Abstract：Peak current-model (PCM) Buck converters are widely employed in power management ICs. As microprocessors integrate continuously, high-bandwidth design has become a requisite for the front-end Buck converters. Accurate small-signal modeling is crucial for analyzing system stability and designing high-performance controllers. Existing models neglect control signal ripples (CSRs) in steady-state and extended-spectrum under small-signal perturbation transferred by voltage-loop, which makes significant errors under high control bandwidth and fails to guide controller design. To portray the high-frequency characteristics of the system and direct the design of high-bandwidth controllers, this paper proposed a high-frequency model for PCM Buck converters. An optimal controller design method was conducted based on the proposed model and genetic algorithm. Firstly, this paper emphasized that different types of CSRs are initiated by different types of controllers. Subsequently, influences caused by differentiable CSRs were analyzed, wherein the impact of differentiable ripples on the system can be equivalent to the derivative values at crossing points. The spectrum coupling from the voltage-loop and current-loop was incorporated, and the maximum frequency point corresponding to -20 dB amplitude of the single-frequency loop gain was taken as the selection boundary of the extended spectrum to simplify the model. Thereby an accurate small-signal model was obtained. Analytical expressions for loop gain, audio susceptibility, input impedance, and output impedance were derived based on matrix operations. Lastly, based on the proposed high-frequency model, an efficient optimization design of high-bandwidth controllers was conducted by combining genetic algorithm. To assert the accuracy of the proposed model and the effectiveness of the optimal controller design method, this paper devised two cases and conducted simulations and experimental verifications. For case Ⅰ, the loop gain predicted by the proposed model (Bandwidth: 222.5 kHz, Phase margin: 29.9°) matches well with the simulated results (Bandwidth: 224.3 kHz, Phase margin: 29.8°). For case Ⅱ, the loop gain predicted by the proposed model (Bandwidth: 161.9 kHz, Phase margin: 13.1°) also matches well with the simulated results (Bandwidth: 162.0 kHz, Phase margin: 12.8°). The parameters of case Ⅱ were leveraged to construct an experimental platform. The loop gain of the system is measured using a Venable Frequency Analyzer. The experimental results (Bandwidth: 162.5 kHz, Phase margin: 16.4°) further confirm the accuracy of the proposed model. Deviations between them are mainly due to parameter variations and measurement errors in the real system. The simulation-based genetic algorithm optimization method in Simulink was redone to illustrate the efficiency of the proposed optimal controller design method. To achieve a fair comparison, the genetic algorithm optimization calculation was also carried out in Matlab, and even with the same computer settings, case Ⅰ takes up to 4.8 h and case Ⅱ takes up to 3.8 h. The proposed optimal controller design method takes only 55 s and 53 s respectively, which are hundreds of times more efficient, showcasing its effectiveness. Compared with the time-domain simulation-based parameter search method, the ability to attain a quantitative stability margin design by setting Lpm_limit is another advantage by utilizing the precise analytical model. Simulation and experimental results demonstrate that the proposed high-frequency model is accurate enough to portray frequency domain characteristics and forecast system stability precisely, compared with existing models. Additionally, the proposed optimal controller design method enables fast and efficient implementation of high-bandwidth controller designs. The proposed high-frequency model belongs to an analytical model and significantly reduces the computational burden on computers. Combining it with a genetic algorithm results in complementary benefits. This combination facilitates quick and precise appraisal of individual fitness during the iteration process, thereby reducing design time considerably and offering practical value in engineering applications.
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2024, Vol. 39 
