Practical Analog Filters Overview Types of practical filters Filter specifications Tradeoffs Many examples
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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
2 Ideal Filters 1 Lowpass 1 Highpass 1 Notch ω c ω ω c ω ω c ω 1 Bandpass 1 Bandstop ω c1 ω c2 ω ω c1 ω c2 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 c1 <ω<ω c2 Bandstop filters pass two ranges: ω<ω c1 and ω>ω c2 Notch filters pass all frequencies except ω = ω c J. McNames Portland State University ECE 222 Practical Analog Filters Ver
3 Ideal Filters Comments 1 Lowpass 1 Highpass 1 Notch ω c ω ω c ω ω c ω 1 Bandpass 1 Bandstop ω c1 ω c2 ω ω c1 ω c2 ω Phase is not shown ω c is called the cutoff frequency Generally, the ideal phase is 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
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
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
6 Example 1: Lowpass Filter Specifications Design a lowpass filter that meets the following specifications: The passband ripple is no more than.4455 db (.95 H(jω) 1) The stopband attenuation is at least 26.2 db ( H(jω).5) The passband ranges from 45 rad/s The stopband ranges from 55 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
7 Example 2: Butterworth Lowpass 1 Butterworth Lowpass Filter Transfer Function Order: 21.8 H(jω) Frequency (rad/sec) J. McNames Portland State University ECE 222 Practical Analog Filters Ver
8 Example 2: Butterworth Lowpass Butterworth Lowpass Filter Transfer Function Order:21 5 H(jω) (db) J. McNames Portland State University ECE 222 Practical Analog Filters Ver
9 Example 2: Butterworth Lowpass Butterworth Lowpass Filter Pole Zero Plot Order:21 4 Poles 3 2 Imaginary Axis Real Axis 5 J. McNames Portland State University ECE 222 Practical Analog Filters Ver
10 Example 2: Butterworth Lowpass 15 Butterworth Lowpass Filter Impulse Response Order: h(t) Time (s) J. McNames Portland State University ECE 222 Practical Analog Filters Ver
11 Example 2: Butterworth Lowpass 1.4 Butterworth Lowpass Filter Step Response Order: h(t) Time (s) J. McNames Portland State University ECE 222 Practical Analog Filters Ver
12 Example 2: Chebyshev-I Lowpass 1 Chebyshev I Lowpass Filter Transfer Function Order: 8.8 H(jω) Frequency (rad/sec) J. McNames Portland State University ECE 222 Practical Analog Filters Ver
13 Example 2: Chebyshev-I Lowpass Chebyshev I Lowpass Filter Transfer Function Order:8 5 H(jω) (db) J. McNames Portland State University ECE 222 Practical Analog Filters Ver
14 Example 2: Chebyshev-I Lowpass Chebyshev I Lowpass Filter Pole Zero Plot Order:8 Poles Imaginary Axis Real Axis J. McNames Portland State University ECE 222 Practical Analog Filters Ver
15 Example 2: Chebyshev-I Lowpass 15 Chebyshev I Lowpass Filter Impulse Response Order:8 1 5 h(t) Time (s) J. McNames Portland State University ECE 222 Practical Analog Filters Ver
16 Example 2: Chebyshev-I Lowpass 1.4 Chebyshev I Lowpass Filter Step Response Order: h(t) Time (s) J. McNames Portland State University ECE 222 Practical Analog Filters Ver
17 Example 2: Chebyshev-II Lowpass 1 Chebyshev II Lowpass Filter Transfer Function Order: 8.8 H(jω) Frequency (rad/sec) J. McNames Portland State University ECE 222 Practical Analog Filters Ver
18 Example 2: Chebyshev-II Lowpass Chebyshev II Lowpass Filter Transfer Function Order:8 5 H(jω) (db) J. McNames Portland State University ECE 222 Practical Analog Filters Ver
19 Example 2: Chebyshev-II Lowpass Chebyshev II Lowpass Filter Pole Zero Plot Order:8 2 Poles Zeros Imaginary Axis Real Axis J. McNames Portland State University ECE 222 Practical Analog Filters Ver
20 Example 2: Chebyshev-II Lowpass 15 Chebyshev II Lowpass Filter Impulse Response Order:8 1 5 h(t) Time (s) J. McNames Portland State University ECE 222 Practical Analog Filters Ver
21 Example 2: Chebyshev-II Lowpass 1.4 Chebyshev II Lowpass Filter Step Response Order: h(t) Time (s) J. McNames Portland State University ECE 222 Practical Analog Filters Ver
22 Example 2: Elliptic Lowpass 1 Elliptic Lowpass Filter Transfer Function Order: 5.8 H(jω) Frequency (rad/sec) J. McNames Portland State University ECE 222 Practical Analog Filters Ver
23 Example 2: Elliptic Lowpass Elliptic Lowpass Filter Transfer Function Order:5 5 H(jω) (db) J. McNames Portland State University ECE 222 Practical Analog Filters Ver
24 Example 2: Elliptic Lowpass 6 4 Elliptic Lowpass Filter Pole Zero Plot Order:5 Poles Zeros Imaginary Axis Real Axis J. McNames Portland State University ECE 222 Practical Analog Filters Ver
25 Example 2: Elliptic Lowpass 15 Elliptic Lowpass Filter Impulse Response Order:5 1 5 h(t) Time (s) J. McNames Portland State University ECE 222 Practical Analog Filters Ver
26 Example 2: Elliptic Lowpass 1.4 Elliptic Lowpass Filter Step Response Order: h(t) Time (s) J. McNames Portland State University ECE 222 Practical Analog Filters Ver
27 Example 3: Highpass Filter Specifications Design an elliptic highpass filter that meets the following specifications: The passband ripple is no more than.4455 db (.95 H(jω) 1) The stopband attenuation is at least 26.2 db ( H(jω).5) The passband ranges from 55 rad/s The stopband ranges from 45 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
28 Example 3: Elliptic Highpass 1 Elliptic Highpass Filter Transfer Function Order: 5.8 H(jω) Frequency (rad/sec) J. McNames Portland State University ECE 222 Practical Analog Filters Ver
29 Example 3: Elliptic Highpass Elliptic Highpass Filter Transfer Function Order:5 5 H(jω) (db) J. McNames Portland State University ECE 222 Practical Analog Filters Ver
30 Example 3: Elliptic Highpass Elliptic Highpass Filter Pole Zero Plot Order:5 5 Poles Zeros Imaginary Axis Real Axis J. McNames Portland State University ECE 222 Practical Analog Filters Ver
31 Example 3: Elliptic Highpass 2 Elliptic Highpass Filter Impulse Response Order:5 2 4 h(t) Time (s) J. McNames Portland State University ECE 222 Practical Analog Filters Ver
32 Example 3: Elliptic Highpass 1 Elliptic Highpass Filter Step Response Order:5.8.6 h(t) Time (s) J. McNames Portland State University ECE 222 Practical Analog Filters Ver
33 Example 3: Relevant MATLAB Code Wp = 55; % Passband ends Ws = 45; % Stopband begins Rp = -2*log1(.95); % Maximum deviation from 1 in the passband (db) Rs = -2*log1(.5); % 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
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.4455 db (.95 H(jω) 1) The stopband attenuation is at least 26.2 db ( H(jω).5) The passband ranges from rad/s The stopband ranges from 4 rad/s and 5 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
35 Example 4: Chebyshev-I Bandpass 1 Chebyshev I Bandpass Filter Transfer Function Order: 8.8 H(jω) Frequency (rad/sec) J. McNames Portland State University ECE 222 Practical Analog Filters Ver
36 Example 4: Chebyshev-I Bandpass Chebyshev I Bandpass Filter Transfer Function Order:8 5 H(jω) (db) J. McNames Portland State University ECE 222 Practical Analog Filters Ver
37 Example 4: Chebyshev-I Bandpass 5 Chebyshev I Bandpass Filter Pole Zero Plot Order:8 Poles Zeros Imaginary Axis Real Axis J. McNames Portland State University ECE 222 Practical Analog Filters Ver
38 Example 4: Chebyshev-I Bandpass 4 Chebyshev I Bandpass Filter Impulse Response Order: h(t) Time (s) J. McNames Portland State University ECE 222 Practical Analog Filters Ver
39 Example 4: Chebyshev-I Bandpass.8 Chebyshev I Bandpass Filter Step Response Order: h(t) Time (s) J. McNames Portland State University ECE 222 Practical Analog Filters Ver
40 Example 4: Relevant MATLAB Code Wp = [45 55]; % Passband ends Ws = [4 6]; % Stopband begins Rp = -2*log1(.95); % Maximum deviation from 1 in the passband (db) Rs = -2*log1(.5); % 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
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.4455 db (.95 H(jω) 1) The stopband attenuation is at least 26.2 db ( H(jω).5) The passband ranges from 4 rad/s and 5 rad/s The stopband ranges from 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
42 Example 5: Chebyshev-II Bandstop 1 Chebyshev II Bandstop Filter Transfer Function Order: 8.8 H(jω) Frequency (rad/sec) J. McNames Portland State University ECE 222 Practical Analog Filters Ver
43 Example 5: Chebyshev-II Bandstop Chebyshev II Bandstop Filter Transfer Function Order:8 5 H(jω) (db) J. McNames Portland State University ECE 222 Practical Analog Filters Ver
44 Example 5: Chebyshev-II Bandstop 5 Chebyshev II Bandstop Filter Pole Zero Plot Order:8 Poles Zeros Imaginary Axis Real Axis J. McNames Portland State University ECE 222 Practical Analog Filters Ver
45 Example 5: Chebyshev-II Bandstop 2 Chebyshev II Bandstop Filter Impulse Response Order:8 1 h(t) Time (s) J. McNames Portland State University ECE 222 Practical Analog Filters Ver
46 Example 5: Chebyshev-II Bandstop 1.3 Chebyshev II Bandstop Filter Step Response Order: h(t) Time (s) J. McNames Portland State University ECE 222 Practical Analog Filters Ver
47 Example 5: Relevant MATLAB Code Wp = [4 6]; % Passband ends Ws = [45 55]; % Stopband begins Rp = -2*log1(.95); % Maximum deviation from 1 in the passband (db) Rs = -2*log1(.5); % 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
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
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