This paper is concerned with the synthesis of the voltage transfer function of an unterminated RC ladder network. Given

the constraint on

and

is well known and the realization procedure is straightforward. However, for many applications, it is important to realize the maximum possible gain (

) associated with a given transfer function. This paper presents a method of determining

from the given

. Furthermore, it is shown that if the maximum gain occurs at dc or at infinite frequency,

can be realized exactly. If the maximum gain occurs at a finite frequency,

can be approached arbitrarily closely.