Recurrent neural networks (RNN) emerged as powerful tools to model and analyze the nonlinear behavior of electronic circuits accurately and quickly.Efforts to improve the accuracy of RNN will lead to the design of better-quality products, which is essential in various fields such as the design of energy harvesting (EH) systems. EH techniques can provide the electrical energy needed for low-power electronics without the need for a battery or with minimal dependency. Due to the importance of the active voltage balancing circuit in EH systems, we have proposed a new macromodeling method called dropout local-feedback deep recurrent neural network (Dropout-LFDRNN) to model and analyze this circuit along with two other nonlinear circuits asexamples. This technique is an advance over the LFDRNN macromodeling method, and based on the obtained results from the measurements, we were able to build a fast macromodel for the active balancing circuit, which outperforms conventional deep recurrent neural network modeling method in terms of accuracy without sacrificing speed. It is worth mentioning that this proposed technique in this paper can be considered a viable approach for modeling and analysis of nonlinear electronic components and circuits. In addition to the advantage of generating a more accurate model, the model based on the Dropout-LFDRNN approach is much faster than the existing transistor-level models.

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This paper proposes a hybrid approach combining Recurrent Neural Network (RNN) and polynomial regression methods for time-domain modeling of nonlinear circuits. The proposed hybrid RNNpolynomial regression (HRPR) method merges RNN and polynomial regression which leads to a significant reduction in training time while providing speedup in simulation compared to both conventional RNN and existing models in simulation tools without sacrificing accuracy. The proposed HRPR method comprises two steps: First, an RNN structure is generated, and then, the output of the RNN is combined with external input(s) of the circuit to perform a regression. Applying this method causes part of the training process to be done by polynomial regression which is simpler than training an RNN. Also, the RNN used in the HRPR method has a simpler structure than a single conventional RNN used for modeling the same component. To verify the validity of the proposed method, modeling and comparisons of three nonlinear examples are presented in this paper.INDEX TERMS Computer-aided design (CAD), recurrent neural network, polynomial regression, nonlinear components modeling, simulation.