Analysis and Modeling of Energy Consumption in RLC Tree Circuits

Abstract

In this paper, the energy consumption of resistance-inductance-capacitance ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RLC</i> ) trees is analytically modeled. In particular, the results obtained by the same authors for <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RC</i> tree circuits are generalized, allowing for a deep understanding of the impact of the inductance. The modeling approach proposed relies on the adoption of an equivalent second-order <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RLC</i> circuit, whose energy consumption is evaluated in a closed form. These results are then extended to <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RLC</i> circuits with arbitrary order, deriving a simple and accurate model. The energy dependence on the input rise time is also analyzed in detail, identifying the ranges for which the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RLC</i> circuit can be approximated to a simple capacitance or an <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RC</i> circuit. The model equations provide an insight into the dependence of the energy consumption on the circuit parameters. Indeed, the energy is explicitly expressed as a function of the resistances, capacitances and inductances of the original network. The energy model proposed is shown to be accurate enough for modeling purposes through comparison with SPICE simulations, as the error is typically in the order of a few percentage points.