Computer Aided Improvement of Linear Phase Bandpass Filters.
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING
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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 dboct., 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 filters 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
- Electrical and Electronic Equipment