A note on transfer and driving-point functions of iterated ladder networks

A sequence of identical, linear, nonreciprocal processes is equivalent to a ladder network comprising reciprocal elements whose values increase in geometric progression. Thus the ladder with geometric progression is a generalization of the usual iterated ladder network. Simple formulas are derived for the transfer and driving point functions of such ladders. In the special case of the iterated ladder with reciprocal elements, these formulas are simplified even further; and it is shown that the factors
(ZY + 1)
,
(ZY + 2)
, and
(ZY + 3)
recur periodically in the numerators and denominators of the network functions as the number of stages is increased.