Computer Aided Improvement of Linear Phase Bandpass Filters.
F W Mooney, William Protzman · Defense Technical Information Center (DTIC) · 1968
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)