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Steady-State and Small-Signal Analysis of High-Ratio Hybrid Buck Converters With Enhancement to State-Space-Averaging Methodology 基于状态-空间平均方法的高比混合降压变换器稳态和小信号分析
IF 5.2 1区 工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2025-08-25 DOI: 10.1109/TCSI.2025.3594347
Muhammad Rizwan Khan;Xun Liu;Xin Zhang;Cheng Huang
This paper proposes convergence enhancement to state-space averaging (SSA) methodology for steady-state and small-signal analysis of high-ratio hybrid DC-DC converters, first using analysis of Double-Step-Down (DSD) topology, including parasitics, as an example, then extending to other hybrid topologies with different numbers of capacitors and inductors. The enhanced SSA method can be used to: 1) derive small-signal control-to-output transfer functions, which is essential to optimize the compensator for fast and stable closed-loop operation; 2) calculate steady-state inductor currents, output voltage, input current and the voltage(s) across the flying capacitor(s), $V_{CFs}$ , which is important to determine steady-state characteristics and performance; 3) include circuit non-idealities such as parasitics and timing mismatches; and 4) evaluate $V_{CF}$ balancing property by the proposed matrix invertibility principle and added constants, and determine whether dedicated $V_{CF}$ balancing circuits can be eliminated, which is considered an important benefit with reduced complexity and improved reliability. The theoretical results of DSD are then plotted in MATLAB and verified in simulations using PSIM and Cadence periodic transfer function (PXF) analysis, and measurement results using GaN devices. The simulation and measurement results match well with theoretical analysis. The enhancement is then extended beyond the DSD topology to analyze emerging hybrid topologies with more switched inductors and capacitors, future-proofing its capability to be applicable to new hybrid topologies.
本文首先以双降压(DSD)拓扑(包括寄生)分析为例,将状态空间平均(SSA)方法的收敛性增强应用于高比混合DC-DC转换器的稳态和小信号分析,然后将其推广到其他具有不同电容和电感数量的混合拓扑。改进的SSA方法可以用于:1)导出小信号控制输出传递函数,这是优化补偿器以实现快速稳定闭环运行所必需的;2)计算稳态电感电流、输出电压、输入电流和跨越飞行电容的电压$V_{CFs}$,这对确定稳态特性和性能很重要;3)包含电路非理想性,如寄生和时序不匹配;4)利用提出的矩阵可变性原理和增加的常数来评估$V_{CF}$的平衡特性,并确定是否可以取消专用的$V_{CF}$平衡电路,这被认为是降低复杂性和提高可靠性的重要好处。然后在MATLAB中绘制DSD的理论结果,并使用PSIM和Cadence周期传递函数(PXF)分析进行仿真验证,以及使用GaN器件的测量结果。仿真和实测结果与理论分析吻合较好。然后,该增强功能扩展到DSD拓扑之外,以分析具有更多开关电感和电容器的新兴混合拓扑,使其能够适用于新的混合拓扑。
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引用次数: 0
Non-Linearity Analysis of Drain-Source Capacitance in Extended Continuous Class-F Power Amplifier 扩展连续型f类功率放大器漏源电容的非线性分析
IF 5.2 1区 工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2025-08-18 DOI: 10.1109/TCSI.2025.3596129
Kamini Singh;Karun Rawat
This work presents a new design space of Extended continuous class-F (ECCF) power amplifiers with resistive second harmonic impedance after including the effect of non-linear drain-to-source capacitance $C_{mathbf {ds}}~_{mathbf {}}$ of a transistor. The expression of current waveforms is modified to include the impact of nonlinear drain to source capacitance in this mode. The analysis shows that this non-linear capacitance generates harmonic current, which alters the load trajectory on the Smith chart by achieving active and modified passive second harmonic loads. These active harmonic loads at the current reference plane of the transistor represent an active harmonic injection that increases the drain efficiency. Consequently, a design methodology is proposed to obtain passive loads for matching that ensures this active harmonic injection at the current reference plane of the transistor provides an efficiency improvement in the ECCF mode while maintaining the operation more than the octave frequency range. The proposed theory is validated by designing a power amplifier operating from 0.8-3.0 GHz (115.7% fractional bandwidth) with a measured drain efficiency of 57.24-70.3%, and an output power of 41.7-44.63 dBm. The power amplifier is also tested with modulated signals and linearized using digital predistortion to qualify spectral mask with a measured (Error Vector Magnitude) EVM of 1.54%.
本文在考虑晶体管非线性漏源电容$C_{mathbf {ds}}~_{mathbf{}}$的影响后,提出了一种具有电阻性二次谐波的扩展连续f类(ECCF)功率放大器的新设计空间。对电流波形的表达式进行了修改,以包括该模式下非线性漏极对源电容的影响。分析表明,这种非线性电容产生谐波电流,通过实现主动和修正被动二次谐波负载,改变了史密斯图上的负载轨迹。晶体管电流参考平面上的有源谐波负载代表有源谐波注入,从而提高漏极效率。因此,提出了一种设计方法来获得用于匹配的无源负载,以确保晶体管电流参考平面上的有源谐波注入在ECCF模式中提供效率提高,同时保持工作频率超过倍频程范围。通过设计工作在0.8-3.0 GHz(115.7%分数带宽)范围内的功率放大器,验证了该理论,测量漏极效率为57.24-70.3%,输出功率为41.7-44.63 dBm。对功率放大器进行了调制信号测试,并使用数字预失真进行线性化,以获得测量的(误差矢量幅度)EVM为1.54%的频谱掩模。
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引用次数: 0
Data-Driven Fault-Tolerant Control Framework for EV Dynamic Wireless Power Transfer System Based on Self-Learning Predictor 基于自学习预测器的电动汽车动态无线输电系统数据驱动容错控制框架
IF 5.2 1区 工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2025-08-18 DOI: 10.1109/TCSI.2025.3597288
Jiawang Yue;Zhitao Liu;Hongye Su
This paper aims to develop a constant output voltage controller for dynamic wireless power transfer systems(DWPTSs) incorporating sensor noise filtering and fault tolerance. DWPTSs are designed to alleviate range anxiety in electric vehicles(EVs); however, the output voltage fluctuations are their significant drawback compared to static charging mode. Additionally, DWPTSs also face sensor measurement noise and potential faults that exacerbate system instability. To mitigate above challenges, a data-driven fault-tolerant control framework is designed for DWPTS based on a self-learning predictor, which implements constant voltage regulation with enhanced noise and fault immunity. Specifically, a self-learning predictor is integrated into the feedforward loop of a high-gain extended state observer (ESO) to filter sensor noise. Then, a data memory stack is constructed to store predicted states and estimated disturbances, and a concurrent learning algorithm is introduced to recover control gains online. Finally, a composite anti-disturbance control law is implemented to generate the required control signals for the charging circuit. A notable advantage of this scheme is its ability to simultaneously address both sensor noise and faults, ensuring a constant output voltage during EV driving. Experimental results validate that the designed control framework effectively eliminates output voltage fluctuations and measurement noise, even in the presence of sensor faults.
本文旨在开发一种结合传感器噪声滤波和容错功能的动态无线电力传输系统恒输出电压控制器。dwpts旨在缓解电动汽车(ev)的里程焦虑;然而,与静态充电模式相比,输出电压波动是其显著的缺点。此外,dwpts还面临传感器测量噪声和潜在故障,加剧了系统的不稳定性。为了缓解上述挑战,基于自学习预测器为DWPTS设计了一个数据驱动的容错控制框架,该框架实现了恒电压调节,增强了噪声和故障抗扰性。具体而言,将自学习预测器集成到高增益扩展状态观测器(ESO)的前馈回路中,以滤波传感器噪声。然后,构建数据存储栈来存储预测状态和估计干扰,并引入并发学习算法来在线恢复控制增益。最后,采用复合抗干扰控制律生成充电电路所需的控制信号。该方案的一个显著优点是能够同时解决传感器噪声和故障,确保电动汽车行驶过程中的恒定输出电压。实验结果验证了所设计的控制框架能够有效地消除输出电压波动和测量噪声,即使在传感器存在故障的情况下也是如此。
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引用次数: 0
A Flexible Impedance Modeling Method and Stability Analysis Toward the Cascaded Solid-State Transformer 级联固态变压器柔性阻抗建模方法及稳定性分析
IF 5.2 1区 工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2025-08-14 DOI: 10.1109/TCSI.2025.3586143
Sicong Jin;Xin Zhang;Dehong Xu
The cascaded solid-state transformer (SST) has garnered significant attention in recent years due to its modular advantages, offering improved scalability, efficiency, and fault-tolerant capabilities. However, the modeling of N-module cascaded SSTs and their impedance characteristics remains insufficiently explored, which could hinder the reliable integration of SSTs. To address this issue, this paper proposes a matrix-based modeling method to characterize the N-module SST and establish its corresponding impedance model. A universal module equivalent block diagram, accounting for arbitrary-order harmonic disturbances, is constructed through an initial matrix aggregation. Building upon this, a second matrix aggregation is performed to develop a system-wide equivalent block diagram, which accommodates any combination of modules, thus enabling standardized representation and modular expansion of the N-module SST. Based on the system equivalent block diagram, a transfer-matrix-based method is used to flexibly compute the SST impedance expression. Using the derived impedance model, the impact of factors such as module differences, operating conditions, and hardware parameters on port impedance is discussed. The influence of these factors on overall system stability is also discussed. Finally, the accuracy and validity of the impedance model, along with the related stability analysis, are verified through a hardware-in-the-loop (HIL) experimental setup.
近年来,级联固态变压器(SST)由于其模块化优势,提供了更好的可扩展性、效率和容错能力,引起了人们的极大关注。然而,对于n模块级联SSTs的建模及其阻抗特性的研究仍然不够充分,这可能会阻碍SSTs的可靠集成。针对这一问题,本文提出了一种基于矩阵的建模方法来表征n模海表温度,并建立相应的阻抗模型。通过初始矩阵聚合,构造了考虑任意阶谐波干扰的通用模块等效方框图。在此基础上,执行第二次矩阵聚合以开发系统范围内的等效框图,该框图可容纳模块的任何组合,从而实现n模块SST的标准化表示和模块化扩展。在系统等效方框图的基础上,采用基于传递矩阵的方法灵活地计算海温阻抗表达式。利用导出的阻抗模型,讨论了模块差异、工作条件和硬件参数等因素对端口阻抗的影响。讨论了这些因素对系统整体稳定性的影响。最后,通过硬件在环(HIL)实验装置验证了阻抗模型的准确性和有效性,以及相关的稳定性分析。
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引用次数: 0
Impact of Bifurcations on the Performance of Power Electronic Circuits 分岔对电力电子电路性能的影响
IF 5.2 1区 工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2025-08-14 DOI: 10.1109/TCSI.2025.3595507
Hiroyuki Asahara;Kuntal Mandal;Hiroki Akiba;Nobuyuki Kasa;Takuji Kousaka
This paper investigates the impact of bifurcations on the performance of power electronic circuits. We focus on circuits that include energy-harvesting devices, which exhibit a maximum power point (MPP). In particular, a DC–DC converter with a photovoltaic (PV) module is considered a representative example of such systems to evaluate the relationship between the circuit performance indices (such as power conversion and maximum power point tracking (MPPT) efficiency) and the bifurcation phenomena observed in the system. First, experimental results are reported that evaluate circuit characteristics and performance under MPPT control. Then, a novel mathematical PV model is presented and fully defined using experimentally measured parameters; this model does not necessitate the use of root-finding algorithms. Next, this model is integrated with the switched nonlinear model of a DC–DC converter subject to peak current mode control (PCMC), and a stability analysis of the periodic orbits is performed. Finally, the relationship between circuit performance and observed bifurcation phenomena is investigated and discussed. This research demonstrates the occurrence of both period-doubling and Neimark–Sacker bifurcations in the system considered here, and these features are shown in a two-parameter bifurcation diagram.
本文研究了分岔对电力电子电路性能的影响。我们专注于包含能量收集装置的电路,它具有最大功率点(MPP)。特别是,带有光伏(PV)模块的DC-DC变换器被认为是此类系统的代表性示例,以评估电路性能指标(如功率转换和最大功率点跟踪(MPPT)效率)与系统中观察到的分岔现象之间的关系。首先,报告了在MPPT控制下的电路特性和性能的实验结果。然后,提出了一种新的PV数学模型,并利用实验测量参数对其进行了充分定义;这个模型不需要使用寻根算法。然后,将该模型与峰值电流模式控制(PCMC)下的DC-DC变换器的开关非线性模型相结合,进行周期轨道的稳定性分析。最后,对电路性能与观察到的分岔现象之间的关系进行了研究和讨论。本研究证明了在本文所考虑的系统中存在倍周期分岔和neimmark - sacker分岔,这些特征用双参数分岔图表示。
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引用次数: 0
A 5.3-W 83.7% Peak Efficiency Simultaneous Wireless Power and Data Transfer IC Enabling 10–9 BER 540-kb/s Data Rate or Output Voltage Regulation 一种峰值效率为83.7%的5.3 w同步无线电源和数据传输IC,支持10-9 BER 540-kb/s数据速率或输出电压调节
IF 5.2 1区 工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2025-08-08 DOI: 10.1109/TCSI.2025.3595804
Alessandro Liotta;Elisabetta Moisello;Giovanni Frattini;Pietro Giannelli;Piero Malcovati;Edoardo Bonizzoni
This paper proposes the first simultaneous wireless power and data transfer (SWPDT) integrated circuit (IC) which exploits a Capacitive-Inductive Channel (CI-Channel), enabling concurrent power and data transmission. The communication across the CI-Channel can support data-only transmission or can be incorporated into the system control loop, allowing output voltage regulation through phase-shift control applied at the primary side. The proposed IC can be configured as primary side (power transmitter, P-TX, and data receiver, RX) or secondary side (power receiver, P-RX, and data transmitter, TX). In order to ensure communication robustness, unwanted disturbances are removed through specifically designed Power Blanking and Ringing Blanking circuits. The proposed SWPDT IC test-chip prototype was fabricated using a 130-nm BCD process and experimentally verified considering the complete wireless power transfer (WPT) system, including primary side, CI-Channel and secondary side. The overall system, targeting medium-power industrial applications, achieves a maximum 5.3-W output power, a peak efficiency of 83.7% and a load regulation of 0.09 mV/mA. Moreover, a 540 kb/s data rate with no transmission errors across $10^{9}$ bit acquisitions, corresponding to a bit-error-rate (BER) $lt 10^{-9}$ , was achieved.
本文提出了首个同时无线供电和数据传输(SWPDT)集成电路(IC),该电路利用电容感应通道(CI-Channel),实现了电力和数据的同时传输。跨ci通道的通信可以支持仅数据传输或可以并入系统控制回路,允许通过在初级侧应用相移控制来调节输出电压。建议的IC可以配置为主侧(功率接收器,P-TX和数据接收器,RX)或辅助侧(功率接收器,P-RX和数据发射器,TX)。为了确保通信的鲁棒性,通过特别设计的Power Blanking和ring Blanking电路去除不必要的干扰。提出的SWPDT IC测试芯片原型采用130 nm BCD工艺制作,并考虑完整的无线电力传输(WPT)系统,包括主侧,CI-Channel和二次侧,进行了实验验证。整个系统以中功率工业应用为目标,最大输出功率为5.3 w,峰值效率为83.7%,负载调节为0.09 mV/mA。此外,实现了540 kb/s的数据速率,在$10^{9}$比特采集中没有传输错误,对应于误码率(BER) $lt $10^{-9}$。
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引用次数: 0
Ultralocal Model-Free Logarithmic Sliding-Mode Control for PMSM Angle Robust Tracking With Asymmetric Constraints 非对称约束下永磁同步电机角度鲁棒跟踪的超局部无模型对数滑模控制
IF 5.2 1区 工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2025-08-08 DOI: 10.1109/TCSI.2025.3593415
Zheng Liu;Hanlin Dong;Qianbao Mi;Zhiqiang Ma;Zhaoke Ning;Xudong Wang
This paper primarily introduces a novel prescribed performance control method to achieve rapid and high-precision control in servo systems. Initially, an interesting asymmetric barrier function is proposed, so that the controlled plant with arbitrary initial values can be confined within an asymmetric boundary. To reduce the dependence of controller deployment on physical parameters, an ultralocal model (ULM) approach is adopted and the logarithmic sliding-mode manifold is synthesized to design the controller and observer, resulting in an order-reduced and transient-performance-improved error dynamics. Since there are no non-Lipschitz continuous elements in the logarithmic sliding-mode, the super-twisting algorithm can be used to weaken signal chattering while converging the equivalent error rapidly. The Lyapunov-based direct analysis proves the stability of the controlled servo system with unknown parameters. The superiority of the scheme is verified through a series of simulations and experiments on PMSM platform.
本文主要介绍了一种新的规定性能控制方法,以实现伺服系统的快速、高精度控制。首先,提出了一个有趣的非对称势垒函数,使得具有任意初始值的被控对象可以被限制在一个非对称边界内。为了减少控制器部署对物理参数的依赖,采用超局部模型(ULM)方法,综合对数滑模流形设计控制器和观测器,实现了降阶和瞬态性能改善的误差动力学。由于对数滑模中不存在非lipschitz连续元,超扭转算法可以在快速收敛等效误差的同时减弱信号抖振。基于lyapunov的直接分析证明了未知参数下被控伺服系统的稳定性。通过在永磁同步电机平台上的一系列仿真和实验,验证了该方案的优越性。
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引用次数: 0
Analysis and Design of Load-Independent Class-E Zero-Voltage Switching Power Oscillator 负载无关的e类零电压开关功率振荡器的分析与设计
IF 5.2 1区 工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2025-08-07 DOI: 10.1109/TCSI.2025.3594362
Yutaro Komiyama;Wenqi Zhu;Akihiro Konishi;Kien Nguyen;Hiroo Sekiya
This paper proposes the load-independent class-E Zero-Voltage Switching (ZVS) power oscillator. Conventional class-E power oscillator has a load-dependent phase shift, which hinders sustained oscillation under varying load conditions. Hence, we introduce the class-E power amplifier that ensures the load-independent phase shift in the output current. By incorporating it into an LCLC filter with a resonant-capacitor feedback network, the load-independent self-oscillation is realized. The proposed power oscillator satisfies a phase-shift requirement for sustained oscillation regardless of the load resistance. Furthermore, the proposed circuit exhibits load independence in ZVS, output current, and gate-drive voltage. This paper provides a thorough analysis of the proposed power oscillator, covering its operating principle, power loss prediction, design, and limitations. This paper also gives two design examples with 0.8 MHz and 6.78 MHz oscillation frequencies. In the experiment, the prototype power oscillators achieved 93.8 % and 87.4 % power-conversion efficiencies, respectively. The validity and effectiveness of the proposed power oscillator are demonstrated from the experimental verifications.
提出了一种与负载无关的e类零电压开关(ZVS)功率振荡器。传统的e类功率振荡器具有负载相关的相移,这阻碍了在变负载条件下的持续振荡。因此,我们引入了e类功率放大器,以确保输出电流中的相移与负载无关。通过将其集成到LCLC滤波器中,采用谐振电容反馈网络,实现了与负载无关的自振荡。所提出的功率振荡器满足相移要求,无论负载电阻如何,都能实现持续振荡。此外,所提出的电路在ZVS、输出电流和栅极驱动电压方面具有负载独立性。本文对所提出的功率振荡器进行了全面的分析,包括其工作原理,功率损耗预测,设计和限制。文中还给出了0.8 MHz和6.78 MHz振荡频率的两个设计实例。在实验中,原型功率振荡器的功率转换效率分别达到93.8%和87.4%。实验验证了所提出的功率振荡器的有效性。
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引用次数: 0
A Low-Cost Digital Capacitor Current Estimation Algorithm Based on Parameter Identification for Buck Converter Application 基于参数辨识的低成本Buck变换器数字电容电流估计算法
IF 5.2 1区 工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2025-08-07 DOI: 10.1109/TCSI.2025.3594266
Xin Tong;Zhangyong Chen;Yong Chen;Lehan Xu
In switching converters, capacitor current is a critical feedback parameter due to its ability to rapidly reflect dynamic load variations, making it widely applicable in various control strategies such as current-mode feedback regulation. With the rapid advancement of digital power technology, current detection must be implemented in the digital domain, typically requiring high-bandwidth current sensors and high-speed analog-to-digital converters (ADCs). To address the high-cost challenge associated with capacitor current sampling in digital buck converters, this paper proposes a low-cost digital capacitor current estimation technique based on output voltage information tracking. By analyzing the dynamic characteristics of the output voltage, the method achieves precise estimation of the capacitor current. This paper thoroughly investigates the error issues arising from time constant mismatch in the proposed capacitor current estimation method and introduces an online time constant identification approach based on the output capacitor ( $mathbf {C}_{mathbf {o}}$ ) and its equivalent series resistance (ESR). By dynamically adjusting the estimator parameters, the estimation accuracy is significantly improved. The proposed algorithm is experimentally validated on a buck converter prototype. The results demonstrate that the error in the time constant after identification and correction is controlled within 3%, and the capacitor current estimation accuracy is maintained within 6%.
在开关变换器中,电容电流能够快速反映负载的动态变化,是一个重要的反馈参数,广泛应用于电流型反馈调节等各种控制策略中。随着数字电源技术的快速发展,电流检测必须在数字领域实现,通常需要高带宽电流传感器和高速模数转换器(adc)。针对数字降压变换器中电容电流采样的高成本问题,提出了一种基于输出电压信息跟踪的低成本数字电容电流估计技术。该方法通过分析输出电压的动态特性,实现了对电容电流的精确估计。本文深入研究了电容电流估计方法中时间常数不匹配引起的误差问题,并介绍了一种基于输出电容($mathbf {C}_{mathbf {o}}$)及其等效串联电阻(ESR)的在线时间常数识别方法。通过动态调整估计器参数,显著提高了估计精度。该算法在降压变换器样机上进行了实验验证。结果表明,经辨识校正后的时间常数误差控制在3%以内,电容电流估计精度保持在6%以内。
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引用次数: 0
Achieving < ±25 ppb Frequency Stability With a ±0.125 °C Oven Control on a Si Interposer for an AlScN-on-Si Shear-BAW Resonator 在用于AlScN-on-Si剪切- baw谐振器的Si中间体上,在±0.125°C的烤箱控制下实现<±25 ppb的频率稳定性
IF 5.2 1区 工程技术 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC Pub Date : 2025-08-04 DOI: 10.1109/TCSI.2025.3590669
Everestus Ezike;Ratul Kundu;Shaurya Dabas;Banafsheh Jabbari;Shruti Mishra;Dicheng Mo;Honggyu Kim;Zetian Mi;Roozbeh Tabrizian;Baibhab Chatterjee
A major challenge of long-term clock stability is frequency drift due to temperature variations. This paper describes the design of a proportional, integral, derivative (PID) control system for external ovenization of an AlScN-on-Si Shear-BAW Resonator (S3R), which has a fixed turnover temperature where the $1{^{text {st}}}$ order temperature coefficient of frequency is $approx 0$ ppm/°C. The control system provides $pm ~0.125^{circ }$ C temperature stability and assists in achieving better than $pm ~25$ ppb frequency stability over a temperature range of 15-40°C by maintaining resonator operation near the turnover temperature, where the $2{^{text {nd}}}$ order temperature coefficient of frequency drift is -62.71ppb/°C2. The robust and adaptive PID algorithm (programmed on an external microcontroller unit connected to the interposer) ensures continuous ovenization by configuring the duty cycle of a compact heat actuator (powerMOS) that is placed in <3.5mm> $times 2$ mm resonator and a complementary to absolute temperature sensor (implemented as a 1mm $times 1$ mm, 65nm integrated circuit), that are all held on a thermally conductive 7mm $times$ 7mm Si interposer.
长期时钟稳定性的一个主要挑战是由于温度变化引起的频率漂移。本文描述了一种用于AlScN-on-Si剪切- baw谐振器(S3R)外部烘箱的比例、积分、导数(PID)控制系统的设计,该系统具有固定的翻转温度,其中$1{^{text {st}}}$阶频率温度系数$ $约为0$ ppm/°C。控制系统提供$pm ~0.125^{circ}$ C的温度稳定性,并有助于在15-40°C的温度范围内实现优于$pm ~25$ ppb的频率稳定性,通过保持谐振器在周转温度附近工作,其中$2{^{text{和}}}$阶频率漂移温度系数为-62.71ppb/°C2。鲁棒和自适应PID算法(在连接到中间层的外部微控制器单元上编程)通过配置紧凑型热致动器(powerMOS)的占空比来确保连续烘烤,该致动器放置在$times 2$ mm谐振器中,并补充绝对温度传感器(实现为1mm $times 1$ mm, 65nm集成电路),所有这些都保持在导热7mm $times 7mm Si中间层上。
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