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

This paper presents a parameterization theory of balanced truncation method (BTM) for any evenly distributed RC interconnect and transmission lines and their BTM reduction models. The parameterization theory shows that any evenly distributed RC line circuits of the 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, any time responses and the Bode plots of their BTM reduction models are also the same as the ones of the prototype BTM reduction models, respectively. The simulations demonstrate the theory. The reduction model order can be identified by the prototype model. The new results can be applied to not only the model reduction of interconnects or transmission lines, but also control systems with transmission lines, networks, or time delay units.