Costless Improvement of Converter Efficiency in a Regenerative Braking System with a Brushless DC Machine

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Dear authors, thank you for submitting your article to Electronics. Unfortunately, there is not significant contribution in the proposed article. Some ley issues found in the manuscript are detailed in the following.

1. The authors claim that a new control method is proposed. However, there is not novelty in the control scheme. The only modification made by the authors is in the modulation strategy, where the switches are turned on during the intervals in which their diodes are expected to be forward biased. Such approach is well known in the literature (c.f., synchronous rectification) and constitutes very limited contribution for the research.
2. The analysis detailed in Fig. 1 is incomplete. In the proposed modulation scheme, the diodes will still conduct (even for a short interval) during the dead time required for the proper operation of the circuit. Please note that for high frequency operation, the increased losses associated with the dead time might not be neglectable, and therefore this issue should be addressed by the authors.
3. The equations contained in the manuscript must be revised. For instance, in equations (1)-(5), “ω” appears twice, being one overlapping the symbol “=”. In addition, in equations (2)-(5), the limits of integration (time) do not match the variable on integration (angular frequency).
4. The authors affirm that the control system is given in Fig. 7. However, the block diagram depicted in this figure seems to represent an open loop operation with an imposed duty cycle. A proper control system would require the automatic control of some parameter (e.g., torque, speed, battery power, etc.) of the BLDC under regenerative braking condition.
5. What was the reason for choosing a 200 V MOSFET for the prototype if the converter is fed by only 24 V? The choice of a lower voltage rating device would probably lead to higher efficiency levels.

Author Response

Dear Reviewer,

I would like to express my sincere gratitude for your thorough review of the manuscript
and for the valuable comments and suggestions you have provided. Your feedback constitutes
a significant contribution to the improvement of the article and is greatly appreciated.

In this response document, I provide detailed and substantive answers to all the issues raised.
The points you highlighted have been carefully addressed and incorporated into the revised version of the manuscript.

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Comments 1: The authors claim that a new control method is proposed. However, there is not novelty in the control scheme. The only modification made by the authors is in the modulation strategy, where the switches are turned on during the intervals in which their diodes are expected to be forward biased. Such approach is well known in the literature (c.f., synchronous rectification) and constitutes very limited contribution for the research.

Response 1: Although the developed algorithm refers to the well-known concept of "synchronous" rectification, commonly used in high-efficiency voltage rectifiers, its application in regenerative braking of BLDC machines has not yet been the subject of any scientific publications. Its development required a detailed analysis of the conduction of the transistor-diode switches present in the converter structure, and its effectiveness was confirmed by a clear increase in the converter’s efficiency and the power delivered to the battery. Therefore, the presented solution constitutes a significant research contribution in this field, particularly in low-voltage systems. An additional advantage of the developed control method is the possibility of its implementation without the need to modify the converter topology typical for drive systems (three-phase transistor bridge) or change the hardware platform of the control system. The algorithm can be executed on standard DSP processors commonly used in drive applications.

The missing content has been added in Chapter 8.

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Comments 2: The analysis detailed in Fig. 1 is incomplete. In the proposed modulation scheme, the diodes will still conduct (even for a short interval) during the dead time required for the proper operation of the circuit. Please note that for high frequency operation, the increased losses associated with the dead time might not be neglectable, and therefore this issue should be addressed by the authors.

Response 2: In the analyzed system, diode conduction occurs during the dead time. This phenomenon can lead to increased power losses, especially when operating at high transistor switching frequencies. The control system uses a PWM modulation frequency of 20kHz, which lies within the typical range used in drive systems (up to 20kHz). At this frequency, the share of dead time in the modulation period is negligibly small, and the intrinsic diode conduction losses are marginal. In the case of higher switching frequencies, which are not typical for classical drive systems, the impact of dead time becomes significant. This leads to increased power losses in the conducting diodes, which negatively affects the overall efficiency of the converter. In such cases, it is advisable to use transistors with very short switching times, manufactured using modern semiconductor technologies such as GaN or SiC. These components are characterized not only by shorter turn-on and turn-off times (which allows for a reduction of dead time), but also by very low channel resistance, further reducing conduction losses. It is worth emphasizing that the developed control algorithm can also be directly implemented in converters based on GaN or SiC technology, without the need for any hardware modifications.

The missing content regarding the omission of the description of diode conduction during the dead time has been added in Chapter 3.2 (below Figure 1), while a detailed analysis and justification of this decision have been provided in Chapter 7.

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Comments 3: The equations contained in the manuscript must be revised. For instance, in equations (1)-(5), “ω” appears twice, being one overlapping the symbol “=”. In addition, in equations (2)-(5), the limits of integration (time) do not match the variable on integration (angular frequency).

Response 3: In equation (1), the redundant symbol "w" overlapping the equality sign has been removed - this was an editorial error that occurred during equation formatting. In equations (2) - (5), the integration variable has been changed from dω to dt to reflect the physical meaning of the integral: the function u_L(t), which is a function of time, is integrated over the intervals: 0 ÷ t_on and t_on ÷ t_off.

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Comments 4: The authors affirm that the control system is given in Fig. 7. However, the block diagram depicted in this figure seems to represent an open loop operation with an imposed duty cycle. A proper control system would require the automatic control of some parameter (e.g., torque, speed, battery power, etc.) of the BLDC under regenerative braking condition.

Response 4: This article focuses on the analysis of the converter efficiency and the power delivered to the battery in the steady-state operating conditions of the system, i.e., at fixed values of the machine’s rotational speed and the PWM duty cycle. The goal was to compare two control methods: the classical control method (CCCM) and the new method utilizing reverse conduction of field-effect transistors (RCCM). In this context, as correctly noted, the term “control system” is misleading because the presented model does not include automatic regulation of any system parameters (e.g., torque, speed, or power), and the control pulses are generated in an open-loop feedback. A full analysis of the machine operation in regenerative braking mode requires consideration of dynamic states, which necessitates the development of a fully automatic control system and will be the subject of further research on the system.

Accordingly, the captions of Figures 6 and 7 were changed to "Pulse generator", and the missing content was added to Chapter 5.

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Comments 5: What was the reason for choosing a 200 V MOSFET for the prototype if the converter is fed by only 24 V? The choice of a lower voltage rating device would probably lead to higher efficiency levels.

Response 5: The use of MOSFET transistors with a rated voltage significantly exceeding the system’s supply voltage adversely affects the converter’s efficiency. However, the prototype converter used IRFP90N20D transistors with a Drain-to-Source Voltage of 200V, characterized by low source-drain channel resistance, relatively low cost, and easy availability. This choice was also justified by the need to ensure research flexibility - the converter is also used in experiments with machines of higher rated voltage, where the use of transistors with a higher voltage rating is necessary. In the next stages of the work, the construction of a low-voltage version of the converter is planned, in which transistors with a rated voltage approximately 2 ÷ 2.5 times higher than the operating voltage of the system described in the article will be used. This solution will allow further improvement of the converter’s efficiency due to lower source-drain channel resistance, which strongly depends on the transistor’s rated voltage - the lower the rated voltage, the lower the on-state resistance is typically.

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Important note to facilitate locating the introduced changes in the manuscript with marked changes (Manuscript_with_M_Cs.docx file):

a)  the additional content addressing the reviewers’ comments has been highlighted in blue

b)  the parts of the article that were edited for clarity and structure, in accordance with the editorial recommendations, have been highlighted in green. These editorial changes are numerous but do not affect the scientific content presented in the previous version of the manuscript.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The paper presents an innovative regenerative braking control method for a BLDC motor using the reverse conduction of MOSFETs, which reduces conduction losses compared to the classical diode‑based approach. The work is well‑structured, featuring a mathematical model, MATLAB/Simulink simulations, and experimental results. However, when evaluated against the current state of global knowledge and engineering best practices, several significant weaknesses emerge, detailed below.

1. Limitations of the Mathematical Model.
- Simplified current waveform: The model assumes constant phase currents and sinusoidal phase voltages. In real operation, currents are highly pulsed, affecting both MOSFET and winding losses. 
- Neglect of switching losses: Only static conduction losses (R_DS(on)) are considered, whereas dynamic losses—dependent on PWM frequency and MOSFET capacitances can account for several percent of total losses at 20 kHz PWM.
- Omission of commutation transients: Effects such as diode conduction during MOSFET turn‑off are not modeled, leading to underestimation of losses, particularly at 50% duty cycle.

2. Shortcomings of the MATLAB/Simulink Simulations.
- Idealized component models: Although inductances and I–V characteristics are included, thermal behavior of MOSFETs, electrical noise, and EMI are omitted.
- Static battery voltage: Simulations assume a fixed supply voltage, whereas in experiments the battery voltage rises during charging, which softens current peaks and improves efficiency. This discrepancy hinders real‑world applicability.

3. Experimental and Literature Comparison.
- Limited test range: Efficiency was measured only up to D=54% (RCCM) and D=51% (CCCM) before reaching the motor’s rated current. Absence of high‑current tests limits conclusions for higher‑power vehicle applications.
- No comparison with wide‑bandgap devices: The paper merely mentions SiC/GaN MOSFETs in the conclusion without presenting any simulations or measurements. Recent studies show that wide‑bandgap devices, with faster switching and lower conduction losses, can offer far greater benefits than silicon MOSFETs.
- Lack of thermal and reliability analysis: There is no discussion of heat dissipation, potential hot spots, or environmental effects on system longevity—critical aspects for industrial and automotive deployments.

4. Implementation Challenges and Scalability.
- Control algorithm complexity: While the authors claim advanced microcontrollers are unnecessary, managing 12 sectors with Hall sensors plus reverse‑conduction MOSFET timing significantly complicates software and hardware compared to standard sensorless methods.
- EMI considerations omitted: Reverse MOSFET conduction introduces steep current edges, which may exacerbate electromagnetic interference and necessitate additional filtering, increasing cost and size.
- Limited voltage applicability: The method is demonstrated at 24 V. There is no analysis for higher voltages (e.g., 400 V EV systems), where reverse‑conduction benefits diminish and isolation challenges grow.

5. Bibliographic and Content Gaps.
- Insufficient sensorless control references: The paper cites EMF zero‑crossing and observer methods but ignores the latest publications and standards in BLDC/PM motor sensorless control for automotive applications.
- No cost‑benefit analysis: The claim of “no additional cost” is unsupported by any estimation of potential EMI filtering, cooling systems, or increased software development efforts.

Author Response

Dear Reviewer,

Thank you very much for the insightful and positive review of the article entitled "Costless improvement of converter efficiency in a regenerative braking system with a Brushless DC machine". I am pleased that the proposed method has been recognized as a valuable contribution to the development of control algorithms aimed at improving converter efficiency in BLDC motor drives.

The comments included in the review accurately highlight the limitations of the adopted mathematical and simulation model, as well as aspects that require further investigation. The identified shortcomings pertain, among others, to the omission of transient phenomena (especially those occurring during the dead-time of the transistors), dynamic losses, thermal issues, implementation challenges, and scalability problems. These all constitute important directions for further work
on the system.

In the remainder of this response, I will address all comments raised in the review, with particular emphasis on the issues that were not covered in the article.

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Comments 1: Limitations of the Mathematical Model.

- Simplified current waveform: The model assumes constant phase currents and sinusoidal phase voltages. In real operation, currents are highly pulsed, affecting both MOSFET and winding losses.

- Neglect of switching losses: Only static conduction losses (R_DS(on)) are considered, whereas dynamic losses - dependent on PWM frequency and MOSFET capacitances can account for several percent of total losses at 20 kHz PWM.

- Omission of commutation transients: Effects such as diode conduction during MOSFET turn‑off are not modelled, leading to underestimation of losses, particularly at 50% duty cycle.

Response 1: The article employs certain simplifications in the mathematical model, particularly the assumption of constant phase currents in the machine and the omission of dynamic transistor losses. As noted in Section 4, "Mathematical representation of the regenerative braking system", the model accounts only for static losses related to the R_DSon channel resistance, while dynamic losses resulting from transistor switching are neglected. At a PWM switching frequency of 20kHz,
these losses do not exceed 2% of the total converter losses.

The assumption of constant machine phase current was made in order to develop a clear and analytically solvable mathematical model. This approach enables direct analysis of how selected system parameters affect the converter efficiency and the power transferred to the battery. Similar simplifications have also been used in other widely cited scientific publications referenced in
the article.

However, the paper does not address the effect of diode conduction during dead time, which occurs during transistor switching. This phenomenon is indeed present in the analysed system and may lead to an underestimation of power losses in the converter, particularly when operating at higher switching frequencies and with higher machine phase currents (for a 50% duty cycle). In the presented system, a PWM modulation frequency of 20kHz was applied, which falls within the typical range for conventional BLDC drive systems. At this frequency, the dead time constitutes a small portion of the modulation period, and the associated power losses are negligible. In applications requiring higher switching frequencies (which is not typical for standard drive systems), the impact of dead time becomes more significant. It leads to increased diode conduction losses, which negatively affect converter efficiency. In such cases, it is advisable to use transistors based on modern semiconductor technologies such as GaN or SiC. These devices offer significantly shorter switching times (which allows for reduced dead time) and very low channel resistance, thereby further limiting conduction losses and improving the effectiveness of the proposed control algorithm.

The previously missing content, supplementing the discussion of diode conduction during
dead time, has been added in Chapter 7 - Discussion.

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Comments 2: Shortcomings of the MATLAB/Simulink Simulations.

- Idealized component models: Although inductances and I–V characteristics are included, thermal behaviour of MOSFETs, electrical noise, and EMI are omitted.

- Static battery voltage: Simulations assume a fixed supply voltage, whereas in experiments the battery voltage rises during charging, which softens current peaks and improves efficiency. This discrepancy hinders real‑world applicability.

Response 2: The component models available in the Matlab-Simulink software tool libraries assume linear current-voltage characteristics and do not account for the effects of temperature or electromagnetic interference (EMI). Despite this, the simulation results obtained closely reflect the outcomes of experimental studies. Ultimately, the development of more complex mathematical and simulation models is planned, which will include the transient states of transistors and diodes, as well as component characteristics closer to those occurring in the real system. However, this will require significantly greater computational complexity and will lead to a radical complication of the mathematical model.

Referring to the second remark - in the theoretical analyses, a constant battery voltage of 24V was assumed, whereas in the actual experimental setup, this voltage increased as a result of the charging process. This approach was dictated by the adopted research methodology: the simulation models were intended to correspond to the structure of the experimental setup, in which two lead-acid batteries connected in series with a total voltage of 24V were used. Future work plans include taking into account the variable battery voltage both in the average-value model and in the simulation model implemented in Matlab-Simulink software.

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Comments 3: Experimental and Literature Comparison.

- Limited test range: Efficiency was measured only up to D=54% (RCCM) and D=51% (CCCM) before reaching the motor’s rated current. Absence of high‑current tests limits conclusions for higher‑power vehicle.

- No comparison with wide‑bandgap devices: The paper merely mentions SiC/GaN MOSFETs in the conclusion without presenting any simulations or measurements. Recent studies show that wide‑bandgap devices, with faster switching and lower conduction losses, can offer far greater benefits than silicon MOSFETs.

- Lack of thermal and reliability analysis: There is no discussion of heat dissipation, potential hot spots, or environmental effects on system longevity—critical aspects for industrial and automotive deployments.

Response 3: The limitation of the experimental study range to a duty cycle of 54% for the (RCCM) algorithm and 51% for (CCCM) results from the characteristics of the analysed control algorithm. This is due to the summation of the battery voltage with the machine phase voltages during the energy recovery phase, which leads to a rapid increase in the machine's phase current to its rated value - further increasing the duty cycle value would risk demagnetising the magnet circuit of the machine. Future publications will present alternative control algorithms, also utilising reverse conduction of MOSFETs, that will enable converter operation over a wider range of duty cycles.

With regard to the lack of comparisons with wide-bandgap transistors (SiC/GaN), it should be noted that their implementation requires the design of a dedicated printed circuit board (PCB). This is due to the much higher switching frequencies typical of such transistors, where PCB layout geometry and the minimisation of parasitic inductance are critical and directly affect the safety and performance of the converter. The currently used silicon transistors are significantly more cost-effective and still widely used in industrial applications, which justifies their use at the concept verification stage of the developed control algorithm.

The absence of thermal analysis and system reliability assessment is primarily due to limitations in available research resources. Reliability analysis requires long-term testing under various environmental conditions. Thermal analysis (e.g., identifying thermal bridges, evaluating heat losses in transistors) in turn requires access to expensive measurement equipment, such as thermal imaging cameras or climate chambers, which are currently not available to the author. Nevertheless, both reliability considerations and thermal analysis represent a valid direction for further research, particularly in the context of the potential commercialisation of the proposed control algorithm.

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Comments 4: Implementation Challenges and Scalability.

- Control algorithm complexity: While the authors claim advanced microcontrollers are unnecessary, managing 12 sectors with Hall sensors plus reverse‑conduction MOSFET timing significantly complicates software and hardware compared to standard sensorless methods.

- EMI considerations omitted: Reverse MOSFET conduction introduces steep current edges, which may exacerbate electromagnetic interference and necessitate additional filtering, increasing cost and size.

- Limited voltage applicability: The method is demonstrated at 24 V. There is no analysis for higher voltages (e.g., 400 V EV systems), where reverse‑conduction benefits diminish and isolation challenges grow.

Response 4: The current level of advancement in single-chip microcontrollers (such as the dsPIC33FJ128MC706 used in the control system) allows for the implementation of complex control algorithms. The performance of these devices continues to increase, making it possible to implement even more advanced control methods - something that was not feasible just a few years ago.

During the research, no issues related to EMI disturbances were observed. There were no cross-conduction or shoot-through faults in the converter, which was continuously monitored using current probes and a power analyser. The converter’s printed circuit board was carefully designed to minimise connection lengths and ensure full isolation of gate signals.

The developed control algorithm is dedicated to low-voltage energy recovery systems used during braking processes, such as in light electric vehicles (e.g., scooters or mopeds) and small wind power systems.

The missing content has been added in Chapter 8 - Conclusions.

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Comments 5: Bibliographic and Content Gaps.

- Insufficient sensorless control references: The paper cites EMF zero‑crossing and observer methods but ignores the latest publications and standards in BLDC/PM motor sensorless control for automotive applications.

- No cost‑benefit analysis: The claim of “no additional cost” is unsupported by any estimation of potential EMI filtering, cooling systems, or increased software development efforts.

Response 5: The literature review focused primarily on discussing the current state of knowledge regarding control algorithms that utilise Hall sensors for rotor position detection. The aim of the article was not to analyse sensorless algorithms; therefore, it does not include a detailed discussion of the latest publications and standards related to sensorless control of BLDC/PM motors in automotive applications.

A comprehensive cost analysis would require a comparison of various converter configurations employing different semiconductor devices, depending on the power levels, currents, and voltages present in the system. The term costless, as used in the article title, refers to the fact that the proposed control algorithm can be implemented on standard hardware platforms used with BLDC motors, without requiring any modifications to the converter’s structure.

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Important note to facilitate locating the introduced changes in the manuscript with marked changes (Manuscript_with_M_Cs.docx file):

a)  the additional content addressing the reviewers’ comments has been highlighted in blue

b)  the parts of the article that were edited for clarity and structure, in accordance with the editorial recommendations, have been highlighted in green. These editorial changes are numerous but do not affect the scientific content presented in the previous version of the manuscript.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Dear authors, thank you for submitting your revised article to Electronics. Based on the authors’ response, I still believe that just extending the concept of reverse-channel conduction of MOSFETs, often used in synchronous rectification, to reverse braking in BLDC drive applications is of limited scientific contribution. In addition, some responses provided to my comments were unsatisfactory, as explained in the following.

Response to comment #2 was unsatisfactory. In my opinion, the authors should include the extra stages depicting the current path through the diodes during the dead time in Fig. 1 d). In addition, although conventional drive systems use relatively low frequency, modern solutions, as even mentioned by the authors, might employ GaN or SiC devices. In such cases, much higher switching frequencies would be employed and also the forward voltage of the reverse diodes are much higher than their Si-based counterparts.

Response to comment #4 was unsatisfactory. There is a misconception in the article in regards to “control” and “modulation”. The authors refer to the proposed scheme as “control method”. However, it is actually a “modulation method”. Referring to it as “control method” leads to the reading understanding that a control system will be investigated.

Author Response

Dear Reviewer,

I would like to sincerely thank you for your valuable comments and clarifications. In particular, I appreciate your remarks regarding the need to accurately represent the current paths within the transistor-diode modules, which are present in a real system due to the required transistor dead time. I am also grateful for your suggestion to apply appropriate terminology in the context of the new modulation method presented in the paper, which involves the use of reverse-conducting field-effect transistors.

In the following section, I will briefly outline the scope of the changes introduced
in the manuscript and indicate how they can be identified in the text.

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Comments 2: Response to comment #2 was unsatisfactory. In my opinion, the authors should include the extra stages depicting the current path through the diodes during the dead time in Fig. 1 d). In addition, although conventional drive systems use relatively low frequency, modern solutions, as even mentioned by the authors, might employ GaN or SiC devices. In such cases, much higher switching frequencies would be employed and also the forward voltage of the reverse diodes are much higher than their Si-based counterparts.

Response 2: In the revised version of the manuscript, Figure 2 has been added to illustrate the current paths occurring in the transistor-diode modules during the transistor turn-on and turn-off processes, which are affected by the dead time (t_on and toff). A detailed description of the commutation sequence of the diodes and transistors in the converter is provided below the Figure 2, using the first sector as an example, which is fully representative of the remaining sectors.

The missing content has been added in Section 1 (highlighted in green).

The author would also like to clarify the scope of the presented work. The article focuses on a new converter modulation method designed for operation with a BLDC machine in generator mode. In motor drive applications, high PWM switching frequencies are generally not used; therefore, the diode conduction losses that occur during transistor switching events are negligible. However, for much higher switching frequencies (particularly in systems employing GaN or SiC transistors) these losses should indeed be taken into account, especially considering the significantly higher reverse conduction voltages of wide-bandgap devices compared to their silicon-based counterparts.

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Comments 4: Response to comment #4 was unsatisfactory. There is a misconception in the article in regards to “control” and “modulation”. The authors refer to the proposed scheme as “control method”. However, it is actually a “modulation method”. Referring to it as “control method” leads to the reading understanding that a control system will be investigated.

Response 4: Throughout the manuscript, the term control method has been replaced with modulation method - this term appeared multiple times. The author fully agrees with the reviewer’s comment that the expression control method can be misleading, as it suggests an automatic adjustment of the transistor duty cycle (D) in response to changes in load torque or rotor speed - which is not the case.

The corrections (changing "control method" to "modulation method") have been highlighted in blue.

Reviewer 2 Report

Comments and Suggestions for Authors

Thank you for responding to the review and incorporating some of the comments into the revised version of the article. I have no further comments.

Author Response

Dear Reviewer,

I would like to inform you about additional changes made in response to the second reviewer. I appreciate the clarification of comments from the reviewer who recommended a major revision. In my previous response, some issues raised in two remarks were not fully understood, which required further additions to the manuscript.

The changes included a broader analysis of the transitional states occurring in the transistor-diode modules, supplemented by Figure 2 and a relevant commentary on diode and transistor commutation (highlighted in green). Another comment concerned the incorrect terminology used for the modulation method presented in the article - it was originally called a control method, but as rightly pointed out by the reviewer, this terminology was corrected throughout the manuscript (changes highlighted in blue).

Round 3

Reviewer 1 Report

Comments and Suggestions for Authors

Dear authors, thank you for submitting your revised article to Electronics. Actions were taken to address the issues explained in my previous review. However, I still believe that using the reverse conduction of the MOSFET channel constitutes very little scientific contribution, even though in a different than usual application.