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

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 Notch 1 1 1 ω c ω c ω c ω ω ω Bandpass Bandstop 1 1 ω c 1 ω c 2 ω c 1 ω c 2 ω ω • There are five ideal filters • Lowpass filters pass low frequencies: ω < ω c • Highpass filters pass high frequencies: ω > ω c • Bandpass filters pass a range of frequencies: ω c 1 < ω < ω c 2 • Bandstop filters pass two ranges: ω < ω c 1 and ω > ω c 2 • Notch filters pass all frequencies except ω ∼ = ω c J. McNames Portland State University ECE 222 Practical Analog Filters Ver. 1.04 2

Ideal Filters Comments Lowpass Highpass Notch 1 1 1 ω c ω c ω c ω ω ω Bandpass Bandstop 1 1 ω c 1 ω c 2 ω c 1 ω c 2 ω ω • Phase is not shown • ω c 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

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

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

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

Example 2: Butterworth Lowpass Butterworth Lowpass Filter Transfer Function Order: 21 1 0.8 0.6 |H(j ω )| 0.4 0.2 0 0 100 200 300 400 500 600 700 800 900 1000 Frequency (rad/sec) J. McNames Portland State University ECE 222 Practical Analog Filters Ver. 1.04 7

Example 2: Butterworth Lowpass Butterworth Lowpass Filter Transfer Function Order:21 0 −5 −10 |H(j ω )| (dB) −15 −20 −25 −30 2 3 10 10 J. McNames Portland State University ECE 222 Practical Analog Filters Ver. 1.04 8

Example 2: Butterworth Lowpass Butterworth Lowpass Filter Pole−Zero Plot Order:21 Poles 400 300 200 Imaginary Axis 100 0 −100 −200 −300 −400 −1000 −500 0 500 Real Axis J. McNames Portland State University ECE 222 Practical Analog Filters Ver. 1.04 9

Example 2: Butterworth Lowpass Butterworth Lowpass Filter Impulse Response Order:21 150 100 50 h(t) 0 −50 −100 0 0.05 0.1 0.15 0.2 0.25 Time (s) J. McNames Portland State University ECE 222 Practical Analog Filters Ver. 1.04 10

Example 2: Butterworth Lowpass Butterworth Lowpass Filter Step Response Order:21 1.4 1.2 1 0.8 h(t) 0.6 0.4 0.2 0 0 0.05 0.1 0.15 0.2 0.25 Time (s) J. McNames Portland State University ECE 222 Practical Analog Filters Ver. 1.04 11

Example 2: Chebyshev-I Lowpass Chebyshev−I Lowpass Filter Transfer Function Order: 8 1 0.8 0.6 |H(j ω )| 0.4 0.2 0 0 100 200 300 400 500 600 700 800 900 1000 Frequency (rad/sec) J. McNames Portland State University ECE 222 Practical Analog Filters Ver. 1.04 12

Example 2: Chebyshev-I Lowpass Chebyshev−I Lowpass Filter Transfer Function Order:8 0 −5 −10 |H(j ω )| (dB) −15 −20 −25 −30 2 3 10 10 J. McNames Portland State University ECE 222 Practical Analog Filters Ver. 1.04 13

Example 2: Chebyshev-I Lowpass Chebyshev−I Lowpass Filter Pole−Zero Plot Order:8 400 Poles 300 200 Imaginary Axis 100 0 −100 −200 −300 −400 −800 −600 −400 −200 0 200 400 600 Real Axis J. McNames Portland State University ECE 222 Practical Analog Filters Ver. 1.04 14

Example 2: Chebyshev-I Lowpass Chebyshev−I Lowpass Filter Impulse Response Order:8 150 100 50 h(t) 0 −50 −100 0 0.05 0.1 0.15 0.2 0.25 Time (s) J. McNames Portland State University ECE 222 Practical Analog Filters Ver. 1.04 15

Example 2: Chebyshev-I Lowpass Chebyshev−I Lowpass Filter Step Response Order:8 1.4 1.2 1 0.8 h(t) 0.6 0.4 0.2 0 0 0.05 0.1 0.15 0.2 0.25 Time (s) J. McNames Portland State University ECE 222 Practical Analog Filters Ver. 1.04 16

Example 2: Chebyshev-II Lowpass Chebyshev−II Lowpass Filter Transfer Function Order: 8 1 0.8 0.6 |H(j ω )| 0.4 0.2 0 0 100 200 300 400 500 600 700 800 900 1000 Frequency (rad/sec) J. McNames Portland State University ECE 222 Practical Analog Filters Ver. 1.04 17

Example 2: Chebyshev-II Lowpass Chebyshev−II Lowpass Filter Transfer Function Order:8 0 −5 −10 |H(j ω )| (dB) −15 −20 −25 −30 2 3 10 10 J. McNames Portland State University ECE 222 Practical Analog Filters Ver. 1.04 18

Example 2: Chebyshev-II Lowpass Chebyshev−II Lowpass Filter Pole−Zero Plot Order:8 Poles 2000 Zeros 1000 Imaginary Axis 0 −1000 −2000 −4000 −3000 −2000 −1000 0 1000 2000 3000 4000 Real Axis J. McNames Portland State University ECE 222 Practical Analog Filters Ver. 1.04 19

Example 2: Chebyshev-II Lowpass Chebyshev−II Lowpass Filter Impulse Response Order:8 150 100 50 0 h(t) −50 −100 −150 −200 0 0.05 0.1 0.15 0.2 0.25 Time (s) J. McNames Portland State University ECE 222 Practical Analog Filters Ver. 1.04 20

Example 2: Chebyshev-II Lowpass Chebyshev−II Lowpass Filter Step Response Order:8 1.4 1.2 1 0.8 h(t) 0.6 0.4 0.2 0 0 0.05 0.1 0.15 0.2 0.25 Time (s) J. McNames Portland State University ECE 222 Practical Analog Filters Ver. 1.04 21

Example 2: Elliptic Lowpass Elliptic Lowpass Filter Transfer Function Order: 5 1 0.8 0.6 |H(j ω )| 0.4 0.2 0 0 100 200 300 400 500 600 700 800 900 1000 Frequency (rad/sec) J. McNames Portland State University ECE 222 Practical Analog Filters Ver. 1.04 22

Example 2: Elliptic Lowpass Elliptic Lowpass Filter Transfer Function Order:5 0 −5 −10 |H(j ω )| (dB) −15 −20 −25 −30 2 3 10 10 J. McNames Portland State University ECE 222 Practical Analog Filters Ver. 1.04 23

Example 2: Elliptic Lowpass Elliptic Lowpass Filter Pole−Zero Plot Order:5 600 Poles Zeros 400 200 Imaginary Axis 0 −200 −400 −600 −1200 −1000 −800 −600 −400 −200 0 200 400 600 800 Real Axis J. McNames Portland State University ECE 222 Practical Analog Filters Ver. 1.04 24

Example 2: Elliptic Lowpass Elliptic Lowpass Filter Impulse Response Order:5 150 100 50 h(t) 0 −50 −100 0 0.05 0.1 0.15 0.2 0.25 Time (s) J. McNames Portland State University ECE 222 Practical Analog Filters Ver. 1.04 25

Example 2: Elliptic Lowpass Elliptic Lowpass Filter Step Response Order:5 1.4 1.2 1 0.8 h(t) 0.6 0.4 0.2 0 0 0.05 0.1 0.15 0.2 0.25 Time (s) J. McNames Portland State University ECE 222 Practical Analog Filters Ver. 1.04 26

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

Example 3: Elliptic Highpass Elliptic Highpass Filter Transfer Function Order: 5 1 0.8 0.6 |H(j ω )| 0.4 0.2 0 0 100 200 300 400 500 600 700 800 900 1000 Frequency (rad/sec) J. McNames Portland State University ECE 222 Practical Analog Filters Ver. 1.04 28