Designing a lowpass Butterworth filter

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SUMMARY

The discussion focuses on designing a lowpass Butterworth filter with a passband edge frequency of 10 kHz and a stopband frequency of 30 kHz, requiring a minimum stopband attenuation of 50 dB and a maximum passband attenuation of 0.4 dB. The user struggles with calculating the filter order, using the formula n = log(ε/√(A²-1))/log(Ωp/Ωs), which results in a complex number. Additionally, the discussion highlights the limitations of Butterworth filters compared to Chebyshev and elliptic filters, emphasizing the latter's superior performance in terms of selectivity and pulse response. The user is advised to consider alternative filter designs for better efficiency.

PREREQUISITES
  • Understanding of filter design principles, specifically Butterworth filters.
  • Familiarity with frequency response concepts, including passband and stopband definitions.
  • Knowledge of attenuation calculations and the significance of dB in filter design.
  • Experience with filter design software, such as FilterCad.
NEXT STEPS
  • Research the design and characteristics of Chebyshev filters.
  • Explore elliptic filter design techniques for improved performance.
  • Learn about the implications of filter order on circuit complexity and performance.
  • Investigate the use of FilterCad for practical filter design and simulation.
USEFUL FOR

Electrical engineers, signal processing specialists, and students involved in filter design and analysis, particularly those seeking to optimize lowpass filter performance.

rusty009
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Hi all,

I am trying to design a lowpass filter using the following conditions

Passband edge f = 10 Khz (Ωp)
passband stop f = 30 Khz (Ωs)
Minimum stopband attenuation = 50db (1/A)
Maximum passband attenuation = 0.4db( 1/\sqrt{1+ε<sup>2</sup>} )

and am having quite a lot of trouble with it. I have tried to determine the order but it comes out as a complex number, the formula I am using is,

n= log( ε/\sqrt{(A<sup>2</sup>-1)})/log(Ω[/B]p/Ωs)

can anyone help me out? Thanks
 
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There, download FilterCad:
http://www.linear.com/designtools/software/

By the way, Butterworth is just the worst of all filters except the straight wire. Huge number of poles and components for a given selectivity, AND by far worst pulse response for a given selectivity. Chebychev is better, elliptic even better, and inverse (or type II) Chebychev better.

So unless some kind of teacher imposes you the Chebychev, take a more sensible option.
 

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