Adaptive synchronous rectification (SR) is a good solution to solve duty cycle loss for resonant converter. Usually, whether the synchronous rectifier is turned OFF prematurely or late can be detected by whether the body diode is conducted on or not. However, when the switching frequency is below the resonant frequency, both SR turning-OFF prematurely and late may generate body diode conduction (BDC), which will cause logic errors in the conventional adaptive SR strategy. Then, a large reverse current from load to source will occur, which damages the efficiency. To solve the problem, the time-domain modeling of the SR drain-tosource voltage is established to analyze the mechanism of BDC caused by SR turning-off late. Moreover, an improved adaptive SR driving scheme is proposed, which can identify the two different types of BDC and tune SR to be turned OFF exactly. Finally, a prototype is built to verify the established model and the proposed SR method. The prototype proves that both the duty cycle loss and the reverse current are eliminated and efficiency improvement of is achieved. 自适应同步整流（SR）是解决 谐振变换器占空比损耗的良好解决方案。通常，同步整流器是否过早关闭或延迟关闭可以通过体二极管是否导通来检测。然而，当开关频率低于谐振频率时，SR过早关断和过晚关断都可能产生体二极管导通（BDC），这将导致传统自适应SR策略中的逻辑误差。然后，从负载到电源会产生较大的反向电流，从而损害效率。针对该问题，建立了SR漏源电压的时域建模，分析了SR晚关断导致BDC的机理。此外，该文还提出了一种改进的自适应SR驱动方案，该方案可以识别两种不同类型的BDC，并精确地调谐SR的关闭。最后，构建原型 对已建立的模型和所提出的SR方法进行验证。该原型证明了消除了占空比损耗和反向电流，并实现了效率的 提高。
Index Terms-Adaptive synchronous rectification, body diode conduction (BDC), efficiency optimization, high frequency, resonant converter, reverse current, ZCS. 索引术语-自适应同步整流、体二极管导通 （BDC）、效率优化、高频、 谐振转换器、反向电流、ZCS。
I. INTRODUCTION 一、引言
ECENTLY, the rapid development of information technology has increased the demand for high-power-density power supplies. Thus, the requirement for both the switching frequency and efficiency are becoming higher and higher. As shown in Fig. 1, LLC resonant converter with synchronous rectification is an excellent candidate for high-frequency and high-efficiency applications due to the features of achieving 实际上，信息技术的快速发展增加了对高功率密度电源的需求。因此，对开关频率和效率的要求越来越高。如图1所示，具有同步整流功能的LLC谐振转换器是高频和高效率应用的绝佳候选者，因为它具有以下特点：
Fig. 1. LLC resonant converter with synchronous rectification. 图 1.具有同步整流功能的LLC谐振转换器。
zero voltage switching (ZVS) for primary switches and zero current switching (ZCS) for secondary switches [1]-[4]. The performance of synchronous rectification is one of the keys to improving efficiency. However, as the switching frequency increases, the duty cycle loss caused by stray inductance is more and more serious [5]. The conventional sensing based scheme is no longer suitable for high-frequency applications. Research on high-frequency SR strategies is becoming more and more important. 初级开关为零电压开关（ZVS），次级开关为零电流开关（ZCS）[1]-[4]。同步整流的性能是提高效率的关键之一。然而，随着开关频率的增加，杂散电感引起的占空比损耗越来越严重[5]。传统的 基于传感的方案不再适用于高频应用。对高频SR策略的研究变得越来越重要。
Over the last few years, the synchronous rectification of resonant converter can be classified into: current sensing based method [6]-[11]; sensing based method [12]-[19]; primaryside voltage sensing-based method [20], [21]; and the adaptive driving method [5], [22]-[30]. 近几年来，谐振变换器的同步整流 可分为：基于电流检测的方法[6]-[11]; 基于传感的方法[12]-[19];基于初级侧电压检测的方法[20]，[21];以及自适应驾驶方法[5]，[22]-[30]。
A. Current Sensing-Based Method A. 基于电流检测的方法
Sampling the zero-crossing point of (the current through the synchronous rectifier) to generate the driving signals is the most direct SR solution [6]-[9]. However, sensing the secondary-side current will result in large sampling loss and volume, which is unacceptable. As shown in Fig. 2, the improved method is the indirect current sensing-based scheme. By sensing the resonant inductor current and magnetizing inductor current and comparing between two current signals, the driving signal for SR can be generated. In the literature [10], the resonant current is sampled by a current transformer, and the magnetizing current is obtained by the integration of the voltage across the transformer. In the literature [11], an external inductor is paralleled with the magnetizing inductance and 对过零点 （通过同步整流器的电流）进行采样以产生驱动信号是最直接的SR解决方案[6]-[9]。然而，检测次级侧电流将导致较大的采样损耗和体积，这是不可接受的。如图2所示，改进的方法是基于间接电流检测的方案。通过检测谐振电感电流和磁化电感电流，并比较两个电流信号，可以生成SR的驱动信号。在文献[10]中，谐振电流 由电流互感器采样，并通过对变压器两端的电压进行积分来获得磁化电流。在文献[11]中，外部电感器 与磁化电感 并联，并且
Fig. 2. Current sensing-based SR strategy. 图 2.基于电流检测的SR策略。
is much smaller than . Thus, the magnetizing current flows through the external inductor, which can be sampled to drive SR. The drawbacks of these indirect strategies are that the sensing loss is still considerable; the current transformer introduces the additional volume; the isolation performance is degraded; and the parameter deviation will seriously affect the performance of synchronous rectification. 比 小得多。因此，磁化电流流过外部电感器，可以对外部电感器进行采样以驱动SR。这些间接策略的缺点是传感损失仍然相当大;电流互感器引入额外的体积;隔离性能下降;参数偏差会严重影响同步整流的性能。
B. VDS Sensing-Based Method B. 基于VDS传感的方法
In the literature [12], is sampled and converted to the signal through a well-designed impedance network. The method owns the ultralow-cost but is sensitive to the switching frequency. sensing based method is widely applied in the smart driver integrated circuits(ICs) [13], [14] due to the feature of low sensing loss. While for the high-frequency resonant converter, di/dt of the secondary-side current increases drastically, which enlarges the duty cycle loss (see Fig. 3) caused by the stray inductance [15]. The compensation scheme [13], [15]-[19] is especially important for high-frequency applications. 在文献[12]中， 通过精心设计的阻抗网络进行采样并转换为 信号。该方法具有超低成本，但对开关频率敏感。 基于传感的方法由于具有低传感损耗的特点，在智能驱动集成电路（IC）中得到了广泛的应用[13]，[14]。而对于高频 谐振转换器，次级侧电流的di/dt急剧增加，这扩大了由杂散电感引起的占空比损耗（见图3）[15]。补偿方案[13]、[15]-[19]对于高频应用尤为重要。
In the literature [15], an active RC compensation network is designed to sense the actual voltage on . In the literature [16], two switches are simplified in the compensation network with no change of performance. In the literature [13], [17], a well-designed inductor is in series at the source terminal to balance the phase leading generated by the equivalent series inductance(ESL). In the literature [18], the gate drive voltage is deliberately reduced before SR turning-OFF to increase . Then, the early turning-OFF problem caused by ESL can be relieved. In the literature [19], the same effect is achieved through different drive timings for parallel MOSFET to relieve duty cycle loss. These methods can compensate for the influence 在文献[15]中，有源RC补偿网络被设计用于检测上 的实际电压。在文献[16]中，在补偿网络中简化了两个开关，性能没有变化。在文献[13]、[17]中，在源端串联了一个设计良好的电感器，以平衡等效串联电感（ESL）产生的相位超前。在文献[18]中，在SR关断之前故意降低栅极驱动电压以增加 。然后，可以缓解 ESL 导致的早期关闭问题。在文献[19]中，通过不同的并联MOSFET驱动时序可以达到相同的效果，以减轻占空比损耗。这些方法可以补偿影响
Fig. 4. Adaptive SR strategy proposed in [5]. 图 4.[5]中提出的自适应SR策略。
of stray inductance to reduce duty cycle loss at the cost of circuit complexity. However, the parameters such as the stray inductance and should be extracted and the performance of compensation depends sensitively on the accuracy of these extracted parameters. Moreover, it is difficult to design a compensator suitable for all working conditions, since varies at different temperatures. 的杂散电感，以降低占空比损耗，但代价是电路复杂性。然而， 杂散电感等参数和补偿性能敏感地取决于这些提取参数的精度。此外，由于 在不同温度下会有所不同，因此很难设计出适合所有工作条件的补偿器。
C. Primary-Side Voltage Sensing-Based Method C. 基于初级侧电压检测的方法
Based on the operation principles of the resonant converter, SR only conducts during operation stage. Therefore, the SR driving signal can be generated by the recognition of operation stage [31], which can be obtained by sampling the primary-side voltage. In the literature [20], the polarities of the half-bridge midpoint voltage and the voltage of the transformer are sampled and compared to determine operation stage. In the literature [21], the sampled resonant capacitor voltage is integrated and compared with both input and output voltage to determine operation stage. The two methods can significantly reduce the sampling loss and immune to the high-frequency noise. 根据 谐振变换器的工作原理，SR仅在 工作阶段导通。因此，SR驱动信号可以通过 识别工作级[31]产生，该信号可以通过对初级侧电压进行采样来获得。在文献[20]中，对半桥中点电压和变压器电压的极性进行采样和比较，以确定 工作阶段。在文献[21]中，对采样谐振电容电压 进行积分，并与输入和输出电压进行比较，以确定 工作级。这两种方法都能显著降低采样损耗，不受高频噪声的影响。
D. Adaptive SR Driving Method D. 自适应SR驱动方式
The adaptive SR driving scheme introduces the concept of closed-loop to thoroughly eliminate duty cycle loss. The gate driver signal of the current cycle is tuned by the sensed turning. OFF status of the previous cycle. 自适应SR驱动方案引入了闭环概念，彻底消除了占空比损耗。电流周期的栅极驱动器信号由感测的律速进行调谐。上一个周期的 OFF 状态。
The features of the body diode conduction (BDC) are used to identify whether SR is turned OFF prematurely or late. As shown in Fig. 4, a universal adaptive driving scheme is proposed in the literature [5], where the turning-OFF point lags when BDC is detected and leads when BDC does not occur. In the literature [22], the adaptive driving scheme is applied to the low-cost microcontroller through multi-cycle adjustment. In the 体二极管传导 （BDC） 的特征用于识别 SR 是过早关闭还是延迟关闭。如图4所示，文献[5]提出了一种通用的自适应驱动方案，其中当检测到BDC时，律断点滞后，当BDC不发生时，律断点领先。文献[22]中，自适应驱动方案通过多周期调整应用于低成本微控制器。在
Fig. 5. BDC caused by SR turning-OFF late. 图 5.SR 关闭延迟导致的 BDC。
literature [23], the body diode information is sensed to add delay to eliminate the duty cycle loss. In the literature [25], the regulation of turning-OFF point is achieved by the regulation of the turning-OFF voltage threshold and multilevel thresholds are set to ensure fast and accurate regulation. In the literature [26], an analytic-adaptive SR strategy is proposed for improving the transient-state performance. The dual verification strategy for SR turning-OFF is proposed in [27] to regulate the proper turning-OFF point of SR. 文献[23]中，体二极管信息被检测以增加延迟以消除占空比损耗。文献[25]中，通过调节关断电压阈值来实现关断点的调节，并设置多级阈值，确保快速准确的调节。文献[26]提出了一种分析自适应SR策略来改善瞬态性能。文献[27]提出了SR关断的双重验证策略，以规范SR的正确关断点。
With the development of these years, adaptive SR strategy has gradually been accepted by the industry. Several IC products [28]-[30] have adopted the concept to solve the duty cycle loss. Meanwhile, with the development of the performance of the lowcost microcontrollers, it will become more and more popular to use adaptive SR strategies to solve the high-frequency SR problems. 随着这些年的发展，自适应SR策略逐渐被业界所接受。一些IC产品[28]-[30]采用了这一概念来解决占空比损耗问题。同时，随着低成本微控制器性能的发展，使用自适应SR策略解决高频SR问题将越来越流行。
The similarity of these adaptive schemes is that sensing BDC to identify the turning-OFF information of the current cycle and BDC represents that SR turns OFF prematurely. As shown in Fig. 5, when the SR turns OFF late, the reverse current will charge the junction capacitance, and the subsequent resonance process will also cause BDC [24]. In other words, both turning-OFF prematurely and late will lead to the conduction of the body diode. If the detected BDC is caused by SR turning-OFF late, the control logic in [5] and [22] will be reversed, causing a large reverse current from the load to the source. 这些自适应方案的相似之处在于，感应 BDC 以识别当前周期的关断信息，而 BDC 表示 SR 过早关闭。如图5所示，当SR关断较晚时，反向电流将对结电容充电，随后的谐振过程也会引起BDC[24]。换言之，过早关断和过晚关断都会导致体二极管导通。如果检测到的BDC是由SR关断较晚引起的，则[5]和[22]中的控制逻辑将反转，从而导致从负载到电源的反向电流很大。
In this article, the issue of BDC caused by turning-OFF late is analyzed quantitatively through the model for sr during the dead-time. Moreover, an improved adaptive SR strategy is proposed to distinguish the two different types of BDC and to take the corresponding measures to regulate the turning-OFF point. The proposed method can solve the problems of the reverse current from load to the source caused by SR turning-OFF late. Meanwhile, the proposed method is fully compatible with the conventional adaptive SR strategy. 本文通过死区 期间sr模型定量分析了延迟关断导致的BDC问题。此外，提出了一种改进的自适应SR策略来区分两种不同类型的BDC，并采取相应的措施来调节关断点。该方法可以解决SR关断较晚导致负载到电源的反向电流问题。同时，所提方法与传统的自适应SR策略完全兼容。
This article is structured as follows. The time-domain model between the drain-source voltage sr of SR and the reverse current is established in Section II. Then, the generation mechanism and the condition of BDC caused by turning-OFF late are discussed quantitatively. In Section III, the sampling circuits and the control logic of the proposed adaptive SR strategy are described. The sampling circuits are simple and low-loss, 本文的结构如下。第二节建立了SR漏源电压 sr与反向电流 之间的时域模型。然后，定量讨论了延迟关断导致的BDC的产生机理和情况;在第III节中，描述了所提出的自适应SR策略的采样电路和控制逻辑。采样电路简单，损耗低，
Fig. 6. Definition of the symbol of the related voltage and current. 图 6.相关电压和电流符号的定义。
while the control logic is compatible with the conventional adaptive SR strategy. A comparison of different SR driving schemes is presented in Section IV. Finally, the experimental results and the conclusion are given in Sections V and VI, respectively 而控制逻辑与传统的自适应SR策略兼容。第四节介绍了不同SR驱动方案的比较。最后，实验结果和结论分别在第五节和第六节给出
II. ISSUE OF BDC CAUSED BY SR TURNING-OFF LATE II. SR关闭延迟导致的BDC问题
In this section, the principle of the BDC after turning OFF late will be analyzed. Since this type of BDC only occurs at the condition of , the other two conditions are not discussed in this section, but will be covered in the following section. For the convenience of the effective presentation, the symbol of the related voltage and current are defined as follows. 在本节中，将分析延迟关闭后BDC的原理。由于这种类型的 BDC 仅在 的条件下发生，因此本节不讨论其他两个条件，但将在下一节中介绍。为了便于有效显示，相关电压和电流的符号定义如下。
Resonant current . 谐振电流 。
Magnetic current . 磁电流 。
Midpoint voltage of the half bridge . 半桥 的中点电压。
Drain-source voltage of the synchronous rectifier . 同步整流器 的漏源电压。
Voltage across the transformer . 变压器 两端的电压。
Voltage across the resonant capacitor . 谐振电容两端的电压 。
As shown in Fig. 6, the positive directions of and are from to and from to , respectively. The positive directions of , and pri are from to , from to , and from a to d. 如图 6 所示，和 的 正方向分别为 from to 和 from to 。和 pri 的 正方向是 from to 、from to 和 from a to d。
Fig. 7 shows the main voltage and current waveform during the dead-time when . There are three stages before the BDC. The equivalent circuits of these stages are shown in Fig. 8 . 图 7 显示了死区期间 的主要电压和电流波形。BDC 之前有三个阶段。这些级的等效电路如图8所示。
Stage : At , the resonant current equals the magnetic current and the current through decreases to 0 . Since is still , keeps falling to the negative. The current is transferring from the load to the source. During this stage, .sr is slightly larger than 0 and is clamped to be . At , this stage ends when is turned OFF. 阶段 ：在 时，谐振电流 等于磁电流 ，通过 的电流减小到 0。由于 是静止 的， 所以一直下降到负数。电流从负载传递到电源。在此阶段， .sr 略大于 0，并被 钳制为 。在 时，此阶段在关闭时 结束。
Stage : After is turned OFF, the reversed charges the junction capacitance of , causing .sr to rise. The amplitude of gradually decreases as increases. When returns reaches the peak value of this stage. At this time, equals to . This is a multiresonance process composed of the four energy storage devices , and . Then, 'sr will continue to decrease and may cause the at the lowest point (shown as the red dashed circle in Fig. 7). As shown in Fig.9, the simplified equivalent circuits of stage 阶段 ：关断后 ，反向 充电的结电容 ，导致 .sr上升。的 振幅随着 的增加而逐渐减小。当回报 达到此阶段的峰值时 。此时， 等于 .这是一个由四个储能装置 组成的多谐振过程 。然后，'sr 将继续减小， 并可能导致最低点（ 如图 7 中的红色虚线圆圈所示）。如图9所示，简化后的平台等效电路
Fig. 7. Main waveforms during the dead-time when . 图 7.死区期间 的主要波形。
2 can be obtained by converting the junction capacitance of the synchronous rectifier to the primary side. 2可以通过将同步整流器的结电容转换为初级侧来获得。
Based on Kirchhoff's law, the Time-Domain Equations of this stage can be obtained that 根据基尔霍夫定律，可以得到这个阶段的时域方程
where is the sum of the primary-side parasitic capacitance of the transformer and the equivalent junction capacitance converted from the synchronous rectifier. The voltage of can be represented by the voltage across . 其中 ，变压器的初级侧寄生电容与从同步整流器转换而来的等效结电容之和。的 电压可以用两端 的电压来表示。
Through Laplace transformation, (1) can be transformed into 通过拉普拉斯变换，（1）可以转化为
Then, can be represented that 那么， 可以表示为
where , and are the coefficients related to the initial values of the voltage and current and can be represented that 其中 ， 和 是与电压和电流的初始值相关的系数，可以表示为
where and are the constant related to the resonant parameters and can be represented that 其中 和 是与谐振参数相关的常数，可以表示为
The time-domain equation of can be obtained by inverse Laplace transformation 的 时域方程可以通过逆拉普拉斯变换得到
where and are the angular frequency resonated by , , and and can be represented that 其中 和 是角 频率共振 ， 和 可以表示为
According to the actual parameters of several hundred resonant converters, is a relatively large value, the order of magnitudes is about , which represents the oscillation frequency of is a relatively small value, the order of magnitudes is about , which represents the envelope frequency of the during the dead-time. 根据几百 个谐振转换器的实际参数， 是一个比较大的值，数量级约为 ，这代表振荡频率的 是一个比较小的值，数量级约为 ，代表死区 期间的包络频率。
The relationship between and the initial voltage and current value of this stage can be obtained by simplifying (7). 该级的初始电压电流值与初始电压电流值之间的关系 可以通过简化（7）得到。
Fig. 9. Equivalent circuits of each stage before BDC 图 9.BDC之前各级的等效电路
Eq. (9) shown at the bottom of this page, where , , and are the constant only related to , and and can be represented that 式（9）显示在本页底部，其中 、 和 是仅与 相关的常数，并且 可以表示为
The condition for the of Is That resonates to below - diode. Equivalently, Should Meet the requirement that 的 条件是 谐振到二 极管下方。等效地， 应满足以下要求
Fig. 10 shows the waveform of at different reverse current. The black line represents the condition of no reverse current, the blue line represents little reverse current and the boundary condition of BDC, and the black line represents the condition of large reverse current and BDC. It can be deduced from Fig. 10 that a) Since is much smaller than , the influence of component on is much smaller than the component within one or two oscillation periods. 图10显示了不同反向电流 下的波形。黑线表示无反向电流的状况，蓝线表示小反向电流和BDC的边界条件，黑线表示大反向电流和BDC的状况。从图10可以推断出，a）由于 远小于 ，在一两个振荡周期内， 分量对 分 量的影响远小于该分量。
b) The component makes gradually increase. If the first valley value of sr cannot satisfy the condition of , the body diode will not be conducted. b） 组件逐渐 增加。如果 sr 的第一个谷值不能满足 的 条件，则体二极管将不导通。
c) Increasing the reverse current will enlarge the magnitude of . If the reverse current is large enough, the effect of component on increasing can be balanced, and then the first valley value of sr may satisfy the condition of BDC (red line). c） 增加反向电流 将扩大 的大小。如果反向电流足够大， 则可以平衡分量对增加 的影响，然后 sr的第一谷值可以满足BDC（红线）的条件。
d) This type of BDC cannot be generated from SR turningOFF early or exactly. Therefore, the two types of BDC are mutually exclusive, which is one of the bases for the proposed SR control strategy. d） 此类型的 BDC 无法提前或完全从 SR 关闭生成。因此，两种类型的BDC是相互排斥的，这是所提出的SR控制策略的基础之一。
Stage : If is turned ofF before reaches the valley value, stage 3 will occur. Stage 3 is a special case, which usually occurs when the switching frequency is slightly smaller than the resonant frequency. Under this circumstance, there is not enough time for to 阶段 ：如果 在达到谷值之前 转动F，则将发生阶段3。第 3 级是一种特殊情况，通常发生在开关频率略小于谐振频率时。在这种情况下，没有足够的时间进行
Fig. 10. sr waveform versus different reverse currents . 图 10. SR 波形与不同反向电流的关系。
complete one oscillation cycle, and the primary-side is turned OFF. 完成一个振荡周期，初级侧 关闭。
When is turned OFF, pri drops rapidly, and the equivalent circuit of this stage is shown in Fig. 11. Based on Kirchhoff's law, the time-domain equations of stage 3 can be obtained that 当关闭时 ， pri迅速下降，该级的等效电路如图11所示。根据基尔霍夫定律，可以得到第 3 阶段的时域方程：
The differences between (12) and (1) are that is replaced with . Similar to the derivation process of stage 2, the time-domain equation of for stage 3 can be obtained that (13) shown at the bottom of this page, where and are the angular frequency resonated by , and and can be represented that (14) shown at the bottom of this page. （12） 和 （1） 之间的区别是 替换为 。与阶段 2 的推导过程类似，阶段 3 的 时域方程可以得到 （13） 显示在本页底部，其中 和 是 和 共振的角频率，并且可以表示为 （14） 显示在本页底部。
The differences between (14) and (8) are that is replaced with '. Based on the numeral calculation, both and are the relatively large values when compared with the switching frequency and will change the value of rapidly during stage 3. （14）和（8）的区别是 用 '.根据数值计算，两者 和 的值都是比较大的，与开关频率相比，在阶段3期间的值会 迅速变化。
Where , and are the constant that is similar to (10) (the only difference is that is replaced with ') and can be represented that 其中 ， 和 是类似于 （10） 的常数（唯一的区别是 用 '代替），可以表示为
Fig. 12 shows the comparison of sr between stages 2 and 3 . The waveforms of the different 'sr separate when is turned OFF. The effect of stage 3 is to enlarge the resonant frequency of . 图 12 显示了阶段 2 和阶段 3 之间的 sr 比较。不同 'sr 的波形在关闭时 分开。第 3 阶段的作用是放大 的 谐振频率。
Based on the established model and the numerical calculation verification, if turns OFF during the fall of sr , the possibility of BDC will be strengthened [see Fig. 12(a)]; if turns OFF during the rise of , the trend of BDC will be reduced [see Fig. 12(b)]. In any case, the later the SR is turned ofF, the larger the reverse current and the more possible reverse BDC will occur. 根据已建立的模型和数值计算验证，如果 在 sr下降期间关闭，则BDC的可能性将得到加强[见图12（a）];如果 在上升 期间关闭，则BDC的趋势将减少[见图12（b）]。无论如何，SR越晚被调到F，反向电流越大，发生反向BDC的可能性就越大。
Based on the analysis above, one of the necessary conditions for reverse BDC is , because sufficient time is required to make drop below diode after SR turning-OFF. Another necessary condition is that SR is turned OFF late and reverse current ( ) should have sufficient value. As shown in Fig. 13, the status of with SR can be divided into the following four situations. 基于上述分析，反向BDC的必要条件之一是 ，因为在SR关断后，需要足够的时间使 二极管降至二极管以下 。另一个必要条件是 SR 关闭较晚，并且反向电流 （ ） 应具有足够的值。如图13所示，带有SR的 状态可分为以下四种情况。
(b) （二）
Fig. 12. Effect of stage 3 (a) strengthening and (b) weakening the trend of BDC. 图 12.第3阶段（a）加强和（b）削弱BDC趋势的影响。
Fig. 13. Status of with SR 图 13.与 SR 的 状态
Early ): As long as SR is turned OFF early, BDC will occur (blue area). 早期 ）：只要 SR 提前关闭，就会发生 BDC（蓝色区域）。
(Late): When and SR turns OFF late, reverse BDC may occur (green area). （延迟）：当 SR 关闭较晚时 ，可能会发生反向 BDC（绿色区域）。
Fig. 14. Sampling circuits of the proposed adaptive SR driving scheme 图 14.所提出的自适应SR驱动方案的采样电路
Shoot Through: When and SR turning-OFF is turned too late, shoot through will occur, which must be prohibited (red area). 击穿：当 SR 关闭关闭转得太晚时 ，将发生击穿，必须禁止（红色区域）。
Non-BDC: In the remaining area, BDC cannot be detected. At this time, SR may be turned OFF exactly or slightly later. This interval owns enough fault tolerance. If works in this area, both high efficiency and safety can be guaranteed. 非 BDC：在其余区域中，无法检测到 BDC。此时，SR 可能会完全关闭或稍晚关闭。此间隔具有足够的容错能力。如果 在该区域工作，则可以保证高效率和安全性。
To improve the robustness of the conventional adaptive SR strategy, it is necessary to determine whether BDC is caused by turning-OFF early or late. In Section III, the improved adaptive SR strategy is proposed, which can determine the types of BDC and perform the corresponding strategy. 为了提高传统自适应 SR 策略的鲁棒性，有必要确定 BDC 是由提前关闭还是延迟关闭引起的。在第三节中，提出了改进的自适应SR策略，该策略可以确定BDC的类型并执行相应的策略。
III. Proposed Adaptive SYnchronOUS RECTIFICATION DRIVING STRATEGY 三、自适应同步整流驱动策略
To identify whether the sampled BDC is caused by turningOFF early or late, an additional comparator is required. Fig. 14 shows the sampling circuit of the proposed adaptive SR driving scheme. The specification of the comparator is LT1715, which contains two comparators inside. The input voltage range of LT1715 is from to . Therefore, the sampling signal should be scaled down to adapt to the input voltage range. The negative reference voltage is set to be higher than , while is set to be slightly greater than . The signal represents and the rising edge is the valid signal. Meanwhile, the signal represents the possibility of BDC caused by SR turning-OFF late, and the falling edge is the valid signal. 要确定采样的 BDC 是由提前关闭还是延迟关闭引起的，需要额外的比较器。图14显示了所提出的自适应SR驱动方案的采样电路。比较器的规格是LT1715，内部包含两个比较器。LT1715 的输入电压范围为 至 。因此，应按比例缩小采样信号以适应输入电压范围。负基准电压 设置为高于 ，而 设置为略大 于 。信号 表示 ，上升沿是有效信号。同时，该信号 表示SR关断较晚导致BDC的可能性，下降沿为有效信号。
One of the comparators is used to detect BDC. Signal rises when the sampled drain-source voltage is lower than , which indicates that the body diode is conducted on. Signal can be applied to regulate both the turn-ON point and the turning-OFF point. As shown in Fig. 15, should be smaller than the valley value of during the conduction and be larger than the threshold voltage of the body diode. Therefore, meets the 其中一个比较器用于检测 BDC。当采样的漏源电压 低于 时，信号 上升，这表示体二极管导通。信号 可用于调节导通点和关断点。如图15所示， 导通 过程中的谷值应小于正体二极管的阈值。因此， 满足
Fig. 15. Range of the reference voltage. 图 15.基准电压的范围。
requirement that 要求
Another comparator is used to distinguish the type of BDC. Signal is available when decreases from higher than to lower than , which indicates the possibility to generate BDC caused by SR turning-OFF late. Moreover, the signal can also be used to reset the driving signal for another synchronous rectifier. As shown in Fig. 15, should be larger than the peak value of during the conduction and be smaller than the first peak value during the resonant period. Therefore, meets the requirement that 另一个比较器用于区分 BDC 的类型。当信号 从高于 降低到低于 时可用，这表明 SR 关闭延迟导致 BDC 的可能性。此外，该信号 还可用于复位另一个同步整流器的驱动信号。如图15所示， 在导通 期间应大于峰值，在谐振周期内应小于第一峰值。因此， 满足以下要求
By detecting whether the signal exists or not, the proposed SR strategy can be divided into two conditions. As shown in Fig. 16, when (the switching frequency) is larger than (the resonant frequency) or is slightly smaller than , there is not enough time for to resonate half of the high-frequency oscillation cycle after SR is turned OFF. It means that there will 通过检测 信号是否存在，所提出的SR策略可以分为两个条件。如图16所示，当 （开关频率）大于 （谐振频率）或 略小于 时，SR关闭后，没有足够的时间 谐振高频 振荡周期的一半。这意味着会有
be no falling edge of the signal, and will not occur when turning-OFF late. Then, the conventional adaptive SR driving scheme can work normally under this condition. The turning-OFF point lags when BDC is detected and leads when BDC does not occur. 不是 信号的下降沿，并且在关闭较晚时 不会发生。然后，传统的自适应SR驱动方案可以在这种条件下正常工作。当检测到 BDC 时，关闭点滞后，当 BDC 未发生时，关闭点会领先。
As shown in Fig. 17, when is smaller than will resonate for enough time and a falling edge of signal will appear after SR is turned OFF. Therefore, both turning-OFF early and late can lead to BDC. In this condition, the conventional adaptive SR driving scheme cannot work normally. It is necessary to determine the type of BDC (turning-OFF early or late). Fig. 17(a) shows the condition of SR turning-OFF prematurely, where BDC occurs before signal . Fig. 17(b) shows the condition of SR turning-OFF late, where the signal appears before BDC is 如图 17 所示，当 小于 将谐振足够长的时间，并且在 SR 关闭后会出现信号 的下降沿。因此，提前和延迟关闭都可能导致 BDC。在这种情况下，传统的自适应SR驱动方案无法正常工作。有必要确定 BDC 的类型（提前或延迟关闭）。图17（a）显示了SR过早关断的情况，其中BDC发生在信号 之前。图17（b）显示了SR在BDC之前关闭的条件，其中信号 出现在BDC之前
Fig. 16. Timing sequential of the sampling circuits when no valid signal is detected or is slightly smaller than ). 图 16.当未检测到 有效 信号或 略小于 时，采样电路的定时顺序。
TABLE I 表一
STATES OF THE SYNCHRONOUS RECTIFICATION 同步整流的状态
State 州
Coding 编码
Situation 情况
State 1 状态 1
完全关闭或延迟关闭
Turning-off exactly
or turning-off late
State 2 状态 2
提前 关闭
Turning-off early
State 3 状态 3
提前 关闭 延迟 关闭
Turning-off early
Turning-off late
detected. The two different types of BDC can be distinguished by the order of the signal and the signal. Fig. 17(c) represents the circumstance of turning-OFF slightly late or exactly. 检测。两种不同类型的BDC可以通过 信号和 信号的顺序来区分。图17（c）表示稍微晚或完全关闭的情况。
For the convenience of digital implementation, the states of SR are classified and coded by the sampled signal. As given in Table I, the state of SR can be divided into the following four states according to the combination of the sampled signals and . Fig. 18 shows the detecting process and the control strategy for the four states of SR. First, check whether signal 为了便于数字实现，SR的状态由采样信号进行分类和编码。如表I所示，根据采样信号 和 的组合，SR的状态可分为以下四种状态。图18显示了SR四种状态的检测过程和控制策略。一、检查信号 是否
Fig. 17. Timing sequential of the sampling circuits when signal is detected . 图 17.检测到 信号时 采样电路的定时顺序。
is available. If signal is invalid, SR is at state. 1) If signal is valid, then identify whether signal is valid. If the signal is invalid, SR is at State. 2) If both signal B and signal are valid, the order between and should be determined. If is before , SR is at state 3 . Otherwise, it is state 4 . 可用。如果信号 无效，则 SR 处于状态。1）如果信号 有效，则确定信号 是否有效。如果 信号无效，则 SR 处于状态。2） 如果信号 B 和信号 都有效，则应确定 和 之间的 顺序。如果 是 之前 ，则 SR 处于状态 3 。否则，它是状态 4 。
State 0 is the initial state, which indicates that the current status of SR is unknown and needs to be identified first. 状态 0 为初始状态，表示 SR 当前状态未知，需要先识别。
State 1 is coded as , which represents no BDC is detected. No matter state 1 occurs at the circumstances of or , state 1 always represents that SR is turned OFF slightly late or exactly. The strategy for state 1 is leading the turning-OFF point until the BDC is detected. Then, lagging the turning-OFF point until BDC disappears again. 状态 1 编码为 ，表示未检测到 BDC。无论状态 1 在 或 的情况下出现，状态 1 总是表示 SR 在稍晚或完全关闭时关闭。状态 1 的策略是引导关闭点，直到检测到 BDC。然后，滞后关闭点，直到 BDC 再次消失。
State 2 is coded as , which represents that BDC can only be caused by turning-OFF prematurely. State 2 usually occurs when or is slightly smaller than . The strategy for state 2 is lagging the turning-OFF point until the BDC cannot be detected. 状态 2 编码为 ，表示 BDC 只能由过早关闭 OFF 引起。状态 2 通常发生在 或 略小于 时。状态 2 的策略是滞后于关闭点，直到无法检测到 BDC。
States 3 and 4 are coded as BR and RB, respectively. Both of the states occur when is smaller than and have the potential to achieve BDC caused by turning-OFF late. For state 3, BDC occurs before the falling edge of signal , which represents that the BDC is caused by SR turning-OFF early. The strategy for state 3 is the same as state 2 . For state 4 , BDC occurs after the falling edge of signal , which represents that BDC is caused by SR turning-OFF late. The strategy for state 4 is leading the turning-OFF point until BDC cannot be detected. Then, continue to lead the turning-OFF point until BDC appears again. Finally, lagging the turning-OFF point until no BDC is detected. 状态 3 和 4 分别编码为 BR 和 RB。这两种状态都发生在 小于 并且有可能因延迟关闭而实现 BDC 时。对于状态 3，BDC 出现在信号 的下降沿之前，这表示 BDC 是由 SR 提前关闭引起的。状态 3 的策略与状态 2 相同。对于状态 4，BDC 发生在信号 的下降沿之后，表示 BDC 是由 SR 关闭较晚引起的。状态 4 的策略是引导关闭点，直到无法检测到 BDC。然后，继续引导关闭点，直到 BDC 再次出现。最后，滞后关断点，直到未检测到 BDC。
State 5 is the steady state, which means the turning-OFF point is regulated to the optimal point. Then, the SR control strategy enters the dormant state and detects whether BDC occurs again. If BDC is detected, the SR strategy restarts to state 0 . 状态 5 是稳态，这意味着关断点被调节到最佳点。然后，SR控制策略进入休眠状态，并检测BDC是否再次发生。如果检测到 BDC，SR 策略将重新启动到状态 0 。
The strategy for states 1-4 can regulate the turning-OFF point to achieve ZCS of SR and enter the steady state. 状态1-4的策略可以调节关断点，实现SR的ZCS，进入稳态。
IV. COMPARISON WITH OTHER AdAPTIVE SR DRIVING SCHEME IV. 与其他AdAPTIVE SR驾驶方案的比较
A comparison of different SR control strategies is illustrated in Table II. Different types of SR methods are compared for their performance of the target items, and set as strong, medium, and weak according to the order of their performance. 表二说明了不同SR控制策略的比较。比较不同类型的SR方法对目标项目的性能，并根据其性能顺序设置为强、中、弱。
Theoretically, the current sensing based scheme is the most direct SR driving scheme [6], [7]. The benefits of the current sensing-based scheme are the elimination of duty cycle loss and prevention of reverse conduction. Moreover, the sampling circuit is the simplest and the cost is the lowest among other SR schemes. However, the extra loss introduced by the sampling circuits prevents it from being used directly. In the literature [10], [11], the indirect current sensing schemes are proposed. The core of these methods is to determine the secondary-side SR current by the subtraction between the sampled resonant current (integrated by the voltage across resonant capacitor ) and the sampled magnetic current (integrated by the voltage across the transformer). Then, the loss from the sampling circuits is significantly reduced. However, the performance is greatly affected by the deviation of circuit parameters such as the resonant capacitor , the magnetic inductor and turn ratios . It is difficult to eliminate the duty cycle loss or to prevent reverse conduction when the circuit parameters deviate. The cost for this type of SR method depends on the complexity of the implementation. 从理论上讲，基于电流检测的方案是最直接的SR驱动方案[6]，[7]。电流检测方案的优点是消除了占空比损耗和防止反向传导。此外，采样电路是其他SR方案中最简单的，成本最低。然而，采样电路引入的额外损耗使其无法直接使用。文献[10]、[11]提出了间接电流传感方案。这些方法的核心是通过采样谐振电流 （由谐振电容器两端的电压积分 ）和采样磁电流 （由变压器两端的电压积分）之间的减法来确定次级侧 SR 电流。然后，采样电路的损耗显著降低。然而，性能受到谐振电容 、磁感 和匝数比等电路参数偏差的极大影响 。当电路参数偏离时，很难消除占空比损耗或防止反向导通。这种类型的 SR 方法的成本取决于实现的复杂性。
The sensing based schemes introduce the lowest sampling loss and are widely applied in smart drivers [13], [14]. The cost for this type of SR method is low due to the implementation of IC. However, the performance of sensing based schemes is greatly influenced by ESL and owns the worst duty cycle loss. Moreover, for high-frequency applications, the duty cycle loss will become more and more serious due to the sharp increase 基于 传感的方案具有最低的采样损耗，在智能驱动器中得到了广泛的应用[13]，[14]。由于IC的实施，这种SR方法的成本很低。然而，基于 检测的方案的性能受ESL的影响很大，并且具有最严重的占空比损耗。而且，对于高频应用来说，由于占空比损耗的急剧增加，占空比损耗会越来越严重
Fig. 18. Control flowchart of the proposed SR tuning process. 图 18.建议的SR调优过程的控制流程图。
TABLE II 表二
COMPARISON OF SR CONTROL STRATEGIES SR控制策略的 比较
Control category 控制类别
Current sensing based 基于电流检测
sensing based 基于传感
Adaptive based 基于自适应
Sub-category 子类别
direct 直接
Indirect 间接
无偿
Without
compensation
有补偿
With
compensation
常规自适应
Conventional
adaptive
所提出的方法
The proposed
method
Reference 参考
采样电路损耗低
Low loss of the
sampling circuits
weak 弱
medium 中等
strong 强
medium 中等
medium 中等
medium 中等
采样电路复杂度低
Low complexity of
the sampling circuits
strong 强
weak 弱
strong 强
medium 中等
strong 强
medium 中等
Low duty-cycle-loss 低占空比损耗
strong 强
medium 中等
weak 弱
medium 中等
strong 强
strong 强
防止反向传导的能力
Ability to prevent
reverse conduction
strong 强
medium 中等
strong 强
medium 中等
weak 弱
strong 强
对电路参数漂移具有鲁棒性
Robust to the circuit
parameter drift
strong 强
weak 弱
medium 中等
weak 弱
strong 强
strong 强
易于通过IC/MCU实现
Easy to be realized
by IC/MCU
strong 强
weak 弱
strong 强
medium 中等
strong 强
strong 强
适用于高开关频率
Fit for high
switching frequency
strong 强
medium 中等
weak 弱
medium 中等
中（计算速度）
medium
(calculation
speed)
中（计算速度）
medium
(calculation
speed)
Fast regulating speed 调节速度快
strong 强
strong 强
strong 强
strong 强
weak 弱
weak 弱
Low cost 低成本
strong 强
medium 中等
strong 强
medium 中等
weak 弱
weak 弱
in . The compensation schemes [15]-[17] for sensing based method are introduced to reduce the duty cycle loss. The core of the compensation schemes is to balance the voltage caused by ESL through the Wheatstone bridge and to determine the actual voltage across . However, the complexity of the sampling circuit is increased. Moreover, the main drawback is that the compensation parameters are sensitive to the values of parasitic parameters, which are greatly affected by temperature. Therefore, the steady-state performance (duty cycle loss and reverse conduction) depends on the accuracy of stray inductance and . 在 .介绍了基于 传感方法的补偿方案[15]-[17]，以降低占空比损耗。补偿方案的核心是平衡ESL通过惠斯通电桥引起的电压，并确定两端 的实际电压。然而，采样电路的复杂性增加了。此外，主要缺点是补偿参数对寄生参数的值敏感，寄生参数受温度影响很大。因此，稳态性能（占空比损耗和反向导通）取决于杂散电感的精度和 。
The adaptive SR driving strategy [5], [22] can theoretically eliminate duty cycle loss through the simple sampling circuits and the simple control logic. Moreover, the method is insensitive to the stray parameters. The core of this method is to determine whether the turning-OFF point is premature by detecting BDC. Since BDC can also be caused by SR turning-OFF late, the conventional adaptive SR driving strategy may result in reverse 自适应SR驱动策略[5]，[22]理论上可以通过简单的采样电路和简单的控制逻辑消除占空比损耗。此外，该方法对杂散参数不敏感。该方法的核心是通过检测BDC来判断关断点是否过早。由于 BDC 也可能是由 SR 关断较晚引起的，因此传统的自适应 SR 驱动策略可能会导致反向
Fig. 19. Designed prototype for with SR. 图 19.为 SR设计原型。
conduction under the working condition of . The main drawback of this method is the regulating speed, which costs a relatively long time to regulate the turning-OFF point to the optimal position. 在工作 条件下的传导。这种方法的主要缺点是调节速度快，将关断点调节到最佳位置需要相对较长的时间。
In this article, the proposed SR driving scheme inherits the advantages and disadvantages of the conventional adaptive SR scheme. Moreover, the problem of reverse conduction is solved at the cost of slightly increasing sampling complexity. The cost for this method is higher than other SR methods due to the additional comparator and micro-controller unit(MCU). However, if the proposed method could be implemented by the integrated circuits, the cost would approach the sensing-based method. The proposed scheme owns the features of simple and low-loss sampling circuits, good performance (both duty cycle loss and reverse conduction are eliminated), and insensitive to stray parameters. Therefore, the proposed SR driving scheme can be a good candidate for synchronous rectification. 本文所提出的SR驱动方案继承了传统自适应SR方案的优缺点。此外，反向传导问题的解决是以略微增加采样复杂度为代价的。由于增加了比较器和微控制器单元 （MCU），这种方法的成本高于其他 SR 方法。但是，如果所提出的方法可以通过集成电路实现，则成本将接近基于 传感的方法。该方案具有采样电路简单、损耗低、性能好（占空比损耗和反向导通均消除）、对杂散参数不敏感等特点。因此，所提出的SR驱动方案可以很好地用于 同步整流。
V. EXPERIMENTAL RESULTS 五、实验结果
A prototype of resonant converter with synchronous rectification, as shown in Fig. 19, has been built to verify the established model and the proposed adaptive SR method above. The specifications of the prototype are as follows: input voltage , output voltage , maximum output current , switching frequency varies from 330 to . Fig. 19 shows the power stage, the control stage, and the comparator board. Fig. 20 shows the enlarged view of the printed circuit board(PCB) of the comparator board, which is plugged on the secondary side of the resonant converter, comparing with the two threshold voltages and to determine the features of BDC and reverse current. The sampled signals and are transferred to the microcontroller to regulate the turning-OFF point. 如图19所示，构建了具有同步整流功能 的谐振变换器 原型，验证了已建立的模型和上面提出的自适应SR方法。原型的规格如下：输入电压 、输出电压 、最大输出电流 、开关频率 从330到 330不等。图19显示了 功率级、控制级和比较板。图20显示了插入谐振转换器次级侧 的比较板的印刷电路板（PCB）的放大图，与两个阈值电压进行比较 ， 并 确定BDC和反向电流的特性。采样后的信号 被传输到微控制器以调节关断点。
Table III gives the specific parameter of the designed prototype. Both the primary and secondary switches are chosen to be gallium nitride(GaN) devices for high-frequency switching. 表III给出了设计原型的具体参数。初级开关和次级开关均被选为用于高频开关的氮化镓（GaN）器件。
Fig. 20. PCB of the sampling circuits. 图 20.采样电路的PCB。
TABLE III 表三
DESIGN SPECIFICATION OF THE PROTOTYPE. 原型的设计规范。
Components 组件
Parameters 参数
初级交换机
Primary Switches
氮化镓系统GS66506T ，
GaN System GS66506T
,
次级交换机 和
Secondary Switches
and
氮化镓系统GS61008T
GaN System GS61008T
Transformer 变压器
EQ38-3F46铁氧体磁芯;初级侧系列; 次级侧平行;
EQ38-3F46 ferrite core;
Primary side series;
Secondary side parallel;
Resonant inductor 谐振电感
EQ18-3F46铁氧体磁芯;
EQ18-3F46 ferrite core;
谐振电容器
Resonant capacitor
、多人陶瓷电容器 （MLCC）
, multiplayer
ceramic capacitors (MLCC)
Input Capacitor 输入电容
, electrolytic capacitor 电解电容器
Output Capacitor 输出电容
Microcontroller 微控制器
STM32F334R8
SR comparator SR比较器
LT1715
Si8273 from Silicon Lab and UCC27611 from Texas Instruments are chosen to drive the primary and secondary GaN devices, respectively. Ferrite core material 3F46 from Ferroxcube is selected for transformer and inductor due to its performance for high-frequency applications. Planar cores are selected for the consideration of high power density. STM32F334R8 from STMicroelectronics is selected as the microcontroller due to its integrated high-resolution pulsewidth modulation generator. Thus, the time resolution is . LT1715 from Linear Technology is chosen as the comparator for sampling the status of SR due to propagation delay and TTL/CMOS compatible output. The charge pump IC TPS60402 (with the voltage divider resistors) is chosen to generate the negative reference voltage . Silicon Lab 的 Si8273 和 Texas Instruments 的 UCC27611 分别用于驱动初级和次级 GaN 器件。Ferroxcube的铁氧体磁芯材料3F46因其在高频应用中的性能而被选用于变压器和电感器。选择平面磁芯是为了考虑高功率密度。意法半导体的STM32F334R8因其集成的高分辨率脉宽调制发生器而被选为微控制器。因此，时间分辨率 为 。选择 Linear Technology 的 LT1715 作为比较器，用于对传播延迟和 TTL/CMOS 兼容输出引起的 SR 状态进行采样。选择电荷泵IC TPS60402（带分压电阻）来产生负基准电压 。
Figs. 21 and 22 show the results of the sampling circuits. The SR gate-to-source voltage (dark red line), resonant current (green line), and magnetizing current (pink line) are shown in the upper part of the figures. In fact, is not measurable and is obtained by integrating the primaryside voltage across the transformer. here is used to mark the appropriate SR turning-OFF point. The SR drain-to-source voltage (blue line), the sampled signal (red line), and the sampled signal (yellow line) are also listed in the figures. The red shaded area is the detecting window for the sampled 图21和图22显示了采样电路的结果。SR栅源电压 （深红色线）、谐振电流 （绿线）和磁化电流 （粉色线）如图上半部分所示。事实上， 它是不可测量的，是通过对变压器两端的初级侧电压进行积分而获得的。 此处用于标记适当的 SR 关闭点。图中还列出了SR漏源电压 （蓝线）、采 样信号（红线）和采 样信号（黄线）。红色阴影区域是采样的检测窗口
Fig. 21. Results of the sampling circuits when . (a) SR turning OFF premature. (b) SR turning OFF exactly. (c) SR turning OFF late. 图 21.采样电路的结果。 （a） SR 过早关闭。（b） SR 完全关闭。（c） SR 关闭较晚。
Fig. 22. Results of the sampling circuits when . (a) SR turning OFF early and (b) SR turning OFF exactly. 图 22.采样电路的结果。 （a） SR 提前关闭，（b） SR 完全关闭。
signals and . The falling edge of the signal is valid, which represents that is low enough for sr to perform the resonance process mentioned in Section II. The rising edge of the signal is valid, which means that the body diode of SR is conducted on. Fig. 21 shows the circumstance of , the valid signal can be detected in the detecting window. When SR is turned ofF prematurely [shown in Fig. 21(a)], the 信号 和 . 信号的下降沿是有效的，这表示 该信号足够低，sr可以执行第二节中提到的谐振过程。 信号的上升沿有效，这意味着SR的体二极管导通。图21示出了在检测窗口中可以检测到有效 信号的情况 。当SR过早地从F转向[如图21（a）所示]时，
(a) （一）
(b) （二）
Fig. 23. Verification of the established model in Section II. 图 23.验证第二节中已建立的模型。
state BR can be sampled; when SR is turned OFF exactly [see Fig. 21(b)], the state/BR can be sampled; when SR is turned OFF too late, the state can be sampled. Fig. 22 shows the circumstance of , the valid signal cannot be detected in the detecting window. When SR is turned OFF prematurely [see Fig. 22(a)], the state can be sampled; when SR is turned OFF exactly or too late [see Fig. 22(b)], the state can be sampled. In the digital implementation, the range of can be identified through the existence of the valid signal, and then the different SR strategies can be implemented. In the case of , the conventional adaptive SR scheme can be used; while for the circumstance of , the issue of BDC caused by SR turning-OFF late should be considered. 状态 BR 可以采样;当SR完全关闭时[见图21（b）]，可以对状态/BR进行采样;当 SR 关闭得太晚时，可以对状态 进行采样。图22显示了在检测窗口中无法检测到有效 信号的情况 。当SR过早关闭[见图22（a）]时，可以对状态 进行采样;当 SR 完全关闭或太晚关闭时 [见图 22（b）]，可以对状态 进行采样。在数字实现中，可以通过有效 信号的存在来识别范围 ，然后可以实施不同的SR策略。在这种情况下 ，可以使用常规的自适应SR方案;而对于这种情况 ，应考虑 SR 关闭延迟导致的 BDC 问题。
To verify the proposed model in Section II, the waveforms for different turning-OFF points are compared in Fig. 23. The adopted , and of the prototype are , and , respectively. Meanwhile, is extracted to be through the finite-element software. According to the model proposed in Section II, the angular frequency of oscillation during the dead time . It can be seen from Fig. 23 that the oscillation frequency is , which is consistent with the model. According to the model, the larger the reverse current at the turning-OFF point, the larger the oscillation amplitude. In Fig. 23(a), the two SR turning-OFF points only differ by , but the amplitudes of sr differ by 4.25 V. In Fig. 23(b), the two SR turning-OFF points differ , but the amplitudes of sr only differ by . The phenomenon can be well explained by the proposed model. Both the two comparison objects in Fig. 23(a) are in the case of SR turning-OFF late. 为了验证第二节中提出的模型，在图23中比较了不同关断点的波形。原型的采用 和 分别是 和 。同时， 通过有限元软件提取。根据第二节提出的模型，死区期间 振荡的角频率。从图23可以看出，振荡频率为 ，与模型一致。根据模型，关断点的反向电流 越大，振荡幅度越大。在图23（a）中，两个SR关断点仅相差4.25 V，但 sr的振幅相差4.25 V。 在图23（b）中，两个SR关断点不同 ，但sr的 振幅仅相差4.25 V。所提出的模型可以很好地解释这种现象。图23（a）中的两个比较对象都是在SR关闭较晚的情况下。
Although the difference of the turning-OFF points is only , the difference for the reverse current in the two cases is relatively large. The comparison objects in Fig. 23(b) are that SR turns OFF early and exactly. Although the SR turning-OFF 虽然关断点的差异只是 ，但两种情况下反向电流的差异相对较大。图23（b）中的比较对象是SR提前且准确地关闭。虽然SR关闭
Fig. 24. Tuning process when and SR turning OFF early. 图 24.调整过程时 和 SR 提前关闭。
Fig. 25. Tuning process when and SR turning OFF late 图 25.调整过程和 SR 关闭延迟
Fig. 26. Tuning process when . 图 26.调整过程时 。
Manuscript received December 31, 2020; revised April 14, 2021 and July 1, 2021; accepted August 18, 2021. Date of publication August 20, 2021; date of current version October 15, 2021. This work was supported in part by the Key Research and Development Plan of Jiangsu under Grant BE2018003-3, in part by the Achievement transformation project of Jiangsu Province under Grant BA2020030, in part by the National Key Research and Development Plan under Grant 2017YFB0402900, and in part by the National Natural Science Foundation of China under Grant 52177172. Recommended for publication by Associate Editor G. Moschopoulos. (Corresponding author: Qi Liu.) 稿件于2020年12月31日收到;2021 年 4 月 14 日和 2021 年 7 月 1 日修订;2021年8月18日接受。发布日期：2021 年 8 月 20 日;当前版本的日期为 2021 年 10 月 15 日。这项工作得到了BE2018003-3号资助下的江苏省重点研发计划、BA2020030资助下的江苏省成果转化项目、2017YFB0402900资助下的国家重点研发计划以及52177172资助下的国家自然科学基金部分支持。推荐由副主编 G. Moschopoulos 出版。（通讯作者：刘琦）
The authors are with the National ASIC System Engineering Research Center, Southeast University, Nanjing 210096, China (e mail: qianqinsong @seu.edu.cn; 1q_seu@126.com; 934047415@qq.com756759234@qq.com; xsyjoy @foxmail.com; swffrog@ seu.edu.cn). 作者就职于中国南京210096东南大学国家ASIC系统工程研究中心（电子邮件：qianqinsong @seu.edu.cn; 1q_seu@126.com; 934047415@qq.com 756759234@qq.com; xsyjoy @foxmail.com; swffrog@ seu.edu.cn）。
Color versions of one or more figures in this article are available at https://doi.org/10.1109/TPEL.2021.3106477. 本文中一个或多个图形的彩色版本可在 https://doi.org/10.1109/TPEL.2021.3106477 上获得。
Digital Object Identifier 10.1109/TPEL. 2021.3106477 数字对象标识符 10.1109/TPEL。2021.3106477
