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Abstract:The main idea of the present research is to propose a new memristor model with a highly nonlinear ionic drift suitable for computer simulations of titanium dioxide memristors for a large region of memristor voltages. For this purpose, a combination of the original Biolek window function and a weighted sinusoidal window function is applied. The new memristor model is based both on the Generalized Boundary Condition Memristor (GBCM) Model and on the Biolek model, but it has an improved property-an increased extent of nonlinearity of the ionic drift due to the additional weighted sinusoidal window function. The modified memristor model proposed here is compared with the Pickett memristor model, which is used here as a reference model. After that, the modified Biolek model is adjusted so that its basic relationships are made almost identical with these of the Pickett model. After several simulations of our new model, it is established that its behavior is similar to the realistic Pickett model but it operates without convergence problems and due to this, it is also appropriate for computer simulations. The modified memristor model proposed here is also compared with the Joglekar memristor model and several advantages of the new model are established.

A new design method for two-dimensional (2-D) recursive digital filters is investigated. The design of the 2-D filter is reduced to a constrained minimization problem the solution of which is achieved by the convergence of an appropriate neural network. The method is tested on a numerical example and compared with previously published methods when applied to the same example. Advantages of the proposed method over the existing ones are discussed as well.

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The investigation of new memory schemes is significant for future generations of electronic devices. The purpose of this research is to present a detailed analysis of the processes in the memory elements of a memory section with memristors and isolating Metal Oxide Semiconductor (MOS) transistors. For the present analysis, a modified window function previously proposed by the author in another memristor model is used. The applied model is based on physical nonlinear current-voltage and state-voltage characteristics. It is suitable for illustration of the processes in the memristors for both writing and reading procedures. The memory scheme is simulated using a nonlinear drift model with an improved window function. The used model was previously adjusted according to the reference Pickett model. The memory circuit is analyzed for writing and reading information procedures. The memristor current-voltage relationship is compared to physical experimental characteristics and to results acquired by the use of basic window functions. A satisfactory coincidence between the corresponding results is established. For the used logical signals, the memory elements operate in a state near to hard-switching mode. It is confirmed that the memristor model with a modified window function applied here is suitable for investigating complex memristor circuits for a general operating mode.