Formulating hybrid equations and state equations for nonlinear circuits using SPICE

Abstract

SUMMARYHybrid equations are often used in the theoretical study of nonlinear resistive circuits because they have an easy-to-analyze structure. They are also advantageous in the numerical analysis of nonlinear resistive circuits because they are separable and consist of a relatively small number of variables. However, the hybrid equations are seldom used in practical applications because their formulation is complicated. In this letter, we propose a simple method for formulating the hybrid equations using SPICE. In the proposed method, we only perform the transient analysis of SPICE on a linear circuit that is obtained through a small modification to the original circuit. It is also shown that state equations for nonlinear dynamic circuits can also be formulated by using the proposed method.

Dynamic behavioral modeling of nonlinear circuits using a novel recurrent neural network technique

“…Although, it is possible to develop methods for modeling of nonlinear circuits using RNN consisting only global feedbacks, 13,[18][19][20][21][22][23][24][27][28][29]31 but there are major demerits for global feedbacks including slow convergence of learning. Although, it is possible to develop methods for modeling of nonlinear circuits using RNN consisting only global feedbacks, 13,[18][19][20][21][22][23][24][27][28][29]31 but there are major demerits for global feedbacks including slow convergence of learning.…”

“…There are several techniques for modeling nonlinear circuits: equivalent circuits, 13 model order reduction, [14][15][16] behavioral modeling, 17,18 statistical modeling approaches, 19 etc. [20][21][22][23] In equivalent circuit-based approaches, the device is converted to an equivalent circuit which has simpler circuit topology. Model order reduction approach is based on deriving reduced set of nonlinear differential equation from original circuit equation.…”

“…• Global feedback: These connections globally link up the outputs of the neural network to the input layer. Although, it is possible to develop methods for modeling of nonlinear circuits using RNN consisting only global feedbacks, 13,[18][19][20][21][22][23][24][27][28][29]31 but there are major demerits for global feedbacks including slow convergence of learning. • Local feedback: By employing specific kind of neurons, which have time-delayed feedbacks (proposed in this paper), it is possible to construct new RNN structure.…”

Caracterización de circuitos no lineales : análisis de modelos algebraico-diferenciales mediante la teoría de grafos

“…Consideremos el circuito de la Figura 4.1 [142]. Enél podemos observar dos diodos que asumiremos gobernados por sendas ecuaciones no lineales dependientes de la tensión de la forma i d 1 = g 1 (v d 1 ), i d 2 = g 2 (v d 2 ).…”

“…La suma de productos memresistivos, asociados a todos los bosques del menor resultante de contraer las ramas VC y eliminar las ramas IL, es distinta de cero.La suma de productos de capacidades asociadas a todos los bosques del menor normal de tipo C es distinta de cero.La suma de productos de inductancias asociadas a todos los cobosques del menor normal de tipo L es distinta de cero.4.6. Casos de estudioEn esta sección se ilustrará la caracterización delíndice en casos no lineales sin restricciones de pasividad utilizando algunos circuitos tomados de[142]. El objetivo es emplear ejemplos muy sencillos que permitan ilustrar fácilmente la aproximación estructural desarrollada en este capítulo, conforme a la cual la propiedad analítica central (elíndice) de los circuitos aquí considerados puede obtenerse en términos puramente topológicos, incluso sin necesidad de calcular explícitamente el modelo del circuito.…”