Maximum Gain Realization of an RC Ladder Network

This paper is concerned with the synthesis of the voltage transfer function of an unterminated RC ladder network. GivenA (p) = V_2/V_1 = K N(p)/D(p)the constraint onNandDis well known and the realization procedure is straightforward. However, for many applications, it is important to realize the maximum possible gain (K max) associated with a given transfer function. This paper presents a method of determiningKₘₐₓfrom the givenA(p). Furthermore, it is shown that if the maximum gain occurs at dc or at infinite frequency,Kₘₐₓcan be realized exactly. If the maximum gain occurs at a finite frequency,Kₘₐₓcan be approached arbitrarily closely.