Dragos Niculae

Circuit analysis of frequency splitting phenomena in wireless power transfer systems

The paper treats the wireless power transfer systems with series-series resonators from the point of view of the frequency splitting and bifurcation phenomena. We develop an exact mathematical model of the splitting phenomena (splitting equation) based on the algebraic equation theory, which allows finding exact values of the splitting frequencies. This is extremely useful to setup the magnetic coupling for any connection of the wireless power transfer systems. It is also investigated the variation of the splitting frequencies and the transferred power peaks in function of the magnetic coupling. The exact analysis of the frequency bifurcation phenomena is also studied and the relationship between frequency bifurcation and splitting is elucidated. It is also found an exact mathematical procedure, based on the algebraic equation theory, which allows finding exact values of the bifurcation coupling and the bifurcations frequencies. The theoretical results are validated by numerical simulations based on frequency analysis with different values of the system parameters and by a 10-W prototype with planar spiral coils [10].

On wireless power transfer

The paper is a general survey on power transfer by induction. The physical principle is pointed out and the constraints for an optimal operation applied both to the emitter and receiver are specified. Couple mode theory is used to study the wireless power transfer and a comparison with the circuit theory results is made. The analysis is focused on the power transfer efficiency in connection with the mutual inductance. An accurate method for mutual inductance computation is presented and the power transfer optimization is performed for different geometrical configurations which involve different mutual inductances.

On exact circuit analysis of frequency splitting and bifurcation phenomena in wireless power transfer systems

The paper is focused on the exact analysis of the frequency splitting and bifurcation phenomena in the wireless power transfer (WPT) systems with series-parallel, parallel-series and parallel-parallel resonators. Starting from the analysis in sinusoidal behavior of a WPT system we build, using the algebraic equation theory, the exact splitting mathematical model for any connection of the WPT systems and whether this phenomenon exists or not. It is also investigated the exact analysis of the frequency bifurcation phenomena and the relationship between frequency bifurcation and splitting for all connections named before. In this way it is possible to find exactly the splitting and bifurcation couplings. The splitting and bifurcation frequencies and the load power peak curves are computed with respect to the constructive parameters of the system. Finally, the theoretical results are validated by numerical simulations.

On analog circuit parameter estimation

Our paper presents a new method to estimate the analog circuit parameters based on some measurements performed on the real circuit, the parameters of interest being those which are difficult or impossible to be measured directly. Starting from the equivalent scheme of an analog circuit in sinusoidal behavior, we generate the network function in full symbolic form, obtaining an appropriate frequency space representation based on the complex or Laplace modified nodal equations. The magnitude and the phase of the complex transfer function can be measured by supplying the circuit with a variable frequency sinusoidal voltage. Using the measured parameters as reference and the symbolic transfer function computed before, the model parameters of interest are obtained by an iterative identification algorithm based on Output Error method. In this paper are defined two new objective functions which can be minimized using one of the fminimax or fminunc functions from the Matlab toolbox. Both algorithms are based on iterative computation starting from certain initial values, being efficient for less than four estimated parameters. The algorithms are suitable for linear circuits, as well as for small-signal nonlinear circuits. Finally, the proposed estimation techniques were tested and validated on simulation data on an illustrative example.

A self and mutual inductance calculation resonators with finite element analysis

This paper presents how to implement the finite element method (FEM) to determine the magnetically coupled coils parameters. The method is applied for computing the parameters of the two resonators used in wireless power transfer (WPT). To compute the parameters corresponding to the resistance, self inductance, capacity and mutual inductance (R, L, C and M), we used CEDRAT Flux 2D software. The results of the 2D analyses are used to calculate the circuits parameters in order to compute the wireless power transferred to a load. Using FEM we realized two models: the first one in order to determine the values corresponding to L1, R1, L2, R2 and M and the second model to test its functioning in steady state. The two models differs by an electric circuit used to realize the coupling and the numerical models are modeled using the magnetic quasi-stationary state. The wireless power transfer efficiency depends on the coils shape which can play an important role in the operation of such devices.

Comparative study of the frequency splitting and bifurcation phenomena for equivalent circuits of the wireless power transfer system

This paper presents a study of the frequency splitting and bifurcation phenomena in the wireless power transfer systems. Using electric circuit model methods and mathematical calculus, the two phenomena are analyzed for all the possible configurations of the coupled circuits, i.e. seriesseries, series-parallel, parallel-series and parallel-parallel. For a specific case including two identical printed coils, for each configuration some characteristics are represented graphically and the appearance of each phenomenon is commented. The analytical results and the numerical simulations are correlated and commented comparatively, in order to obtain useful conclusions.

Circuit Analyses with Nullors

This chapter describes the nullor-based modelling of active devices from the circuit level of abstraction. After a brief overview on the nullor concept and its properties, the modelling of active devices not only at the voltage-mode but also at the current-mode and the mixed-mode of operation from two-port and four-terminal network point of view are described in details. The circuit analysis with nullors and the topological approach for transfer function generation by two-graph tree enumeration as well are presented. The generalized topological formula with homogeneous parameters is proved for all the circuit functions, and a simple representation of the four types of controlled sources by admittances is proposed, that allows a uniform treatment of the entire circuit in terms of admittances. In order to implement the procedure, the rules to automatically generate the two graphs and to enumerate the common spanning trees are presented. Some simplifications in the circuit and in the two graph structure before tree generation and a graph representation on levels, improve the efficiency of the tree enumeration procedure. The original approach, in which each edge is labelled with an admittance term, could handle only one type of active element, namely VCCS (voltage controlled current source), but the method was further developed by many researchers for general linear circuits to include virtually all active elements. Some techniques to convert the CCVSs (current controlled voltage sources), VCVSs (voltage controlled voltage sources) and CCCSs (current controlled current sources) in equivalent schemes containing only VCCSs together with admittances and the inductance modelling proposed in the literature are discussed.

The use of S parameters in wireless power transfer system stability

In this paper a series of constants, corresponding to wireless power transfer system (WPTS), are defined, function of S parameters. These constants will be further used for stability factors computation in WPTS. To generate: the reflection coefficients, the standing wave ratio (SWR), the input and output impedances, the input and output active power transmission efficiency, the signal transmission efficiency, the power gains, the various stability coefficients, the centers and radius corresponding to stability circles from the source and from the generator, the S, T, Z and Y matrices and the Smith charts, we developed dedicated functions by using existing routines from the MATLAB Microwave toolbox. The results obtained by simulations were compared to those existing in literature and with experimental ones.

Using S parameters in wireless power transfer analysis

This paper presents the correct formulation of scattering parameters S, using electric circuit theory, and the practical use of these parameters. The purpose is to make more efficient the processes for the information transmission and the wireless electromagnetic energy transfer. The efficiency is seen from the transmission point of view of the signals (from the transmitter to receiver) and from the active power transfer efficiency point of view (from the wireless systems input to the loads connected at their outputs). Starting from the correct formulation of S parameters, their computation takes place automatically based either on state equations or on modified nodal equations of the wireless power transfer systems (WPTS). The two magnetically coupled coils, considered as a passive linear 2-port network in harmonic regime, can be described by a number of equivalent circuits parameters, such as: the transfer coefficients matrix T, the impedance matrix Z, the admittance matrix Y and the matrix corresponding to S parameters. This paper presents the relationships that allow the transition from one matrix to another. To generate: the coefficients corresponding to reflection, the input and output impedances, the input-output (output-input) active power transmission efficiencies, the signal transmission efficiencies, the S, H T, Z and Y matrices, and the Smith charts, we elaborated MATLAB dedicated functions by using the existing routines form the Microwave MATLAB toolbox.

Switched networks analysis with inconsistent initial conditions

Switched networks modelling lead very often to discontinuities of circuits variables corresponding to switching time moments. This phenomenon is said to have inconsistent initial conditions (IIC). The IIC problem appears only for ideal switches in ideal circuits when, after switching, the circuit contains excess elements. As a consequence, Dirac delta functions and their derivatives can occur in the circuits variables variations which are proportional with the discontinuous variables derivatives. This paper presents a very precise method for analyzing the dynamic circuits with IIC, method which has the advantage given by its simplicity. This approach is based on modified nodal method, modelling the ideal switches using time variable resistors. The described algorithm has been implemented in the general program for real switched networks rapid analysis.