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Distributed power supply (DPS) systems are extensively used to supply different electronic equipment and systems such as telecom switching systems. Continuous reduction of supply voltages of digital integrated circuits from the previous industry standard of 5 V down to 1 V or even less has necessitated the use of point-of-load system architectures due to high supply currents. The input currents of the switched-mode power supplies contain typically high ripple currents necessitating the use of noise suppression (EMI) filters to meet the stringent requirements stipulated by international standards. The interactions between the load converters, EMI filters, and supply side converters may adversely affect the stability and performance of the system. The system analysis is typically made based on the behavior of the ratio between the output impedance of the supply side and the input impedance of the load side known as minor-loop gain. Certain forbidden regions in the complex plane have been developed out of which the minor-loop gain should stay in order to guarantee stability. Even if the restrictions for the behavior of the minor-loop gain are well-defined, the accurate prediction of the associated impedances is difficult or even impossible. We propose, in this paper, a method based on input invariance to cancel the load-side interactions in the small-signal sense. The only concern left is then the stability of EMI filters, which may be considered based on the input power of the associated converters.

Switch-mode power supplies usually emit electromagnetic interferences at the switching frequency and its harmonics. Inducing chaos in these systems has recently been suggested as a means of reducing these spectral emissions, yet at the expense of aggravating the overall magnitude of the ripple in the output voltage. We propose here a new nonlinear feedback control method, which induces chaos, and which is able at the same time to achieve low spectral emission and to maintain a small ripple in the output. The feasibility and usefulness of this new and simple method is shown here with a numerical example, which includes a comparison with the previous control method.

The bifurcation phenomena occurring in a current mode controlled buck converter when it shifts from continuous conduction mode (CCM) to discontinuous conduction mode (DCM) have been reported. A sampled data model has been developed considering CCM as well as DCM. The bifurcation phenomena observed in such converters have been verified experimentally.

This paper proposes the idea of mathematical modeling of the buck converter. The modified approach is achieved through the relay feedback (RF) method and the changes are introduced on the converter output with a soft start. Mathematical modeling of the buck converter is achieved by the state-space model (SSM) and converter’s transfer function (TF) to attain stability. By iteration, the proportional-integral (PI) parameters are tuned by a controller that is incorporated in the RF. The output voltage changes are introduced by maintaining the relay-tuned PI control. The concept requires small tuning times which is obtained at a reduced cost. The effectiveness of buck converter using RF is validated in simulation and hardware.

In this paper, an improved voltage-mode constant on-time (COT) control DC–DC buck converter is designed, which makes the DC–DC buck converter have good stability. Firstly, an improved compensation scheme is introduced through the analysis and derivation of the traditional voltage-mode COT controlled buck converter model. Then, according to the application requirements of the design, Simplis software modeling is used to verify the correctness of the theoretical analysis. The 0.13$\mu$m BCD technology is used to tape out the DC–DC converter of the improved voltage mode COT. The input voltage is 3.7–5.5V and the output voltage is 3.3V. The chip test mainly includes heavy-load condition in CCM operation, light-load condition in DCM operation, and load transient response. The test results show that the chip can remain stable under heavy-load and light-load conditions. The overshoot and undershoot in transient response can be quickly restored to steady state during the recovery process. Finally, compared with chips of the same type, it shows that the DC–DC chip for portable electronic equipment designed in this paper adopts an internal compensation structure, which has good stability, simple design, small main chip area, simple peripheral equipment, and good application value.

There are cases in energy supply applications with low-power batteries, where the power required by the load is larger than the supply maximum deliverable power. Using a capacitor to create a high instantaneous power for the load was investigated as a useful solution. To increase the charging efficiency, a stepwise method for charging the capacitor was employed. This paper presents a new pulsed power supply approach in which the charging process is resumed after high instantaneous power delivery. Through this, the loss of residual energy in the capacitor was decreased and load turn-on speed and energy efficiency were significantly improved. The proposed structure consists of a buck converter that charges the capacitor using inductor current. A pulse frequency modulation (PFM) technique was used to generate the necessary signals for the buck converter switches, which resulted in controlling the inductor current. The proposed circuit was designed and simulated in a 0.18 $\mu$m CMOS technology. It was shown that the designed CMOS circuit could reach a peak energy efficiency of 93.2% with a sleep period of 1.05 ms when the load consumes 7.06 $\mu$J of energy.

Using the QR decomposition of the tangent map, we explicitly write the differential equations satisfied by the Lyapunov exponents of a two-dimensional bilinear system, and specialize them to the buck converter in continuous current mode. These equations are solved numerically for an arbitrary value of the bifurcation parameter, and analytically for periodic orbits, recovering for the later results already known from the computation of Floquet exponents.

Zero Average Dynamics (ZAD) control strategy has been developed, applied and widely analyzed in the last decade. Numerous and interesting phenomena have been studied in systems controlled by ZAD strategy. In particular, the ZAD-controlled buck converter has been a source of nonlinear and nonsmooth phenomena, such as period-doubling, merging bands, period-doubling bands, torus destruction, fractal basins of attraction or codimension-2 bifurcations. In this paper, we report a new bifurcation scenario found inside band-merging scenario of ZAD-controlled buck converter. We use a novel qualitative framework named Dynamic Linkcounter (DLC) approach to characterize chaotic attractors between consecutive crisis bifurcations. This approach complements the results that can be obtained with Bandcounter approaches. Self-similar substructures denoted as Complex Dynamic Links (CDLs) are distinguished in multiband chaotic attractors. Geometrical changes in multiband chaotic attractors are detected when the control parameter of ZAD strategy is varied between two consecutive crisis bifurcations. Linkcount subtracting staircases are defined inside band-merging scenario.

In this paper, instabilities and bifurcation behavior in a DC–DC digitally controlled voltage-mode synchronous buck converter (SBC) are studied. The bifurcation diagram of the system under a proportional-integral (PI) compensation is presented. Following the system mathematical description in the continuous time domain, the z-domain pulse transfer function is derived in terms of system parameters. The stability range of the design parameter is obtained in closed form by using the Jury test combined with the describing function (DF) method. Experimental measurements from a laboratory prototype are used to validate the theoretical predictions and the numerical simulations.

In this paper, we study the chaotic dynamics of a voltage-mode controlled buck converter, which is typically a switched piecewise linear system. For the two-dimensional hybrid system, we consider a properly chosen cross-section and the corresponding Poincaré map, and show that the dynamics of the system is semi-conjugate to a 2-shift map, which implies the chaotic behavior of this system. The essential tool is a topological horseshoe theory and numerical method.

The paper includes a novel approach for filtering of nonlinear Buck converter with Constant Power Load in noisy environment based on the Carleman linearization approach. The procedure starts with the modeling of Buck converter with Constant Power Load using Hamiltonian framework resulting in the deterministic model of network i.e., a finite dimensional system of ordinary differential equations. To evaluate the effect of noise on it, a Gaussian noise is embedded in the network through switch, which results in the development of stochastic state model and noise present at measurement terminals is considered for measurement equations. Using Carleman linearization approach, the finite-dimensional nonlinear model is transmuted into a bilinear model of infinite-dimension which can be approximated for any chosen order. As a result, we arrive at the finite-dimensional bilinear model of Buck converter with augmented state vector of higher dimension than the original system. State estimation of stochastic dynamical systems in the presence of noisy measurements is an interesting problem and hence, filtering technique is adopted here. The filtering equations in Itô setting are derived for bilinear systems using probabilistic approach for state estimation. The superiority of the proposed bilinear filtering technique over the benchmark EKF is demonstrated by the numerical simulations.

Sneak circuits in DCM Buck converter with parasitic parameters are investigated in this paper. Comparing with the DCM Buck converter without parasitic parameters, the operating modes increase from three to five in a switching period, which two additional modes are sneak circuits, and they appear under certain conditions. Operational conditions of the sneak circuits are conducted according to state equations of modes. Compared with the DCM Buck converter without parasitic parameters, the output performance of the converter is variated. The theoretical analyses are verified by the simulation results and experimental results.

In this paper, an analytical tuning method of the fractional order PI^λ controller for feedback control system is proposed, it can make the closed loop system with PI^λ controller be equivalent to an expected model, whose transfer function satisfy the Bode’s ideal function, and make the closed loop system have good gain robustness. Then, the Taylor Maclaurin series expansion is applied to the parameters tuning of the PI^λ controller, the PI^λ controller parameters are derived analytically in this paper. Finally, Buck converter with PI^λ controller is used as an application example, the simulation results verify the correctness and effectiveness of the proposed analytical parameter tuning method.

In this paper the study of complex phenomenon in buck converter under voltage mode control, operating in discontinious current mode, within Matlab/Simulink simulation environments is provided. To perform simulations different types of models are used: based on discrete-time maps, differential equations and real elements (including different nonidealities). The main goal of this paper is to detect the ability of various Matlab/Simulink models to identify and to explore different types of complex behaviour, such as chaos and bifurcataions, in switch-mode DC-DC converters, as system parameters are changed, as well as to estalish the possibilities of each model in this kind of investigation. Simulations are carried out by means of Matlab/Simulink simulation environment that provides wide range of blocks and elements for complete investigation procedure, including the implementation of all types of mentioned models and appropriate result data postprocessing and visualization. The verification of accuracy of developed models is based on the detection of Feigenbaum numbers. All models with definite level of precision are able to reveal that under certain circuit parameters period doubling route to chaos is observed.