Elliptic filters with minimal Q-factors

Elliptic filters have minimal Q-factors for a specified ripple factor determined by the value of the characteristic function at the stopband edge frequency. The poles of such a filter are on a circle whose radius is equal to the geometric mean value of the passband and stopband edge frequencies. The Q-factors are determined by means of a simple relation as a function of the stopband edge and zero loss frequencies. As a consequence, the transfer functions of such filters are directly and easily defined by the assigned specifications