Continued   

     The shape factors for the Bandpass Filters and Band Reject Filters listed later on these pages and the can be determined by dividing the frequency difference between the 20dB points or the 40dB points (rejection bandwidth) by the frequency difference between the 3dB points (passband). The specified upper and lower 3, 20 or 40dB points should be geometrically symmetrical to the center frequency. The relationship of the band edges (F₁ &  F₂) to the center frequency (F₀) in a filter that has geometric symmetry is defined as F₀ = F₀ x  F₂. 

     The Linear Phase Flat Delay Bandpass Filters on later pages have arithmetric symmetry to the center frequency. This type of symmetry is defined by F_{0 =}  ½(F₁ x  F₂). This type of filter will always have at least one half of the passband on either side of the center frequency. 

     In this filter catalog, all the Iowpass and bandpass shape factors will result in a number greater than one, while the shape factors in the

     As the shape factor requirement for a particular filter approaches one, the necessary number and quality factor of its capacitors and inductors increases. Extensive experience and knowledge of components, along with the ultimate in computer aided design and computer controlled test equipment, are required to manufacture LC Filters that exhibit these very low shape factors. Allen Avionics offers a wide range of shape factors for each of the Lowpass, Highpass, Bandpass and Band Reject type of filter. By taking advantage of the tables of shape factors for each filter type, you can pick just the right amount of filtering to do your job. Buying more filter than you need can cost a lot.

     The characteristics that the Lowpass, Highpass, Bandpass or Band Reject Filters exhibit are determined by the type of design as well as the number of elements. The Butterworth, Chebyshev, Elliptical, Bessel, Gaussian and the Transitional Gaussian are the best known and most useful designs that are currently used in the filter industry.

     The Butterworth Design is characterized by a ripple-free passband as well as a smooth stop band. Increased attenuation is achieved as the frequencies get further from the passband. For a given shape factor, this design requires more components than the Chebyshev or Elliptic types but the required quality factor of its components is not as high. When a Butterworth filter is specified for a filter application, the additional sections needed to meet a given shape factor will increase over other filter types and can result in increased size and cost.

     The Chebyshev design is characterized by a predetermined amount of passband ripple. The stop band exhibits smooth roll-off and infinite attenuation is approached as the frequency increases. This design requires less components than the Butterworth to realize a given shape factor. Reductions in cost and size can be realized with this type of filter over the Butterworth even though the quality factor demanded of its components is much greater. (See Fig. A and B.)