp = -20*log10(0.95); % Maximum deviation from 1 in the passband (dB) Rs = -20*log10(0.05); % Minimum attenuation in the stopband (dB) [n,wn] = ellipord(Wp,Ws,Rp,Rs,’s’); [B,A] = ellip(n,Rp,Rs,wn,’high’,’s’);

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

33

slide-34
SLIDE 34

Example 4: Bandpass Filter Specifications Design an Chebyshev type I bandpass filter that meets the following specifications:

  • The passband ripple is no more than 0.4455 dB

(0.95 ≤ |H(jω)| ≤ 1)

  • The stopband attenuation is at least 26.02 dB (|H(jω)| ≤ 0.05)
  • The passband ranges from 450–550 rad/s
  • The stopband ranges from 0–400 rad/s and 500–∞ rad/s

Plot the magnitude of the resulting transfer function on a linear-linear plot, the Bode magnitude plot, the pole-zero plot, the impulse response, and the step response.

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

34

slide-35
SLIDE 35

Example 4: Chebyshev-I Bandpass

100 200 300 400 500 600 700 800 900 1000 0.2 0.4 0.6 0.8 1 |H(jω)| Chebyshev−I Bandpass Filter Transfer Function Order: 8 Frequency (rad/sec)

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

35

slide-36
SLIDE 36

Example 4: Chebyshev-I Bandpass

10

2

10

3

−30 −25 −20 −15 −10 −5 |H(jω)| (dB) Chebyshev−I Bandpass Filter Transfer Function Order:8

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

36

slide-37
SLIDE 37

Example 4: Chebyshev-I Bandpass

−800 −600 −400 −200 200 400 600 800 −500 500 Imaginary Axis Real Axis Chebyshev−I Bandpass Filter Pole−Zero Plot Order:8 Poles Zeros

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

37

slide-38
SLIDE 38

Example 4: Chebyshev-I Bandpass

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 −40 −30 −20 −10 10 20 30 40 h(t) Time (s) Chebyshev−I Bandpass Filter Impulse Response Order:8

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

38

slide-39
SLIDE 39

Example 4: Chebyshev-I Bandpass

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 −0.08 −0.06 −0.04 −0.02 0.02 0.04 0.06 0.08 h(t) Time (s) Chebyshev−I Bandpass Filter Step Response Order:8

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

39

slide-40
SLIDE 40

Example 4: Relevant MATLAB Code

Wp = [450 550]; % Passband ends Ws = [400 600]; % Stopband begins Rp = -20*log10(0.95); % Maximum deviation from 1 in the passband (dB) Rs = -20*log10(0.05); % Minimum attenuation in the stopband (dB) [n,wn] = cheb1ord(Wp,Ws,Rp,Rs,’s’); [B,A] = cheby1(n,Rp,wn,’s’);

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

40

slide-41
SLIDE 41

Example 5: Bandstop Filter Specifications Design an Chebyshev type II bandstop filter that meets the following specifications:

  • The passband ripple is no more than 0.4455 dB

(0.95 ≤ |H(jω)| ≤ 1)

  • The stopband attenuation is at least 26.02 dB (|H(jω)| ≤ 0.05)
  • The passband ranges from 0–400 rad/s and 500–∞ rad/s
  • The stopband ranges from 450–550 rad/s

Plot the magnitude of the resulting transfer function on a linear-linear plot, the Bode magnitude plot, the pole-zero plot, the impulse response, and the step response.

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

41

slide-42
SLIDE 42

Example 5: Chebyshev-II Bandstop

100 200 300 400 500 600 700 800 900 1000 0.2 0.4 0.6 0.8 1 |H(jω)| Chebyshev−II Bandstop Filter Transfer Function Order: 8 Frequency (rad/sec)

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

42

slide-43
SLIDE 43

Example 5: Chebyshev-II Bandstop

10

2

10

3

−30 −25 −20 −15 −10 −5 |H(jω)| (dB) Chebyshev−II Bandstop Filter Transfer Function Order:8

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

43

slide-44
SLIDE 44

Example 5: Chebyshev-II Bandstop

−800 −600 −400 −200 200 400 600 800 −500 500 Imaginary Axis Real Axis Chebyshev−II Bandstop Filter Pole−Zero Plot Order:8 Poles Zeros

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

44

slide-45
SLIDE 45

Example 5: Chebyshev-II Bandstop

0.05 0.1 0.15 0.2 0.25 −300 −200 −100 100 200 h(t) Time (s) Chebyshev−II Bandstop Filter Impulse Response Order:8

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

45

slide-46
SLIDE 46

Example 5: Chebyshev-II Bandstop

0.05 0.1 0.15 0.2 0.25 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 h(t) Time (s) Chebyshev−II Bandstop Filter Step Response Order:8

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

46

slide-47
SLIDE 47

Example 5: Relevant MATLAB Code

Wp = [400 600]; % Passband ends Ws = [450 550]; % Stopband begins Rp = -20*log10(0.95); % Maximum deviation from 1 in the passband (dB) Rs = -20*log10(0.05); % Minimum attenuation in the stopband (dB) [n,wn] = cheb2ord(Wp,Ws,Rp,Rs,’s’); [B,A] = cheby2(n,Rs,wn,’stop’,’s’);

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

47

slide-48
SLIDE 48

Practical Filters Summary

  • In most applications, filter design begins with a set of

specifications

  • We can use design tools like MATLAB to solve for the H(s) that

meets a set of frequency specifications

  • We can then use the cascade-form of transfer function synthesis
  • However, there are standard circuits for these types of filters that

are less expensive and more tolerant of errors in component values

  • J. McNames

Portland State University ECE 222 Practical Analog Filters

  • Ver. 1.04

48