Fast Switching Limit Research Articles

Stochastic switching of delayed feedback suppresses oscillations in genetic regulatory systems.

Delays and stochasticity have both served as crucially valuable ingredients in mathematical descriptions of control, physical and biological systems. In this work, we investigate how explicitly dynamical stochasticity in delays modulates the effect of delayed feedback. To do so, we consider a hybrid model where stochastic delays evolve by a continuous-time Markov chain, and between switching events, the system of interest evolves via a deterministic delay equation. Our main contribution is the calculation of an effective delay equation in the fast switching limit. This effective equation maintains the influence of all subsystem delays and cannot be replaced with a single effective delay. To illustrate the relevance of this calculation, we investigate a simple model of stochastically switching delayed feedback motivated by gene regulation. We show that sufficiently fast switching between two oscillatory subsystems can yield stable dynamics.

A −31.7 dBm Sensitivity 0.011 mm2 CMOS On-Chip Rectifier for Microwave Wireless Power Transfer

This paper pursued both the lower operating power limit and small area of on-chip rectifiers for microwave wireless power transfer (MWPT). RF–DC charge pump rectifiers can operate in the fast switching limit at a high frequency of 920 MHz even with a small stage capacitor Cin of 100 fF, which contributes to an area reduction in the on-chip rectifiers. Circuit design starts with Cin determined as small as possible, followed by the determination of switching transistors and the number of stages. Even at an extremely low input power of 1 μW, wiring resistance in RF inputs is critical. Routing of the RF inputs is designed in line with stage capacitors. Bonding pad structure also affects the lower input power limit. Ground-shielded pad design can reduce the lower limit. Various types of RF–DC charge pump rectifiers are fabricated in 65 nm CMOS. An ultra-low-power diode RF–DC charge pump rectifier with 32 stages had a lower input power limit of −31.7 dBm at an output voltage of 1.0 V. Its small silicon area of 0.011 mm2 allows RF–DC rectifiers to be integrated in sensor ICs. More advanced technology providing MIM capacitors with higher capacitance density and placing switching MOSFETs under the MIM capacitors will further reduce the area of RF–DC charge pump rectifiers, allowing them to be integrated in sensor ICs.

Violation of the Second Fluctuation-dissipation Relation and Entropy Production in Nonequilibrium Medium

We investigate a class of nonequilibrium media described by Langevin dynamics that satisfies the local detailed balance. For the effective dynamics of a probe immersed in the medium, we derive an inequality that bounds the violation of the second fluctuation-dissipation relation (FDR). We also discuss the validity of the effective dynamics. In particular, we show that the effective dynamics obtained from nonequilibrium linear response theory is consistent with that obtained from a singular perturbation method. As an example of these results, we propose a simple model for a nonequilibrium medium in which the particles are subjected to potentials that switch stochastically. For this model, we show that the second FDR is recovered in the fast switching limit, although the particles are out of equilibrium.

A Resistor-Network Model of Dickson Charge Pump Using Steady-State Analysis

This paper presents a new average behavioral model, named a resistor-network (RN) model, that accurately predicts the electrical characteristics of the Dickson charge pump (DCP) circuit in the slow-switching limit and the fast-switching limit regions based on steady-state analysis. The RN model describes the steady-state behavior of a single-stage DCP using a network of resistors, which can then be cascaded to model N-stage DCP, taking into account the top- and bottom-plate parasitic capacitances. The RN model provides a comprehensive insight into various design parameters of the DCP, including the input/output current, output voltage, load characteristics, losses caused by parasitics, and power efficiency. Simulation results show that the proposed RN model accurately predicts the output voltage and power efficiency of the DCP over a wide range of switching frequencies, from 0.1 Hz to 1 GHz, with an error of less than 2% at the maximum power efficiency. The RN model provides designers with a simple and effective model to design DCP quickly and efficiently for a broad spectrum of applications, including energy harvesting and flash memory applications.

Occupation time of a run-and-tumble particle with resetting.

We study the positive occupation time of a run-and-tumble particle (RTP) subject to stochastic resetting. Under the resetting protocol, the position of the particle is reset to the origin at a random sequence of times generated by a Poisson process with rate r. The velocity state is reset to ±v with fixed probabilities ρ_{1} and ρ_{-1}=1-ρ_{1}, where v is the speed. We exploit the fact that the moment-generating functions with and without resetting are related by a renewal equation, and the latter generating function can be calculated by solving a corresponding Feynman-Kac equation. This allows us to numerically locate in Laplace space the largest real pole of the moment-generating function with resetting, and thus derive a large deviation principle (LDP) for the occupation time probability density using the Gartner-Ellis theorem. We explore how the LDP depends on the switching rate α of the velocity state, the resetting rate r, and the probability ρ_{1}. First, we show that the corresponding LDP for a Brownian particle with resetting is recovered in the fast switching limit α→∞. We then consider the case of a finite switching rate. In particular, we investigate how a directional bias in the resetting protocol (ρ_{1}≠0.5) skews the LDP rate function so that its minimum is shifted away from the expected fractional occupation time of one-half. The degree of shift increases with r and decreases with α.

Curvature-Based Average Modeling of Switched-Capacitor Converters

A precise, curvature-based, average modeling technique for switched-capacitor (SC) dc–dc converters is proposed. The generalized modeling technique provides a comprehensive characterization of the converter at steady-state, across the full range of practical operating conditions. An expression for the equivalent output impedance is obtained, which relates the slow- and fast-switching limit impedances to the total output impedance. This expression can be used to accurately compute the output voltage without deriving the converter’s state equations and precisely weighs the contribution of each floating capacitor and parasitic resistance on the output impedance. The modeling technique is applied to a unity-gain SC converter, a multiphase binary converter, and a nonsymmetrical parallel–series converter, and the results are compared with existing steady-state models. The accuracy of the model is validated through simulations and experimental measurements.

Switching diffusions and stochastic resetting

We consider a Brownian particle that switches between two different diffusion states (D 0, D 1) according to a two-state Markov chain. We further assume that the particle’s position is reset to an initial value X r at a Poisson rate r, and that the discrete diffusion state is simultaneously reset according to the stationary distribution ρ n , n = 0, 1, of the Markov chain. We derive an explicit expression for the non-equilibrium steady state (NESS) on , which is given by the sum of two decaying exponentials. In the fast switching limit the NESS reduces to the exponential distribution of pure diffusion with stochastic resetting. The effective diffusivity is given by the mean . We then determine the mean first passage time (MFPT) for the particle to be absorbed by a target at the origin, having started at the reset position X r > 0. We proceed by calculating the survival probability in the absence of resetting and then use a last renewal equation to determine the survival probability with resetting. Similar to the NESS, we find that the MFPT depends on the sum of two exponentials, which reduces to a single exponential in the fast switching limit. Finally, we show that the MFPT has a unique minimum as a function of the resetting rate, and explore how the optimal resetting rate depends on other parameters of the system.

Dissipation in Non-Steady State Regulatory Circuits

In order to respond to environmental signals, cells often use small molecular circuits to transmit information about their surroundings. Recently, motivated by specific examples in signaling and gene regulation, a body of work has focused on the properties of circuits that function out of equilibrium and dissipate energy. We briefly review the probabilistic measures of information and dissipation and use simple models to discuss and illustrate trade-offs between information and dissipation in biological circuits. We find that circuits with non-steady state initial conditions can transmit more information at small readout delays than steady state circuits. The dissipative cost of this additional information proves marginal compared to the steady state dissipation. Feedback does not significantly increase the transmitted information for out of steady state circuits but does decrease dissipative costs. Lastly, we discuss the case of bursty gene regulatory circuits that, even in the fast switching limit, function out of equilibrium.

Two Phase (Reconfigurable) Inverting Switched Capacitor Converter for Micro Power Applications and its Accurate Equivalent Resistance Calculation

This brief addresses inverting switched capacitor converter (SCC) for driving the white light emitting diodes (WLEDs). The various voltage conversion ratios (VCRs) are selected to control the WLEDs blacklights, which helps to save the battery life. The major contribution are developing maximum VCRs for power converter integrated circuits (ICs) and equivalent resistance (Req) accurate calculation which includes all conduction and ohmic losses. Furthermore, inverting SCC (ISCC) experimental results are obtained from prototype model. Accurate Req analyses validates the accuracy of proposed topology. It is designed for low voltage of 10 mV to 0.1 V and it provides the output voltage of −100 mV to −0.5 V. Finally, the novelty of accurate Req calculation in this brief is that the calculation results are verified with experimental ones, particularly, at the transition region (between slow switching limit and fast switching limit). On the other hand, calculation, simulation and experimental results perfectly coincide with each other. Accurate equivalent resistance calculation and average current calculation are compared and some of the recent publications providing the merits of the proposed converter are explained.

A New Analysis Way of Three-Phase Switched Capacitor Converter

The paper presents the theoretical analysis way of the switched capacitor converter (SCC). The main goal of this research is to suggest the analysis way of three-phase SCC. A common SCC operates by two phases; charging phase and discharging phase. Therefore, state-space averaging model or slow and fast switching limit (S-FSL) model has been suitable. Although the four-terminal equivalent model can cover all situation including three-phases cases, this model does not include the parameter of frequency and capacitance. Therefore, the four-terminal model has a weakness. In this situation, we selected the Fibonacci sequence SCC operated by three-phase as the target circuit, which topology has been proved to have higher efficiency, small size in the previous research. In the paper, we suggest the new analysis way of the three-phase SCC by combination of the four-terminal equivalent model and RC circuit model from each loop equation of the equivalent circuits of the SCC. By using the suggested way, it is possible to analyze the three-phase SCC, deriving the effect of the load, operation frequency and duty ratio variation. In order to verify the feasibility and the cogency of the suggested analysis way, comparative analysis is implemented by SPICE simulations. The error in the load regulation between the suggested way and the simulation result is negligible. Through this result, we establish the foundation of the analysis of the three-phase SCC.

Synchronization of stochastic hybrid oscillators driven by a common switching environment.

Many systems in biology, physics, and chemistry can be modeled through ordinary differential equations (ODEs), which are piecewise smooth, but switch between different states according to a Markov jump process. In the fast switching limit, the dynamics converges to a deterministic ODE. In this paper, we suppose that this limit ODE supports a stable limit cycle. We demonstrate that a set of such oscillators can synchronize when they are uncoupled, but they share the same switching Markov jump process. The latter is taken to represent the effect of a common randomly switching environment. We determine the leading order of the Lyapunov coefficient governing the rate of decay of the phase difference in the fast switching limit. The analysis bears some similarities to the classical analysis of synchronization of stochastic oscillators subject to common white noise. However, the discrete nature of the Markov jump process raises some difficulties: in fact, we find that the Lyapunov coefficient from the quasi-steady-state approximation differs from the Lyapunov coefficient one obtains from a second order perturbation expansion in the waiting time between jumps. Finally, we demonstrate synchronization numerically in the radial isochron clock model and show that the latter Lyapunov exponent is more accurate.

Analysis and Optimization of Star-Structured Switched-Capacitor Equalizers for Series-Connected Battery Strings

Due to the adjacent cell-to-cell equalization, the classical switched-capacitor equalizer (SCE) has seriously low balancing speed and efficiency for a long battery string. Therefore, a series of star-structured switched-capacitor equalizers are proposed to achieve high balancing speed and efficiency independent of the cell number and the cell voltage distribution without significant influences on the size, cost, control, and reliability compared with the classical SCE. The proposed topologies use the least mosfet s and capacitors to achieve the most direct balancing paths between any two cells, being the optimal switched-capacitor structures. An analysis method for the slow switching limit and the fast switching limit impedances of the proposed equalizers is proposed to provide a theoretical guidance for the selection of the switching frequency. The inherent advantages of the proposed systems are the small size, low cost, simple control, high efficiency, fast speed, easy modularization, and high reliability. A prototype for four lithium-ion battery cells is set up. Experimental results show improved balancing performances with strong robustness. Moreover, the measured peak balancing efficiency is about 93.1% despite faster balancing speed.

A variational method for analyzing limit cycle oscillations in stochastic hybrid systems.

Many systems in biology can be modeled through ordinary differential equations, which are piece-wise continuous, and switch between different states according to a Markov jump process known as a stochastic hybrid system or piecewise deterministic Markov process (PDMP). In the fast switching limit, the dynamics converges to a deterministic ODE. In this paper, we develop a phase reduction method for stochastic hybrid systems that support a stable limit cycle in the deterministic limit. A classic example is the Morris-Lecar model of a neuron, where the switching Markov process is the number of open ion channels and the continuous process is the membrane voltage. We outline a variational principle for the phase reduction, yielding an exact analytic expression for the resulting phase dynamics. We demonstrate that this decomposition is accurate over timescales that are exponential in the switching rate ϵ-1. That is, we show that for a constant C, the probability that the expected time to leave an O(a) neighborhood of the limit cycle is less than T scales as T exp (-Ca/ϵ).

A Delta-Structured Switched-Capacitor Equalizer for Series-Connected Battery Strings

The classical switched-capacitor (SC) equalizer is widely used in battery management systems because of the accurate balancing and ease of implementation. However, it only achieves the adjacent cell-to-cell equalization, and its balancing speed and efficiency become extremely low for multicell series-connected battery strings. Therefore, a delta-structured switched-capacitor equalizer is introduced to achieve a high-speed and high-efficiency any-cells-to-any-cells (AC2AC) equalization at arbitrary imbalanced status for any number of cells. The slow switching limit and fast switching limit impedances of the proposed equalizer are developed to provide a theoretical guidance for the optimized design of the SC equalizers. A prototype for four battery cells was built, and a comparison with existing equalizers was presented. Experimental and comparative results show that the proposed solution exhibits an automatic AC2AC balancing with high reliability and strong robustness. The measured balancing efficiency is up to 94.5%.

Hybrid colored noise process with space-dependent switching rates.

A fundamental issue in the theory of continuous stochastic process is the interpretation of multiplicative white noise, which is often referred to as the Itô-Stratonovich dilemma. From a physical perspective, this reflects the need to introduce additional constraints in order to specify the nature of the noise, whereas from a mathematical perspective it reflects an ambiguity in the formulation of stochastic differential equations (SDEs). Recently, we have identified a mechanism for obtaining an Itô SDE based on a form of temporal disorder. Motivated by switching processes in molecular biology, we considered a Brownian particle that randomly switches between two distinct conformational states with different diffusivities. In each state, the particle undergoes normal diffusion (additive noise) so there is no ambiguity in the interpretation of the noise. However, if the switching rates depend on position, then in the fast switching limit one obtains Brownian motion with a space-dependent diffusivity of the Itô form. In this paper, we extend our theory to include colored additive noise. We show that the nature of the effective multiplicative noise process obtained by taking both the white-noise limit (κ→0) and fast switching limit (ε→0) depends on the order the two limits are taken. If the white-noise limit is taken first, then we obtain Itô, and if the fast switching limit is taken first, then we obtain Stratonovich. Moreover, the form of the effective diffusion coefficient differs in the two cases. The latter result holds even in the case of space-independent transition rates, where one obtains additive noise processes with different diffusion coefficients. Finally, we show that yet another form of multiplicative noise is obtained in the simultaneous limit ε,κ→0 with ε/κ^{2} fixed.

Temporal disorder as a mechanism for spatially heterogeneous diffusion.

A fundamental issue in analyzing diffusion in heterogeneous media is interpreting the space dependence of the associated diffusion coefficient. This reflects the well-known Ito-Stratonovich dilemma for continuous stochastic processes with multiplicative noise. In order to resolve this dilemma it is necessary to introduce additional constraints regarding the underlying physical system. Here we introduce a mechanism for generating nonlinear Brownian motion based on a form of temporal disorder. Motivated by switching processes in molecular biology, we consider a Brownian particle that randomly switches between two distinct conformational states with different diffusivities. In each state the particle undergoes normal diffusion (additive noise) so there is no ambiguity in the interpretation of the noise. However, if the switching rates depend on position, then in the fast-switching limit one obtains Brownian motion with a space-dependent diffusivity. We show that the resulting multiplicative noise process is of the Ito form. In particular, we solve a first-passage time problem for finite switching rates and show that the mean first-passage time reduces to the Ito version in the fast-switching limit.

Topology, Modeling, and Design of Switched-Capacitor-Based Cell Balancing Systems and Their Balancing Exploration

A series of switched-capacitor (SC) cell balancing circuits is proposed for rechargeable energy storage devices like battery and supercapacitor strings in this paper. Taking a basic SC-based cell balancing unit as an equivalent resistor, the behavioral models of the proposed cell balancing circuits are developed to evaluate their balancing performance. Comparing with existing SC-based cell balancing circuits, the main advantage of the proposed circuits is that their balancing speed is independent of both of the number of battery cells and initial mismatch distribution of cell voltages. In order to improve the operation performance of SC-based cell balancing circuits in the respect of minimizing the equivalent resistance, optimizing methodologies of circuit parameters are introduced by referring the concepts of slow switching limit and fast switching limit as well as inductive switching limit of SC power converters. Simulation and experimental results are provided to verify the feasibility of the proposed cell balancing circuits.

A dual source switched-capacitor converter with solar energy integration capability

This paper presents a dual source variable output switched capacitor that can be operated in step down mode. The feature of the converter is that it can be selectively switched between two input sources one being a solar source. Since inductors are eliminated in the circuit topology the converter is light in weight and size. Also EMI issues are minimal due to the absence of inductors. The converter working in the no charge (NC) mode or fast switching limit (FSL) is used to develop the mathematical model. Using this model the equivalent resistance of the converter due to the influence of switch resistance and ESR of the capacitor can be found out. PSIM simulation of the converter gives satisfactory results and a laboratory prototype has been set up for experimental validation using the locally available components. The converter input is fixed at 12 V which can be from a battery source or solar source. The output variable voltage obtained is half, one-third, two-third and unity with respect to the input. The application of this converter can be in portable electronic devices or a processor for future which need three buck voltage levels typically in active, standby and sleep mode.

A dual source switched-capacitor converter with solar energy integration capability

This paper presents a dual source variable output switched capacitor that can be operated in step down mode. The feature of the converter is that it can be selectively switched between two input sources one being a solar source. Since inductors are eliminated in the circuit topology the converter is light in weight and size. Also EMI issues are minimal due to the absence of inductors. The converter working in the no charge (NC) mode or fast switching limit (FSL) is used to develop the mathematical model. Using this model the equivalent resistance of the converter due to the influence of switch resistance and ESR of the capacitor can be found out. PSIM simulation of the converter gives satisfactory results and a laboratory prototype has been set up for experimental validation using the locally available components. The converter input is fixed at 12 V which can be from a battery source or solar source. The output variable voltage obtained is half, one-third, two-third and unity with respect to the input. The application of this converter can be in portable electronic devices or a processor for future which need three buck voltage levels typically in active, standby and sleep mode.

Synchronization in On-Off Stochastic Networks: Windows of Opportunity

We study dynamical networks whose topology and intrinsic parameters stochastically change, on a time scale that ranges from fast to slow. When switching is fast, the stochastic network synchronizes as long as synchronization in the averaged network, obtained by replacing the random variables by their mean, becomes stable. We apply a recently developed general theory of blinking systems to prove global stability of synchronization in the fast switching limit. We use a network of Lorenz systems to derive explicit probabilistic bounds on the switching frequency sufficient for the network to synchronize almost surely and globally. Going beyond fast switching, we consider networks of Rossler and Duffing oscillators and reveal unexpected windows of intermediate switching frequencies in which synchronization in the switching network becomes stable even though it is unstable in the averaged/fast-switching network.