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  Analog Filter Design De...  
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  Analog Filter Design De...  
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Poles (a ± jb)
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Quadratic Expression
  Analog Filter Design De...  
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First, transform each pole location into a quadratic expression similar to that in the denominator of our generic 2nd-order filter. If a quadratic equation has poles of (a ± jb), then it has roots of (s - a - jb) and (s - a + jb).
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In the pole tables, "a" is always negative, so for convenience we declare s² + 2as + a² + b² and use the magnitude of "a," regardless of its sign. To put this into practice, consider a 4th-order Butterworth filter. The poles and the quadratic expression corresponding to each pole location are as follows:
  Analog Filter Design De...  
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First, transform each pole location into a quadratic expression similar to that in the denominator of our generic 2nd-order filter. If a quadratic equation has poles of (a ± jb), then it has roots of (s - a - jb) and (s - a + jb).
Compare text pagesCompare HTM pagesOpen source URLOpen target URLDefine maximintegrated.com as primary domain
In the pole tables, "a" is always negative, so for convenience we declare s² + 2as + a² + b² and use the magnitude of "a," regardless of its sign. To put this into practice, consider a 4th-order Butterworth filter. The poles and the quadratic expression corresponding to each pole location are as follows:
  Analog Filter Design De...  
Show textShow cached sourceOpen source URL
First, transform each pole location into a quadratic expression similar to that in the denominator of our generic 2nd-order filter. If a quadratic equation has poles of (a ± jb), then it has roots of (s - a - jb) and (s - a + jb).
Compare text pagesCompare HTM pagesOpen source URLOpen target URLDefine maximintegrated.com as primary domain
In the pole tables, "a" is always negative, so for convenience we declare s² + 2as + a² + b² and use the magnitude of "a," regardless of its sign. To put this into practice, consider a 4th-order Butterworth filter. The poles and the quadratic expression corresponding to each pole location are as follows:
  Analog Filter Design De...  
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These values, which establish the performance of each type of filter over frequency, are known as the poles of the quadratic equation. Poles usually occur as pairs, in the form of a complex number (a + jb) and its complex conjugate (a - jb).
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The thought of a transfer function with infinite gain may frighten nervous readers, but in practice it isn't a problem. The pole's real part "a" indicates how the filter responds to transients, and its imaginary part "jb" indicates the response over frequency. As long as this real part is negative, the system is stable. The following text explains how to transfer the tables of poles found in many text books into component values suitable for circuit design.
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Theta JB
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  Analog Filter Design De...  
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These values, which establish the performance of each type of filter over frequency, are known as the poles of the quadratic equation. Poles usually occur as pairs, in the form of a complex number (a + jb) and its complex conjugate (a - jb).
Compare text pagesCompare HTM pagesOpen source URLOpen target URLDefine maximintegrated.com as primary domain
The thought of a transfer function with infinite gain may frighten nervous readers, but in practice it isn't a problem. The pole's real part "a" indicates how the filter responds to transients, and its imaginary part "jb" indicates the response over frequency. As long as this real part is negative, the system is stable. The following text explains how to transfer the tables of poles found in many text books into component values suitable for circuit design.
  Analog Filter Design De...  
Show textShow cached sourceOpen source URL
These values, which establish the performance of each type of filter over frequency, are known as the poles of the quadratic equation. Poles usually occur as pairs, in the form of a complex number (a + jb) and its complex conjugate (a - jb).
Compare text pagesCompare HTM pagesOpen source URLOpen target URLDefine maximintegrated.com as primary domain
The thought of a transfer function with infinite gain may frighten nervous readers, but in practice it isn't a problem. The pole's real part "a" indicates how the filter responds to transients, and its imaginary part "jb" indicates the response over frequency. As long as this real part is negative, the system is stable. The following text explains how to transfer the tables of poles found in many text books into component values suitable for circuit design.