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Sept., 1944 RERECORDING CONSOLE, CIRCUITS, AND EQUALIZERS 201
tion to vary in db, or multiple db steps from zero to some maximum amount obtained on the top step of the control ^dial. Equalization, then, and the manner in which it is to be varied, is assumed to be known design information.
Another parameter useful in the design of equalizers is a frequency which we will call (fb) and for which, on any control step, one-half the equalization loss for that step is obtained. That is, the equalizer loss varies from the minimum loss of Eq (3) to the maximum loss of Eq (2) and at one or more frequencies in between these 2 extremes, one-half the difference loss is obtained. Where fb is multivalued with frequency, use is made of the lower value in the formulas of the book, Motion Picture Sound Engineering? and this concept is retained herein. fb, then, is known design information denned as follows:
fb = Frequency of One-half Equalization Loss (5)
Since equalization has been taken as the difference between the maximum and minimum losses as given in Eqs (2) and (3), it is obvious that a given amount of equalization can be obtained for an infinite number of values for these 2 losses as long as their difference is unchanged. But although this difference may remain constant, the equalization characteristics so obtained shift in the fb frequency. Then, for any definite amount of equalization, adjusting the maximum and minimum losses while keeping their difference constant provides' a means of placing fb at a desired frequency. Constant B equalizers hold fb at a constant frequency for all of the steps of the equalizer. The following equation supplies the design means for adjusting the maximum and minimum losses at the proper values for holding fb constant throughout the constant B attenuator range :
(Max. loss ~| |~ Equalization ~| ("Max. Equalization!
on any step = Sinh on same step X Sinn on top step (6)
2 X 8.68 J L 2 X 8.68 J 2 X 8.68
This is a coupling equation relating the 2 known losses contained in the right side of the equation to the unknown loss embodied in the left side of the equation. Eq (6) is derivable by rigorous mathematical processes not given here. Any equalizer having the circuit of Fig. 11, and having its attenuation losses related as in Eq (6) will maintain fb constant with frequency for all its attenuator steps and for any pair of associated inverse reactance circuits.
An important simplication of Eq (6) can be made which avoids the use of hyperbolic functions in most cases. For equalizers having