A new class of multiple-critical-pole equal-ripple rational (MCPER) functions for the design of cascaded RC-active filters with low Q-factors

A new class of multiple-critical-pole equal-ripple rational (MCPER) functions is defined as a generalization of the Caner functions, which are used for the approximation of minimal order filters. Their behaviour is equal-ripple in the passband but the critical pole-pair (i.e, with the highest Q-factor) is multiple as in the case of the MUCROER all-pole functions; furthermore, the transmission zeros, located on the
j\omega
-axis and in number not necessarily equal to the maximum allowed, are evaluated in order to obtain an equal-ripple approximation in the stopband. Then, the highest Q-factor decreases at expense of an increment in the order of the function with respect to the Caner function satisfying the same filtering specifications. Some examples indicate that a reduction in the highest Q-factor of 55 percent, 68 percent, and 71 percent is obtained by increasing the order of the function by 1, 2, and 4, respectively. Thus RC-active filters are realized by cascading more, but less critical, secondorder sections, obtaining a lower overall sensitivity, in addition to a smoother group delay.