A new class of equal-ripple filtering functions with low Q-factors: The MUCROER polynomials

A new class of polynomials is defined as a generalization of the polynomials
1 + {\varepsilon}^{2} \cdot C_{m}^{2}(-jp)
, where
C_{m}
indicates the Chebyshev polynomial of degree
m
; 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 the
j\omega
axis) 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.