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. Given
A (p) = \frac{V_2}{V_1} = K \frac{N(p)}{D(p)}
the constraint on
N
and
D
is 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 determining
K_{\max}
from the given
A(p)
. Furthermore, it is shown that if the maximum gain occurs at dc or at infinite frequency,
K_{\max}
can be realized exactly. If the maximum gain occurs at a finite frequency,
K_{\max}
can be approached arbitrarily closely.