A novel method for the closed-form analysis and design of a 4 ^th-order single-amplifier filter

In this paper we present a new analytical design procedure for arbitrary-order, single-amplifier class-4 active-RC allpole filters. It is already known that only 2^nd- and 3^rd-order filters can be designed analytically using classical design methods [1] and the equations of higher order still defy a closed-form solution. The new design method parses the ladder network into consecutive L-sections, and makes use of their subsequent transfer functions that can be calculated iteratively. This will be demonstrated in an example of the closed-form analysis and design of a special case of a 4^th-order unity-gain LP filter. The Butterworth and Chebyshev approximations with pass-band ripple 0.1-0.2[dB] are considered. The resulting expressions provide insight into the feasibility of realizing a 4 ^th-order filter. The procedure used for the analysis is mainly not only of academic interest, but may have practical significance for special problems.