# Behavioral Modeling of Memristor-Based Rectifier Bridge
## 1 Introduction
In the latter case, the application of the device's behavioral model leads to simpler representations of constructions composed of many different devices. A behavioral model approximates an operator that uniquely maps the domain of the input signals into the domain of the output signals of a nonlinear dynamic system [31; 32; 33; 34]. As a rule, the approximation problem is solved in the mean-square norm on building universal mathematical models. Among behavioral models, we can distinguish the Volterra series [31; 32; 33; 34], multi-dimensional split polynomial [35; 36; 37; 38], numerous structures of regression models [39; 40] and neural networks [41]. Multi-dimensional split polynomial is worth highlighting. This model obtains unique global optimum parameters resulting from approximating the operator of a nonlinear dynamic system in the mean-square norm that is superior to neural networks when we determine a lot of local optimum parameters. The structure of multi-dimensional split polynomial depends on a specific type of the input signal, therefore, this model is less universal but simpler in comparison with the Volterra polynomial. The model simplicity is preferable for the model implementation. Moreover, a feedforward structure of split polynomial is independent of keeping stable regime that is characteristic of feedback mostly relevant to regression models. Thus, multi-dimensional split polynomial has advantages over other mentioned models, which ensure its success in modeling of nonlinear dynamic systems including different memristor-based devices. In this paper, multi-dimensional split polynomial is represented for modeling a rectifying memristor bridge. A rectifier bridge (the Graetz circuit, full-wave rectifier) is a popular device in electrotechnical and radio engineering. Generally, it is an intermediate circuit for converting alternating current (AC) signals into direct current (DC) signals. Modern electronics is mainly using DC voltage for operation, but the energy distribution network works on AC voltage. A diode rectifier feeding an ohmic-capacitive load is the input stage of many devices, which are connected to the distribution grid, such as battery chargers (including those for electric vehicles), computers, household appliances and many others [42]. A rectifier bridge can operate as a passive circuit using diodes or as an active circuit using bipolar junction transistors (BJTs) or field effect transistors (FETs). In any of these cases the current flow on the AC side is non-linear which causes higher order current harmonics. For mains powered devices the magnitude of these harmonics is to be limited [42]. An additional power factor correction (PFC) circuit is needed. The utilization of memristors instead of diodes for the rectifier bridge is a new investigation trend. Due to the nature of a physically realized memristor it is not yet usable for power electronic applications. In order to get an unidirectional valve effect for the current, as it is the case for the rectifier diode, a bipolar switching memristor is required and the operating frequency needs to be in the lower Hertz region [43; 44]. For low power applications the memristor-based rectifier bridge can be used in synapse-based neural networks with programmable synaptic weights [45; 46]. Another application is image processing; by adding a capacitor at the output of the memristive bridge embodies a low-pass filter with time-varying cut-off frequency and transfer function [47]. Thus, the use of memristors in the well-known Graetz circuit essentially expands its application. For investigation of memristor-based devices, both empirical models adapted from the ideal memristor model and models based on physical considerations [48; 49; 50; 51; 52; 53] play an important role.