Computer Aided Improvement of Linear Phase Bandpass Filters.
Abstract
The mathematical model of the Lerner band pass electrical network was altered to achieve linear phase (plus or minus 1.25 degrees) over 100% of a given bandwidth while retaining high attenuation at the band edges. Hypothesizing that changing the original model would result in a composite function of the Lerner model and one of the familiar linear delay models, a phase error function was optimized by moving the two outside poles of the Lerner pole array. Resultant locations were found to lie on a translated parabola, a function exhibiting linear delay when used as a pole array locus for network transfer functions. A low pass model, unrestricted in number of poles, was also developed and tested. Essentially, the two low frequency poles of the array were superimposed on the -sigma axis of the complex s-plane. Results were magnitude ripple plus or minus 0.2 db (95% of pass band), attenuation (steepest descent) greater than -60 db/oct., phase error plus or minus 1.25 degrees (100% of -3 db bandwidth). Step response was comparable to equivalent Butterworth functions. Since present definitions of attenuation appear vague, a unified set of definitions are submitted which completely specify any filter's rate of attenuation. Digital and analog computer programs were written which analyze transfer functions expressed as a sum of equivalent quadratic partial fractions. An analog phase program evaluates phase response accurately to within the limitations of the computer used. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1968
- Accession Number
- AD0842396
Entities
People
- Francis W. Mooney
- William Protzman Jr
Organizations
- Air Force Institute of Technology