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This paper aims to analyze the frequency characteristics of wireless power transfer (WPT) systems with relay resonators in terms of the power delivered to the load and system efficiency. Based on the analytical results, system parameters can be optimized to achieve maximum power transfer and higher system efficiency.

Based on Kirchhoff’s voltage law equations, WPT systems with relay resonators are described by the coupled linear second-order differential equations. Splitting frequencies are estimated by using the matrix theory. In addition, critical coupling conditions are demonstrated based on discriminant analysis.

It was found that multi-maximum values exist for the power delivered to the load and total system efficiency owing to multiple eigenfrequencies of the system. Also, frequency conditions of maximum power transfer and system efficiency, as well as their critical coupling conditions, were quantitatively estimated.

During our analytical process, we assume that quality factors of resonators in the system are high and the crossing coupling between resonators is negligible.

In previous works, the exact analysis of frequency characteristics is limited to WPT systems with two resonators. The appealing feature of this work lies in its ability to present a simplified analytical method with negligible approximation errors for WPT systems with relay resonators.

Electric spring (ES) is a demand response method that can stabilize the voltage of critical loads and improve power quality, especially in a weak power grid with a high proportion of renewable energy sources. Most of existing ESs are implemented by voltage-source inverter (VSI), which has some shortcomings. For example, the DC-link capacitor limits the service life of ES, and the battery is costly and hard to recycle. Besides, conventional VSI cannot boost the voltage, which limits the application of ES in high-voltage occasions. This study aims to propose a novel scheme of ES to solve the above problems.

In this work, an ES topology based on current-source inverter (CSI) without a battery is presented, and a direct current control strategy is proposed. The operating principles, voltage regulation range and parameter design of the proposed ES are discussed in detail.

The proposed ES is applicable to various voltage levels, and the harmonics are effectively suppressed, which have been validated via the experimental results in both ideal and distorted grid conditions.

An ES topology based on battery-less CSI is proposed for the first time, which reduces the cost and prolongs the service time of ES. A novel control strategy is proposed to realize the functions of voltage regulation and harmonic suppression.

This study aims to predict the unstable period-1 orbit (UPO-1) of DC–DC converters and find analytical expressions to describe it.

Nonlinear dynamical phenomena of a peak–current–mode controlled direct current–direct current (DC–DC) Boost converter are discussed briefly first. Then fast fourier transform (FFT) analysis of state variables under different dynamic states is provided, and the characteristic of the harmonic content in different states is summarized. Following these, a scientific hypothesis on the harmonic content of the UPO-1 is presented, and the Equivalent Small Parameter method is adopted then, thus analytic-form expressions of the UPO-1 can be derived.

According to results of theoretical analysis, numerical simulations and experiments, this paper illustrates that, like stable period-1 orbit, the UPO-1 is also made up of the DC component and harmonics with integer times of switching frequency.

This work provides an unreported approach for extracting the UPO-1 of DC–DC converters, which is mainly based on predicting the harmonic structure information of the orbit. According to experimental parts of the work, it shows that the stabilizer can be designed easier by using the proposed method. Additionally, from a broader perspective, the results could also have implications in a wide class of forced oscillation systems.

This paper aims to present a simplified method to analyze the transient characteristics of a fractional-order very high frequency (VHF) resonant boost converter. The transient analytical solutions of state variables obtained by this method could be used as a guide for parameter design and circuit optimization.

The VHF converter is decoupled into a simplified equivalent circuit model and described by the differential equation. The solution of the simplified equivalent circuit model is taken as the main oscillation component of the transient state variable. And the equivalent small parameter method (ESPM) and Kalman filter technology are used to solve the differential equation of the converter to obtain the steady-state ripple component. Then, by superimposing the abovementioned two parts, the approximate transient analytical solution can be acquired. Finally, the influence of the fractional order of the energy storage elements on the transient process of the converter is discussed.

The results from the proposed method agree well with those from simulations, which indicates that the proposed method can effectively analyze the transient characteristic of the fractional-order VHF converter, and the analytical solution derived from the proposed mathematical model shows sufficient accuracy.

This paper proposes for the first time a method to analyze the transient characteristics of a fractional-order VHF resonant boost converter. By combining the main oscillated solution derived from the simplified equivalent circuit model with the steady-state solution based on ESPM, this method can greatly reduce the computation amount to estimate the transient solution. In addition, the discussion on the order of fractional calculus of energy storage components can provide an auxiliary guidance for the selection of circuit parameters and the study of stability.

The purpose of this paper is to find a simpler model for the reactance components in the high-frequency range on the premise of ensuring the accuracy.

In this paper, based on the fractional calculus theory and the traditional integer-order model, a reactance model suitable for high frequency is constructed, and the mutation cross differential evolution algorithm is used to identify the parameters in the model.

By comparing the integer-order model, high-frequency fractional-order model and the actual impedance characteristic curve of inductance and capacitance, it is verified that the proposed model can more accurately reflect the high-frequency characteristics of inductance and capacitance. The simulation and experimental results show that the oscillator constructed based on the proposed model can analyze the frequency and output waveform of the oscillator more accurately.

The model proposed in this paper has a simple structure and contains only two parameters to be identified. At the same time, the model has high precision. The fitting errors of impedance curve and phase-frequency characteristic curve are less than 5%. Therefore, the proposed model is helpful to improve the simplicity and accuracy of circuit system analysis and design.

By investigating the thermal-mechanical interaction between the through silicon via (TSV) and the Cu pad, this study aimed to determine the effect of electroplating defects on the upper surface protrusion and internal stress distribution of the TSV at various temperatures and to provide guidelines for the positioning of TSVs and the optimization of the electroplating process.

A simplified model that consisted of a TSV (100 µm in diameter and 300 µm in height), a covering Cu pad (2 µm thick) and an internal drop-like electroplating defect (which had various dimensions and locations) was developed. The surface overall deformation and stress distribution of these models under various thermal conditions were analyzed and compared.

The Cu pad could barely suppress the upper surface protrusion of the TSV if the temperature was below 250 ?. Interfacial delamination started at the collar of the TSV at about 250 ? and became increasingly pronounced at higher temperatures. The electroplating defect constantly experienced the highest level of strain and stress during the temperature increase, despite its geometry or location. But as its radius expanded or its distance to the upper surface increased, the overall deformation of the upper surface and the stress concentration at the collar of the TSV showed a downward trend.

Previous studies have not examined the influence of the electroplating void on the thermal behavior of the TSV. However, with the proposed methodology, the strain and stress distribution of the TSV under different conditions in terms of temperature, dimension and location of the electroplating void were thoroughly investigated, which might be beneficial to the positioning of TSVs and the optimization of the electroplating process.