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7PracticalFiltersx4 - Practical Analog Filters Overview...

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Ideal Filters Comments 1 Lowpass 1 Highpass 1 Bandpass 1 Bandstop 1 Notch ω ω ω ω ω ω c ω c ω c ω c 1 ω c 1 ω c 2 ω c 2 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. 1.05 3 Practical Analog Filters Overview Types of practical filters Filter specifications Tradeoffs Many examples J. McNames Portland State University ECE 222 Practical Analog Filters Ver. 1.05 1 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. 1.05 4 Ideal Filters 1 Lowpass 1 Highpass 1 Bandpass 1 Bandstop 1 Notch ω ω ω ω ω ω c ω c ω c ω c 1 ω c 1 ω c 2 ω c 2 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. 1.05 2
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Example 1: dB Magnitude Response 0 100 200 300 400 500 600 700 800 900 1000 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 |H(j ω )| Butterworth Lowpass Filter Transfer Function Order: 21 Frequency (rad/sec) J. McNames Portland State University ECE 222 Practical Analog Filters Ver. 1.05 7 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. 1.05 5 Example 1: Linear Magnitude Response 10 2 10 3 -30 -25 -20 -15 -10 -5 0 |H(j ω )| (dB) Butterworth Lowpass Filter Transfer Function Order:21 J. McNames Portland State University ECE 222 Practical Analog Filters Ver. 1.05 8 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 ( ) | ≤ 1 ) The stopband attenuation is at least 26.02 dB ( | H ( ) | ≤ 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,
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