Review Reports

Comments 1: [You mention fan shaped microstrip line to refer to radial stub isn´t it?]

Response 1: Thank you for pointing this out. I agree with this comment. Fan-shaped microstrip lines can serve as a common structural form of radial stubs.

Comments 2: [In table 1 do you compare only with diode rectifiers or do you include , for example GaN HEMT rectifiers? [B]?]

Response 2: Table 1 not only includes comparisons with diode rectifiers, but also includes GaN HEMT rectifiers. Reference B has been revised to Reference [24].

Comments 3: [Seeing the layout of the circuit in Fig. 4 seems that maybe EM simulation would be convenient to take into account additional undesired coupling. Have you completed schematic simulation with Momentum or other EM tool?]

Response 3: Yes，I have completed .EM simulation of the rectifier circuit was performed in the ADS simulation software to reduce the gap between the measured results and the simulation results.

Comments 4: [In the editing of the article, some details mentioned below have been overlooked and should be corrected.]

-Line 223, You say: “In contrast to the conventional approach of measuring low-power microwave rectifier circuits, the rectifier circuit cannot be directly connected to o a microwave source for measurement.”  I think this statement must be rewritten. The rectifier could be connected to any generator, but the point is that you need power high enough to excite rectifier operation, so you need additional amplification.]

Response 4: Thank you for pointing this out. I agree with your point, and the revisions have been made in the manuscript; for reference, please see Line 237-238.

Comments 5: [In figure 8 legends appear in Chinese, which makes difficult to evaluate it.]

Response 5: Thank you for pointing this out. The Chinese annotations in Figure 8 have been revised in new manuscript.

Comments 6: [Equation numbering is not consecutive. After eq 6 appears eq. 8 eq. 7 is missing and eq. 11 is called but does not appear.]

Response 6: Thank you very much for pointing out my detailed mistakes; they have been revised in the original manuscript.

Comments 7: [Reference list in table 1 uses letters (A.B. C.D...) How does it match with the numbered list ofreferences at the end of the paper 1,2,3,...?]

Response 6: Thank you very much for pointing out my detailed mistakes; All references have been cited in the original manuscript, and the letter references A.B.C.D…in the tables have also been converted to numerical citations, which are consistent with the reference list[21-28].

Comments 1: [The authors write:“Considering the area of the rectifier circuit and the insertion loss of the harmonic control network, we only process the 2nd, 3rd, and 4th harmonics” (lines 137-139), “Different from traditional Class-F harmonic control networks, which only perform impedance control on the 2nd and 3rd (two-stage) harmonics to reduce diode loss and improve rectification efficiency, the present invention proposes a novel three-stage Class-F harmonic control network.” (lines 151-154) “A harmonic control network with more stages can better reduce diode loss and further improve rectification efficiency.” (lines 155-156)You should explicitly state why does the proposed design use processing of 2nd, 3rd, and 4th harmonics. Is that dictated by the area of application (as can be summarized from lines 137-139), is the improvement and the distinguishing feature proposed by the authors (from lines 151-156)? It is recommended to state it with referencing to the literature related to recent applications.]

Response 1: Thank you for pointing this out. This design depend on the requirements for high efficiency of rectifier circuits in different application fields.Have added the recent relevant reference[18] on Class F harmonic control theory referenced can be found in Line 157 and explain why we design this as follows:“The more stages a harmonic control network has, the more it can reduce diode loss, and the more it can further improve rectification efficiency. When additionally processing the 4th harmonic (4f₀), the efficiency can be further increased.When controlling harmonics beyond the 4th order, the harmonic control network yields little improvement in efficiency. Moreover, an excessive number of harmonic control networks will increase insertion loss, while also raising design complexity and enlarging the size. As a result, with reference to research literature and application scenarios, a three-stage harmonic control network is selected for the design.”(line138-146).

Comments 2: [Regarding the references. The manuscript has a reference list of 22 sources. They are relevant and up-to-date. However, when scanning the manuscript text, the following can be found: “In Article [B]” (line 54), “In Article [A],” (line 65), “presented in Article [C]” (line 72), “in Articles [C-D]” (line 76), the same numbering in Table 1. Summarizing, there are no citations of the references; the one present in the manuscript cannot be detected by the letter referencing.]

Response 2: Thank you very much for pointing out my detailed mistakes; All references have been cited in the original manuscript, and the letter references A.B.C.D…in the tables have also been converted to numerical citations, which are consistent with the reference list[21-28].

Comments 3: [In the text, the authors write: “(Note: The original text omits the unit "Q", which issupplemented here based on circuit design conventions)" (lines 200-201).l could not quiteunderstand what the authors mean.]

Response 3: The annotations in the original manuscript have been deleted in the revised manuscript due to their lack of practical function.

Comments 4: [lt is recommended to use the equations as they appear in the text to add more consistency tothe explanation. The authors contrary are referencing to equations from (1) to (3) and then.provide them together. The same, with equations (4)-(8).]

Response 4: Thank you for pointing this out.I agree with that.Therefore, We have used the revised equations presented in the manuscript to enhance the consistency of explanation in section 2.1 in this manuscript.

Comments 5: [After equation (8) in line 191 there comes equation (7) in line 258 while in the text, the authors refer to it as to (11).Use consistent numbering and referencing]

Response 5: Regarding the aforementioned errors, revisions have been made in the manuscript. The original Equation (11) has been renumbered to Equation (9)

(in line263,267,272 )to enhance consistency.

Comments 6: [Figure 8 is in Chinese]

Response 6: Thank you for pointing this out. The Chinese annotations in Figure 8 have been revised in new manuscript.

Comments 1: [All references listed should be cited with numbering in the text.]

Response 1: Thank you for pointing this out. We agree with this comment. Therefore, all references have been cited in the original manuscript.

Comments 2: [Freqeuncy responses of the designed circuit should be given.]

Response 2: Sorry,I don’t know what the designed circuit's frequency response exactly is. Below is my understanding of frequency response. If there are any mistakes, please point them out: The frequency response of an RF (Radio Frequency) rectifier circuit describes the variation trend of its RF-to-DC conversion performance (such as rectification efficiency, output DC voltage/current) when the circuit is acted upon by RF input signals with different frequencies; thus, its frequency response is shown in Figure 8(b). The effective operating frequency range of the rectifier circuit is 2.35-2.65 GHz (with rectification efficiency above 70%). and its peak efficiency point is at 2.55 GHz with stable DC output. Parts (a) and (c) of Figure 8 respectively show the variation curves of the rectifier circuit's efficiency with respect to input power and load resistance under a fixed frequency of 2.55 GHz.

Comments 3: [The results shown in Fig. 8  should be explained by theories, perhaps being done according to the frequency responses.]

Response 3: We have provided a theoretical explanation for Figure 8 in the original manuscript, and analyzed the reasons for the slight discrepancies between the measured and simulated efficiency curves.Please see line(274-289).

Response question 1: [Thank you for pointing this out. I agree with this comment. Therefore, a latest theoretical explanation is provided for why the peak efficiency point lies at 2.55 GHz in new manuscript: (Since harmonic control can be divided into Class F harmonic control and continuous Class F harmonic control.Among them, Class F is narrowband harmonic control for a single frequency point. Continuous Class-F, on the basis of Class-F, incorporates a continuous parameter factor α, which enables it to function as wideband harmonic control. Specifically, Class-F belongs to narrowband harmonic control. Only at a single frequency point can the 90-degree overlap between the square voltage waveform and the half-sinusoidal current waveform be achieved. This minimizes diode loss and thereby brings the highest efficiency. Under the condition that the Class F harmonic topology designed for 2.55 GHz is fixed, any frequency deviation will make the system deviate from Class F harmonic control. This further leads to an increase in the overlapping area of voltage and current waveforms, an increase in diode loss, and consequently a decrease in efficiency. Therefore, the rectifier circuit under the Class F harmonic control structure achieves the highest efficiency at 2.55 GHz. (Refer to references on Class F for details). Continuous Class F does not have the problem of rapid efficiency decline due to slight frequency deviation. The introduction of the continuous parameter factor α allows the voltage and current waveforms within a wide frequency band to approximate a square voltage waveform and a half-sinusoidal current waveform with 90-degree overlap—though they are not strictly square or half-sinusoidal. Thus, continuous Class F serves as wideband harmonic control. Although continuous Class F has a wider bandwidth than Class F, its efficiency is slightly lower because its waveforms are not ideal. If continuous Class F were adopted in this study, 2.55 GHz might no longer be the frequency point with the highest efficiency.To sum up, due to the inherent narrowband limitation of Class F harmonic control, the rectifier circuit in this study achieves the highest efficiency at 2.55 GHz.)line(274-296)]

Response question 2: [Thank you for pointing this out.Below are my respective definitions and explanations of the filter, DC filter, third harmonic, and RLC circuit.

A filter is an electronic circuit used to select/pass or suppress signals of specific frequencies. Its core function is to allow target frequency signals to pass while attenuating or blocking non-target frequency signals, based on differences in signal frequency. It can be divided into four basic types according to frequency selection rules, including:Low-pass filter(Allowing low-frequency signals to pass), High-pass filter (Allowing high-frequency signals to pass),Band-pass filter(Allowing signals within a specific frequency band to pass),Band-stop filter(Blocking signals within a specific frequency band).

A DC filter is a specialized subtype of filter. Its core function is to allow the passage of DC signals (with a frequency of 0 Hz) and fundamental frequency signals (the base frequency of a signal, such as 2.55 GHz), while effectively suppressing harmonic signals (signals with frequencies that are integer multiples of the fundamental frequency) and other high-frequency interference signals.It is commonly used in DC power supply systems and microwave rectifier circuits. For instance, at the latter stage of Class -F microwave rectifier circuits, it is employed to retain DC output and filter out the incompletely suppressed harmonic components.

Third harmonic refers to a signal whose frequency is three times the fundamental frequency, and it is a type of harmonic signal (harmonics are integer multiples of the fundamental frequency; for example, the second harmonic is twice the fundamental frequency, and the third harmonic is three times the fundamental frequency).In the Class F harmonic control topology, by controlling the impedance of the third harmonic, the voltage waveform is made to approximate a square wave and the current waveform to approximate a half-sinusoidal wave. This achieves a 90° phase overlap to reduce diode loss.

RLC circuit is a lumped-parameter circuit composed of three components: resistor (Resistor, R), inductor (Inductor, L), and capacitor (Capacitor, C).Essentially, it is a "circuit composition structure". By adjusting the parameter values of R, L, and C, it can form different types of filters such as low-pass, high-pass, and band-pass filters. It has an "equivalent transformation relationship" with microstrip circuits (distributed-parameter structures) — both can achieve the same frequency selection or impedance control functions, with only differences in parameter expression forms (lumped parameters vs. distributed parameters).I n low-frequency circuits, RLC circuits are often used to form simple filters, such as the RLC low-pass filtering unit in power supply filter circuits.In high-frequency scenarios, their functions can be replaced by microstrip structures.]