Showing papers on "Buck converter published in 2022"

Active Disturbance Rejection Control Design With Suppression of Sensor Noise Effects in Application to DC–DC Buck Power Converter

Abstract: The performance of active disturbance rejection control (ADRC) algorithms can be limited in practice by high-frequency measurement noise In this article, this problem is addressed by transforming the high-gain extended state observer (ESO), which is the inherent element of ADRC, into a new cascade observer structure Set of experiments, performed on a dc–dc buck power converter system, show that the new cascade ESO design, compared to the conventional approach, effectively suppresses the detrimental effect of sensor noise overamplification while increasing the estimation/control performance The proposed design is also analyzed with a low-pass filter at the converter output, which is a common technique for reducing measurement noise in industrial applications

Active Disturbance Rejection Control Design With Suppression of Sensor Noise Effects in Application to DC–DC Buck Power Converter

Abstract: The performance of active disturbance rejection control (ADRC) algorithms can be limited in practice by high-frequency measurement noise. In this article, this problem is addressed by transforming the high-gain extended state observer (ESO), which is the inherent element of ADRC, into a new cascade observer structure. Set of experiments, performed on a dc–dc buck power converter system, show that the new cascade ESO design, compared to the conventional approach, effectively suppresses the detrimental effect of sensor noise overamplification while increasing the estimation/control performance. The proposed design is also analyzed with a low-pass filter at the converter output, which is a common technique for reducing measurement noise in industrial applications.

A new artificial ecosystem-based optimization integrated with Nelder-Mead method for PID controller design of buck converter

Abstract: Over the last decade, there has been a constant development in control techniques for DC-DC power converters which can be classified as linear and nonlinear. Researchers focus on obtaining maximum efficiency using linear control techniques to avoid complexity although nonlinear control techniques may achieve full dynamic capabilities of the converter. This paper has a similar purpose in which a novel hybrid metaheuristic optimization algorithm (AEONM) is proposed to design an optimal PID controller for DC-DC buck converter’s output voltage regulation. The AEONM employs artificial ecosystem-based optimization (AEO) algorithm with Nelder-Mead (NM) simplex method to ensure optimal PID controller parameters are efficiently tuned to control output voltage of the buck converter. Initial evaluations are performed on benchmark functions. Then, the performance of AEONM-based PID is validated through comparative results of statistical boxplot, non-parametric test, transient response, frequency response, time-domain integral-error-performance indices, disturbance rejection and robustness using AEO, particle swarm optimization and differential evolution. A comparative performance analysis of transient and frequency responses is also performed against simulated annealing, whale optimization and genetic algorithms for further performance assessment. The comparisons have shown the proposed hybrid AEONM algorithm to be superior in terms of enhancing the buck converter’s transient and frequency responses.

Real-Time Voltage Control Based on a Cascaded Super Twisting Algorithm Structure for DC–DC Converters

Abstract: This article proposes a second-order sliding mode control law, based on a super twisting algorithm (STA), aimed at regulating the output voltage of a dc–dc buck converter. A closed-loop system is designed consisting of two distinct nested loops organized within a cascaded STA structure. Several sliding mode control algorithms are here surveyed for the regulation of a dc–dc buck converter. The STA of second-order sliding mode is also experimented in an HIL system. The comparative evaluations include comparing the output voltage transient responses to load step changes for all developed sliding mode control algorithms and the start-up responses of the output voltage to step changes of the input voltage of the buck converter. Furthermore, theoretical considerations, numerical simulations, and experimental results from a laboratory prototype are compared, at different operating points, for all surveyed control methods. It results from the simulations and experiments that the designed STA achieves the fastest convergence, a consistent chattering reduction, the smallest settling time under loaded situations, and small steady-state error during load changes over all contrasted control methods.

Fuzzy Approximation-Based Fractional-Order Nonsingular Terminal Sliding Mode Controller for DC–DC Buck Converters

Abstract: This article presents a simple and systematic approach to synthesize a robust adaptive fuzzy fractional-order nonsingular terminal sliding mode controller (AFFO-NTSMC) to improve the output voltage tracking control performance of the dc–dc buck converters. The hybrid control method of fractional-order (FO) calculus and NTSMC are combined to create a FO-NTSMC, in which a new FO nonsingular terminal sliding mode surface is established. The idea behind this strategy is the increased flexibility achieved by FO calculation, improving robustness to disturbances and parameters variations provided by the traditional sliding mode controllers as well as finite time convergence properties of the output voltage error to the equilibrium point during the output load changes, simultaneously. In addition, a fuzzy logic system with online adaptive learning algorithm is designed to provide smooth chattering in switching control signal. The stability of the closed-loop system is carefully demonstrated by Lyapunov's theorem. Experimental measurements from a laboratory prototype are presented to demonstrate the effectiveness of the proposed AFFO-NSTSMC algorithm.

A Compact Double-Sided Cooling 650V/30A GaN Power Module With Low Parasitic Parameters

Abstract: Compared with silicon and silicon carbide devices, the unique electrical and structural characteristics of gallium nitride high electron mobility transistors (GaN HEMTs) make them have different requirements for power module integration. This article proposes a novel integration scheme for the high-voltage lateral GaN HEMT dies without bonding wires. Based on the proposed integration scheme, a compact 650 V/30 A GaN power module with low parasitic parameters and high thermal performance is designed. The GaN dies are sandwiched between two ceramic substrates to improve thermal performance and ensure consistent thermal expansion coefficients. The multiple copper layer structure is used to increase wiring flexibility to reduce parasitic parameters. The design of gate and power loop layouts is discussed, and the common-mode (CM) capacitance is optimized. A comprehensive reliability evaluation is also carried out for this integration scheme. Finally, a double-sided cooling 650 V/30 A full-bridge GaN power module with 2.4 cm×1.3 cm×0.17 cm is fabricated. The thermal resistance is reduced by 30%–48% compared with the conventional single-sided cooling module. The power loop and gate loop inductances are reduced to 0.94 nH and 2 nH, respectively, and the CM capacitance is limited to 2.5 pF. The maximum d v /d t of the drain–source voltage is high as 150 V/ns with only 10% overshoot. Based on the power module, a 3.3-kW two-phase interleaved buck converter is developed. It has 820 W/in3 power density and 98.85% peak efficiency.

Single-Stage Doubly Grounded Transformerless PV Grid-Connected Inverter With Boost Function

Abstract: Doubly grounded transformerless grid-connected inverters are widely used in the PV application because of no common mode leakage current. A boost converter should be added into the doubly grounded PV inverters under shading condition to have boost function. However, the inverter with boost capability is a two-stage system and all switches are operated at high frequency, which reduce efficiency of the system. In addition, processing power of the boost converter is high. Therefore, a single-stage doubly grounded transformerless PV grid-connected inverter with boost function is proposed. The proposed inverter consists of two boost and one buck converters. A cooperative control method among different periods is proposed to reduce processing power of the boost converter and simplify the two-stage system to a single-stage system in each period. In addition, only one switch is operated at high frequency in each period, so efficiency of the system can be improved. Operating principle of the proposed inverter is illustrated. Control strategy is designed. Filter design guidelines and example are given. Loss calculation of the proposed inverter is given. Simulation and experimental results of the proposed inverter verify the theoretical analysis. Finally, comparison among other inverters and the proposed inverter is provided.

Real-Time Voltage Control Based on a Cascaded Super Twisting Algorithm Structure for DC–DC Converters

Abstract: This article proposes a second-order sliding mode control law, based on a super twisting algorithm (STA), aimed at regulating the output voltage of a dc–dc buck converter. A closed-loop system is designed consisting of two distinct nested loops organized within a cascaded STA structure. Several sliding mode control algorithms are here surveyed for the regulation of a dc–dc buck converter. The STA of second-order sliding mode is also experimented in an HIL system. The comparative evaluations include comparing the output voltage transient responses to load step changes for all developed sliding mode control algorithms and the start-up responses of the output voltage to step changes of the input voltage of the buck converter. Furthermore, theoretical considerations, numerical simulations, and experimental results from a laboratory prototype are compared, at different operating points, for all surveyed control methods. It results from the simulations and experiments that the designed STA achieves the fastest convergence, a consistent chattering reduction, the smallest settling time under loaded situations, and small steady-state error during load changes over all contrasted control methods.

ZVS-Interleaved Synchronous Buck DC–DC Converter With a Coupled Inductor by Varying Switching Frequency and Deadtime

Abstract: This article proposes a fully digital variable switching frequency and deadtime control method for a synchronous rectifier buck dc–dc converter with an inverse coupled inductor. It does not need auxiliary circuits, zero-crossing detection (ZCD), or high-bandwidth sensors. Even in facing the polyline shape of the current in inductors due to the coupling effect, zero-voltage switching (ZVS) can be achieved with the proposed varying switching frequency control to make the turn off current be constant. Based on ZVS achievement of the power switches, the deadtime is variable to reduce the conduction loss over body diodes further. The modes and resonant process are analyzed in detail. A 1-kW experimental prototype was built to verify the effectiveness of the proposed control method. The peak efficiency is over 99% in the experimental test.

Overshoot Damping and Dynamics Improvement in Wireless Power Transfer Systems Via Receiver-Side Controller Design

Abstract: Buck converters have been extensively used for output regulation in the receiver of series–series compensated wireless power transfer (WPT) systems. Nonetheless, there are two major challenges in the controller design of this class of WPT systems. First, due to the current-source nature and finite dc-link capacitance, a right-half-plane (RHP) zero exists in the WPT receiver, reducing its stability margin and causing limited system dynamics. Second, this RHP zero can cause an overshoot issue in the WPT system. Without proper treatment, this overshoot may largely increase the voltage/current stress of the system and even cause catastrophic failure. However, existing solutions to the above two issues suffer from long communication delays or significantly compromised output regulation, degrading system performance. In this article, the slow dynamics and the overshoot issue of the WPT system are elaborated in theory and a solution is proposed by adding a feedforward path of the dc-link voltage in the receiver's controller. No communication is involved in the proposed control method, and only trivial computation is added to the controller. The proposed method is examined on a WPT prototype. The experimental results show that the two issues of the WPT system can be simultaneously solved by the proposed method while the output regulation of the system is not compromised.

A New Coupled-Inductor-Based Buck–Boost DC–DC Converter for PV Applications

Abstract: A new buck–boost converter with coupled inductors is presented in this article. The converter benefits from low ripple input current, simple control (both power switches operate synchronously), common ground sharing between input and output ports, low-voltage stress across the power switches, positive output voltage, and quadratic voltage gain. Since the proposed converter has continuous input current, it is a proper choice for fuel cell (FC) and photovoltaic applications. Operating principles, mathematical calculation for steady-state operation, and small-signal modeling analysis are described in detail. Finally, an experimental 25-20-200 V prototype has been implemented to confirm all the mathematical derivation and aforementioned features of the proposed buck–boost converter.

Voltage Regulation of DC-DC Buck Converters Feeding CPLs via Deep Reinforcement Learning

Abstract: Modeling accuracy of DC-DC converters may deviate largely in the presence of different variation levels of constant power loads (CPLs), hence is well acknowledged as a main hurdle for the design of advanced model-driven control strategies in the literature. Aiming to enhance the bus voltage regulation performance of DC-DC buck converters, a model-free deep reinforcement learning (DRL) control strategy is proposed in this brief. Firstly, a Markov Decision Process (MDP) model and a deep Q network (DQN) algorithm are utilized for the stabilization issue of the converter. Secondly, through a subgoal reward/penalty mechanism, the control objective and prescribed performance of the system are therefore guaranteed. Moreover, a specified action space is designed to match the switch speed of the switching element. As a distinguishable feature, the settling time under the proposed control scheme is significantly reduced in the occurrence of disturbance, resulting from the fast adaption ability of DRL. The simulation comparison results in reference to PI and fuzzy PI controllers demonstrate the efficacy and superiorities under large signal perturbation conditions.

A Capacitor Current and Capacitor Voltage Ripple Controlled SIDO CCM Buck Converter With Wide Load Range and Reduced Cross Regulation

Abstract: It is well-known that the ripple control technique benefits from fast load transient response and small cross regulation for single-inductor dual-output (SIDO) dc–dc converter. However, existing capacitor current ripple (CCR) controlled SIDO buck converter suffers from incomplete operation state and single switching path. Thus, it has a limited stable load range. In order to extend the stable load range and suppress cross regulation of SIDO buck converter in continuous conduction mode (CCM), a novel ripple control technique, called as capacitor current and capacitor voltage ripple (CCVR) control, is proposed in this article. The operation principle of the proposed CCVR controlled SIDO CCM buck converter is presented, and its discrete iterative map model is established. Furthermore, the stability and stable load range have been discussed by using bifurcation diagrams. Based on the established small signal model, Bode plots are given to show the performance in suppressing cross regulation. Finally, simulation and experiment results are provided to verify the theoretical analysis. It shows that the proposed CCVR control technique can be applied to SIDO CCM buck converter to extend its stable load range and suppress its cross regulation.

An Ultra-Low Quiescent Current Tri-Mode DC-DC Buck Converter With 92.1% Peak Efficiency for IoT Applications

Abstract: An ultra-low quiescent current tri-mode DC-DC buck converter is presented in this paper, which is able to handle a 100,000X load range. In pulse width modulation (PWM) and pulse frequency modulation (PFM) mode, adaptive on-time (AOT) V² control is utilized to achieve seamless mode transition and constant switching frequency in PWM mode. A deep green mode (DGM) is proposed for light load, where both the switching loss and the power of control circuitry are minimized. By reducing the comparator current, a delay-based hysteresis window adaptive to load current is generated, reducing the switching frequency and the loss. Meanwhile, the average current of zero current detector (ZCD) and AOT controller are reduced significantly by dynamic biasing. As a result, the efficiency of the converter is improved while maintaining a reasonable output ripple. The proposed converter is implemented in a $0.18\mu $ m BCD technology. Experimental results show that the converter can provide a 1.6 V output from a 2.7 to 4.7V input for $1\mu $ A to 100 mA load, while consuming only 490nA quiescent current. The proposed converter achieves a 92.1% peak efficiency and efficiency can be maintained above 80% in a load range of $20\mu $ A to 60 mA.

MPPT mechanism based on novel hybrid particle swarm optimization and salp swarm optimization algorithm for battery charging through simulink

Abstract: In this paper, a battery charging model is developed for solar PV system applications. As a means of photovoltaic power controlling system, buck-boost converter with a Maximum Power Point Tracking (MPPT) mechanism is developed in this paper for maximum efficiency. This paper proposed a novel combined technique of hybrid Particle Swarm Optimisation (PSO) and Salp Swarm Optimization (SSO) models to perform Maximum Power Point Tracking mechanisms and obtain a higher efficiency for battery charging. In order to retrieve the maximum power from the PV array, the Maximum Power Point Tracking mechanism is observed which reaches the maximum efficiency and the maximum power is fed through the buck-boost converter into the load. The buck-boost converter steps up the voltage to essential magnitude. The energy drawn from the PV array is used for the battery charging by means of an isolated buck converter since the buck-boost converter is not directly connected to the battery. The Fractional Order Proportional Integral Derivative (FOPID) controller handles the isolated buck converter and battery to enhance the efficiency obtained through the Maximum Power Point Tracking mechanism. The simulation results show higher steady efficiency by using the hybrid PSOSSO algorithm in all stages. The battery is charged without losing the efficiency obtained from the hybrid PSOSSO algorithm-based Maximum Power Point Tracking mechanism. The higher efficiency was obtained as 99.99% at Standard Test Conditions (STC) and 99.52% at PV partial shading conditions (PSCs) by using the new hybrid algorithm.

A New Coupled-Inductor-Based Buck–Boost DC–DC Converter for PV Applications

Abstract: A new buck–boost converter with coupled inductors is presented in this article. The converter benefits from low ripple input current, simple control (both power switches operate synchronously), common ground sharing between input and output ports, low-voltage stress across the power switches, positive output voltage, and quadratic voltage gain. Since the proposed converter has continuous input current, it is a proper choice for fuel cell (FC) and photovoltaic applications. Operating principles, mathematical calculation for steady-state operation, and small-signal modeling analysis are described in detail. Finally, an experimental 25-20-200 V prototype has been implemented to confirm all the mathematical derivation and aforementioned features of the proposed buck–boost converter.

Dead Time Optimization in a GaN-Based Buck Converter

Abstract: A gallium nitride (GaN) field effect transistor can provide superior performance over a Si- mosfet due to its low on -state resistance and low junction capacitances. However, a GaN-based converter exhibits higher dead time loss during reverse conduction. Thus, to improve the efficiency, dead time optimization is required. This article proposes simple models for dead time optimization in a GaN-based buck converter under different load conditions. The proposed models are analytical in nature compared to the conventional models available for Si-based converters. A buck converter prototype is designed using a 100 V GaN device (GS61008P from GaN Systems) and the proposed analytical model-based dead time optimization techniques are validated experimentally. The proposed modeling techniques can be extended for other GaN-based dc–dc converters.

A 32-A, 5-V-Input, 94.2% Peak Efficiency High-Frequency Power Converter Module Featuring Package-Integrated Low-Voltage GaN nMOS Power Transistors

Abstract: A buck converter using a low-voltage GaN nMOS power transistor with 5– $10\times $ superior switching figure-of-merit over Si laterally-diffused MOS (LDMOS) and stacked CMOS at 5 V has been employed to build a high-frequency (3–20 MHz), high-density (9 A/mm²) buck converter for high-performance-compute applications. The GaN-based converter is co-packaged with a CMOS Companion Die on a 4 mm $\times $ 4 mm package and employs on-die gate clamps to minimize the impact of package parasitics for high efficiency. For 5-V input to 1-V output conversion, the converter achieves 94.2% peak efficiency at 3.1-MHz switching frequency with a 40-nH inductor, and >80% peak efficiency at 20 MHz with an air-core inductor.

A Power Adaptive Impedance Reshaping Strategy for Cascaded DC System With Buck-Type Constant Power Load

Abstract: It is well-known that the low-frequency negative input impedance of the constant power load (CPL) is the major cause of the cascaded system instability, and the heavier the power, the worse the stability. In this article, a power adaptive load-side parallel virtual impedance (PALPVI) control strategy is proposed to improve the stability of the cascaded dc system with buck-type CPL. First, a parallel impedance with power adaptability is derived followed up with the derivation of the corresponding compensation controller transfer function to realize it virtually. Considering that the compensation controller is highly dependent on the circuit parameters and needs extra current sensors to acquire the power information, a simplification of the compensation controller is made based on the open-loop characteristics of the buck-type CPL. The final PALPVI control strategy does not require the circuit parameters or any current sensor and has almost no side effect on the dynamic performance. Finally, a 48–24–12 V cascaded dc system is fabricated to verify the feasibility and effectiveness of the proposed PALPVI control strategy.

Design and Analysis of Two-Switch-Based Enhanced Gain Buck–Boost Converters

Abstract: This article presents evolution of two-switch-based enhanced gain buck–boost converter (EGBBC) topologies. All these topologies exhibit quadratic buck–boost voltage transformation ratio together with common ground feature. The basis for these topological evolutions is the cascading of boost followed by restructured ZETA. Direct cascading of boost with ZETA yields a pseudo quadratic conversion ratio and an additional buck stage is mandatory to transform the gain to quadratic buck–boost form. Without adding additional stages and to yet realize the quadratic buck–boost transformation, a modified boost configuration at the front-end together with restructured cascading approach is adopted in the topological evolution. This evolution resulted in three different topologies exhibiting quadratic buck–boost voltage gain named as EGBBC Type-1, Type-2, and Type-3. Exhaustive steady-state and dynamic analysis is presented for Type-1, while brief formulations are listed for Type-2 and 3. Also, a comprehensive review of the reported buck–boost converters is made and compared with EGBBC features. A 10 ∼ 37 W, 15 to 10 V for bucking operation, and 75 V for boosting operation prototype is built for concept validation. A simple two-pole two-zero compensator is adopted for load voltage regulation. Measurement results demonstrate closed-loop system stability, robustness, and voltage regulation both in bucking as well as in boosting operation.

Dynamic prescribed performance sliding mode control for DC-DC buck converter system with mismatched time-varying disturbances.

Abstract: A generalized proportional integral observer (GPIO) based dynamic prescribed performance sliding mode control (DPPSMC) method for DC–DC buck converter with mismatched time-varying disturbance is proposed to achieve high output voltage tracking performance. Firstly, because extended state observer (ESO) could only estimate the constant interference, considering the mismatched time-varying interference, GPIO is designed to estimate the lumped disturbance so as to enhance the anti-disturbance performance. Then, for the sake of further improve the transient performance, the prescribed performance algorithm is introduced. However, the traditional prescribed performance adopts static performance function. The dynamic system tracking error is likely to exceed the boundaries set by performance functions due to external disturbance and uncertainty, leading to the failure of the algorithm. On account of this, a dynamic prescribed performance function (PPF) is put forward in this paper to keep the tracking error of the converter system always within the predefined error boundary and the algorithm failure problem is avoided. Finally, combined with disturbance estimation technology and dynamic PPF, DPPSMC method is designed to dispose mismatched time-varying interference and improve the transient performance. The Lyapunov stability theorem is applied to certify that the proposed control algorithm could stabilize the closed-loop system. Simulation and experimental result verify the meliority of the designed controller.

A robust nonlinear PI-type controller for the DC-DC buck-boost power converter.

Abstract: In this study, a novel Lyapunov function-based robust nonlinear proportional-integral (PI)-type controller for regulating the output voltage of the direct current to direct current (DC-DC) inverting buck-boost power converter operating in continuous conduction mode (CCM) is presented. The control scheme guarantees global asymptotic stability of the closed-loop system even in case of parameter uncertainty. The analysis of the closed-loop trajectories is carried out using Lyapunov method and LaSalle's invariance principle. Robustness to additive disturbances is shown and simple gain tuning guidelines are given. Real-time experiments support the theoretical results. Experimental tests are presented where the proposed PI-type control design is compared with other PI-type schemes found in the literature. The proposed scheme presents very good consistent performance under line and load disturbance.

A New Model Predictive Control Method for Buck-Boost Inverter-Based Photovoltaic Systems

Abstract: This study designed a system consisting of a photovoltaic system and a DC-DC boost converter with buck-boost inverter. A multi-error method, based on model predictive control (MPC), is presented for control of the buck-boost inverter. Incremental conductivity and predictive control methods have also been used to track the maximum power of the photovoltaic system. Due to the fact that inverters are in the category of systems with fast dynamics, in this method, by first determining the system state space and its discrete time model, a switching algorithm is proposed to reduce the larger error for the converter. By using this control method, in addition to reducing the total harmonic distortion (THD), the inverter voltage reaches the set reference value at a high speed. To evaluate the performance of the proposed method, the dynamic performance of the converter at the reference voltage given to the system was investigated. The results of system performance in SIMULINK environment were simulated and analyzed by MATLAB software. According to the simulation results, we can point out the advantage of this system in following the reference signal with high speed and accuracy.

Second-order sliding mode controller design of buck converter with constant power load

Abstract: Multi-converter systems used in DC microgrid feed supply constant power loads (CPL) as well as classical electrical loads. CPL has a non-linear load nature because of the negative impedance effect. This impact causes instability in converter systems within the micro-grid. This paper proposes a super twisting-based second-order sliding mode control (SOSMC) for regulating the output voltage of a DC/DC buck converter feeding CPL. The goal of this method is to suppress the chattering effect and maintaining the robustness under load variations and parametric uncertainties. With the experimental studies constructed in the laboratory and simulations executed in Matlab environment, the proposed SOSMC was compared with classical first-order SMC for the response of the buck converter feeding CPL under various conditions. The simulation and experimental results show the proposed controller has higher tracking precision and stronger robustness during any disturbance in input voltage or CPL power, as well as reducing the chattering effect.

Steady-State Analysis of Series-Resonator Buck Converter

Abstract: The series-capacitor buck converter doubles the duty ratio and equalizes the current between two phases. A series-resonator buck (SRB) converter is realized by adding a resonant tank in series with the series-capacitor C_s . All switches turn- on at zero voltage, and the low-side switches turn- off at zero current. This article focuses on modeling the steady-state operation of the SRB converter. The steady-state model calculates voltage gain, component peak voltages, and resonant inductor peak current. The understanding of the relationships between the voltage gain, regulating variable, and state variables help to optimize the power stage design. The expectations were validated by a 2-MHz converter with a peak efficiency of 98.5%, 48 V at the input and 7 V, 20 A at the output.

Accurate Loop Gain Modeling of Digitally Controlled Buck Converters

Abstract: For the digitally controlled buck converters, the nonlinearity and time periodicity, caused by the pulsewidth modulator (PWM) and sample and hold, make the accurate frequency-domain analysis intractable. In this article, based on the harmonic transfer function (HTF) approach, a precise small-signal continuous-time modeling for the digitally controlled Buck converter operating in continuous-conduction mode (CCM) under constant-frequency voltage-mode control is presented. The sideband components on the closed-loop control are embedded in the model. Thus, this model is accurate within the full frequency domain region, which breaks the limit of Nyquist frequency. Furthermore, by overcoming the barrier of infinite series introduced by the sideband effects, the analytical loop gain expression is derived, which contributes to accurate stability assessment and reduction of computation burden. In addition, the proposed exact small-signal model has explained the reasons why different information injection points lead to different measured loop gains. Simulations and experimental results are conducted to verify the effectiveness of the proposed method.