A new class of equal-ripple filtering functions with low Q-factors: The MUCROER polynomials
AMEDEO PREMOLI · IEEE Transactions on Circuits and Systems · 1974
A new class of polynomials is defined as a generalization of the polynomials1 + {\varepsilon}^{2} \cdot C_{m}^{2}(-jp), whereC_{m}indicates the Chebyshev polynomial of degreem; these polynomials, called multiple critical root equal ripple (MUCROER), are very convneient for the approximation of RC active filter characteristics. Their behavior is equal ripple in the passband but the critical root pair (the one nearest to thej\omegaaxis) is multiple as in the case of the maximally flat MUCROMAF polynomials; then the polynomial degree is higher but the Q factor of the critical root pair is lower than those of the corresponding Chebyshev polynomial. Thus they allow the realization of RC active filters with more sections but with much lower sensitivity. Some design examples show the remarkable reduction of the critical Q factor.