Generalized Wave Digital Filter Realizations of Arbitrary Reciprocal Connection Networks

In this paper, an existing approach for modeling and efficiently implementing arbitrary reciprocal connection networks using wave digital (WD) scattering junctions based on voltage waves is extended to be used in a broader class of WD filters (WDFs) based on different kinds of waves. A generalized wave definition which includes traditional voltage waves, current waves, and power-normalized waves as particular cases is employed. Closed-form formulas for computing the scattering matrices of the junctions are provided. Moreover, the approach is also extended to the family of Biparametric WDFs, which have been recently introduced in the literature

advances in wave digital modeling of linear and nonlinear systems a summary

This brief summarizes some of the main research results that I obtained during the three years, ranging from November 2015 to October 2018, as a Ph.D. student at Politecnico di Milano under the supervision of Professor Augusto Sarti, and that are contained in my doctoral dissertation, entitled "Advances in Wave Digital Modeling of Linear and Nonlinear Systems". The thesis provides contributions to all the main aspects of Wave Digital (WD) modeling of lumped systems: it introduces generalized definitions of wave variables; it presents novel WD models of one- and multi-port linear and nonlinear circuit elements; it discusses systematic techniques for the WD implementation of arbitrary connection networks and it describes a novel iterative method for the implementation of circuits with multiple nonlinear elements. Though WD methods usually focus on the discrete-time implementation of analog audio circuits; the methodologies addressed in the thesis are general enough as to be applicable to whatever system that can be described by an equivalent electric circuit

Digital Filters

The new technology advances provide that a great number of system signals can be easily measured with a low cost. The main problem is that usually only a fraction of the signal is useful for different purposes, for example maintenance, DVD-recorders, computers, electric/electronic circuits, econometric, optimization, etc. Digital filters are the most versatile, practical and effective methods for extracting the information necessary from the signal. They can be dynamic, so they can be automatically or manually adjusted to the external and internal conditions. Presented in this book are the most advanced digital filters including different case studies and the most relevant literature

Analog Implementation of Fractional-Order Elements and Their Applications

With advancements in the theory of fractional calculus and also with widespread engineering application of fractional-order systems, analog implementation of fractional-order integrators and differentiators have received considerable attention. This is due to the fact that this powerful mathematical tool allows us to describe and model a real-world phenomenon more accurately than via classical “integer” methods. Moreover, their additional degree of freedom allows researchers to design accurate and more robust systems that would be impractical or impossible to implement with conventional capacitors. Throughout this thesis, a wide range of problems associated with analog circuit design of fractional-order systems are covered: passive component optimization of resistive-capacitive and resistive-inductive type fractional-order elements, realization of active fractional-order capacitors (FOCs), analog implementation of fractional-order integrators, robust fractional-order proportional-integral control design, investigation of different materials for FOC fabrication having ultra-wide frequency band, low phase error, possible low- and high-frequency realization of fractional-order oscillators in analog domain, mathematical and experimental study of solid-state FOCs in series-, parallel- and interconnected circuit networks. Consequently, the proposed approaches in this thesis are important considerations in beyond the future studies of fractional dynamic systems

Wave-Based Analysis of Large Nonlinear Photovoltaic Arrays

In this paper, a novel analysis method based on wave digital (WD) principles is presented. The method is employed for modeling and efficiently simulating large photovoltaic (PV) arrays under partial shading conditions. The WD method allows rapid exploration of the current-voltage curve at the load of the PV array, given: the irradiation pattern, the nonlinear PV unit model (e.g., exponential junction model with bypass diode) and the corresponding parameters. The maximum power point can therefore easily be deduced. The main features of the proposed method are the use of a scattering matrix that is able to incorporate any PV array topology and the adoption of independent 1-D nonlinear solvers to handle the constitutive equations of PV units. It is shown that the WD method can be considered as an iterative relaxation method that always converges to the PV array solution. Rigorous proof of convergence and results about the speed of convergence are provided. Compared with standard spice-like simulators, the WD method results to be 35 times faster for PV arrays made of some thousands elements. This paves the way to possible implementations of the method in specialized hardware/software for the real time control and optimization of complex PV plants