Novel method for the closed-form analysis and design of a 4 /sup th/ order single-amplifier filter

In this paper we present a new analytical design procedure for arbitrary-order, single-amplifier class-4 active-RC all-pole filters. It is already known that only 2/sup nd/ and 3/sup rd/ order filters can be designed analytically using classical design methods 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 is demonstrated in an example of the closed-form analysis and design of a special case of a 4/sup 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/sup th/ -order filter. The procedure used for the analysis is mainly not only of academic interest, but may have practical significance for special problems.