Continuous gain adjustment of RC low-pass ladder networks through congruent transformation

Through a simple congruent transformation, it is shown that the open-circuit voltage gain of a given RC low-pass ladder network can be continuously and exactly adjusted to a desired value within the upper and lower bounds while at the same time keeping the driving point impedance invariant. It is also observed that the network of minimum gain corresponds to minimum total resistance, and the maximum gain realization results in the minimum total capacitance.