Predistortion techniques for increasing the element tolerances in equiripple passband niters revisited

A well established technique to increase the element tolerances in the design of selective passive filters, or to decrease the adverse effect of limited gain-bandwidth product of operational amplifiers is to use transfer function with a special type of magnitude response for which the passband ripple amplitude decreases with increasing frequency. Recently various techniques have been reported to construct this type of filtering functions but they are either entirely numerical or, at least, require numerical optimization of some relevant parameters. In this paper, an exact method is proposed to find the explicit expression for the predistorted characteristic function of these filters applicable to both polynomial filters and filters with finite attenuation poles of any degree. The ratio of the magnitudes of the first passband ripple to the last passband ripple can be prescribed in advance, according to the required specifications.