Parameterization theory of balanced truncation method for any evenly distributed RC interconnect circuits

This paper presents a parameterization theory of balanced truncation method (BTM) for any evenly distributed RC interconnect (or transmission) lines and their BTM reduction models. The parameterization theory shows that any evenly distributed RC interconnect line circuits of a same order have the same balanced gramian, BTM error upper-bound, and BTM approximation error, which are independent of their RC parameters. Thus, the prototype model is proposed for research to dramatically reduce the computations for various RC parameters. Under normalized (scaled) time axis and frequency axis, the step responses and Bode plots of their BTM reduction models are also the same as ones of the prototype BTM reduction models, respectively. The simulations demonstrate and validate the theory. The reduction model order can be identified by the prototype model. The new results can be applied to not only the interconnect model reduction, but also control systems with transmission lines, Internet or time delay units. Moreover, it may open a new approach for research on time delay systems by using RC interconnect block to substitute some time delay blocks for analysis.