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

In the paper are presented the expressions for all network functions of common-ground, uniform passive ladders having, in general, complex terminations at both their ends. The Elmore's delay and rise times calculated for selected types of RLC ladders have indicated their slight deviation from delay and rise times obtained according to their classical definitions. For common-ground, integrating type RC ladder with voltage-step input, the Elmore's delay- and rise-times are produced in closed-form, both for ladder nodes and points. Furthermore, it is proposed a particular common-ground, uniform RLC ladder being amenable to application as delay line for pulsed and analog input signals. For this ladder, the Elmore's delay and rise times relating to their node voltages are produced in a closed-form, enabling thus with the realization of artificial (a) pulse delay line with arbitrarily and independently specified overall Elmore's delay and rise times and (b) true delay line with arbitrarily specified delay time for frequency bounded analog and/or pulsed input signals. In cases (a) and (b), precise procedures are formulated for calculation of ladder length and of all its RLC parameters. The obtained results are illustrated with several practical examples and are, also, verified through pspice simulation.