Electrical Network Functions of Common-Ground Uniform Passive RLC Ladders and Their Elmore’s Delay and Rise Times

Table 1

Delay and rise times of the point voltages in the considered common-ground, uniform RLC ladder.

n	0	1	2	3	4	5	6
𝑎1 [ms]	0.813	0.680	0.547	0.415	0.286	0.158	0
𝑎2 [μs]	0.323	0.225	0.145	0.082	0.037	0.010	0
𝑏1 [ms]	0.804	0.804	0.804	0.804	0.804	0.804	0.804
𝑏2 [μs]	0.315	0.315	0.315	0.315	0.315	0.315	0.315
𝑇𝐷 [ms]^1	Not applicable	0.124	0.257	0.388	0.518	0.647	0.804
𝑇𝑅 [ms]^1	Not applicable	0.157	0.200	0.229	0.250	0.286	0.326
𝑇𝐷𝑐 [ms]^2	Not applicable	0.115	0.257	0.395	0.528	0.658	0.817
𝑇𝑅𝑐 [ms]^2	Not applicable	0.190	0.252	0.295	0.324	0.349	0.373
𝑢𝑛(∞) [V]^3	5.999	2.999	1.498	0.747	0.370	0.178	0.075

1The times calculated according to Elmore's definitions.
²The times obtained through PSPICE simulation according to the classical definitions of 𝑇_𝐷𝑐 (“50%” delay time) and 𝑇_𝑅𝑐 (“10%–90%” rise time).
³All data are related to the ladder with zero initial conditions.