A Frequency-Independent Phase Shifter
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe paper presents some interesting approaches and ideas to the design of frequency independent phase shifters. The following suggestions are provided to enhance the quality and clarity of the contribution:
* Background material on all-pass systems can be condensed to make the paper more compact
* Paper presentation is somewhat confusing; authors present both numerical optimization and analytical approach to design of frequency independent phases shifters. The conclusions might be enlarged to include some brief comparison of these two approaches and perhaps suggest which might be superior
* Practical design and implementation would be helpful to validate the concepts; perhaps, one or two simple circuit could be implemented in digital to demonstrate the application of the techniques
Author Response
Comment 1: The paper presents some interesting approaches and ideas to the design of frequency independent phase shifters. The following suggestions are provided to enhance the quality and clarity of the contribution:
Response 1: We thank the referee for the positive evaluation of our manuscript and the insightful remarks. We respond to each specific comment below.
Comment 2: Background material on all-pass systems can be condensed to make the paper more compact
Response 2: We thank the referee for this comment and have condensed the section accordingly. Section 2.1 was removed and the text was modified on line 81 and line 99.
Comment 3: Paper presentation is somewhat confusing; authors present both numerical optimization and analytical approach to design of frequency independent phases shifters. The conclusions might be enlarged to include some brief comparison of these two approaches and perhaps suggest which might be superior
Response 3: We thank the referee for this comment. In fact it turns out that the three-stage filter is the best choice and the numerical solution is adequate (as it is for the single-stage filter as well). We enhanced the discussion of this point in the conclusions, lines 424-425, and the final figure, Fig. 17 (now Fig 18) demonstrates this.
Comment 4: Practical design and implementation would be helpful to validate the concepts; perhaps, one or two simple circuit could be implemented in digital to demonstrate the application of the techniques
Response 4: We thank the referee for this comment and have now included examples of digital implementation e.g. see figures 3 and 4.
Reviewer 2 Report
Comments and Suggestions for AuthorsThe paper has been published as M. CSANAD, A. K. F. VAL BAKER, P. OOMEN.
A FREQUENCY INDEPENDENT PHASE SHIFTER. WWW.THEWORKS.INFO, 2023-09-07
https://osf.io/preprints/osf/ps8zy, DOI: 10.31219/osf.io/ps8zy
In this paper, the authors utilize optimization methods to determine a frequency-independent phase shift. They describe a 3-stage filter that provides a variable phase shifter, i.e., ϕ = 0 - 360° without the need for additional amplifiers. As well, they present a new method that reduces the number of filters necessary, improving on both the accuracy and efficiency of current techniques.
The significant shortcomings and omissions of the paper are the following:
1. Fig. 3: All parameters, pointed in the figures, must be deciphered.
2. Equations of other authors must be accompanied by corresponding references in the whole paper text. For example, (2), (3).
3. Arctan and atan in the same designation of this geometric function must be used in the whole paper. Compare (2) and (4).
4. (Line 112): Correct subscript in w0.
5. How can we receive Fig. 6 from Fig. 5?
6. Figs. 5, 6 must be displaced from P. 5 to P. 4.
7. (Line 133): How was received the formula for c2?
8. Figs. 7, 8 must be displaced from P. 6 to P. 4.
9. Comparing (4) and (7), the plus before second term in (7) must be replaced by minus.
10. (Lines 171 – 174): How were received these formulae?
11. In all text: Designations f and F must be the same.
12. How was received formula (11)?
13. (Lines 211 – 212): The average does not depend on variable d, but depend on constants 𝛿𝑚𝑖𝑛 and 𝛿𝑚𝑎x, see (12).
14. Comparing (12) and (13), where is it right: 𝜔𝑚𝑖𝑛/𝜔𝑚𝑎x or 𝜔𝑚𝑎x/𝜔𝑚𝑖𝑛?
15. (Lines 330 – 332): How can be justified the optimal choice, pointed in Line 332?
16. (Line 334): How was it empirically justified that the three parameters (𝜔1, 𝜉2, 𝜔0,1) can be fixed almost arbitrarily?
17. (Lines 337 – 340): What are the grounds for the pointed optimal choice of the parameters.
18. (Line 340): Why the minus sign states before X3?
19. How was received representation (24) on the base of (15) and (16)?
20. Summary should be extended for account of the results obtained.
Author Response
Comment 1: In this paper, the authors utilize optimization methods to determine a frequency-independent phase shift. They describe a 3-stage filter that provides a variable phase shifter, i.e., ϕ = 0 - 360° without the need for additional amplifiers. As well, they present a new method that reduces the number of filters necessary, improving on both the accuracy and efficiency of current techniques.
Response 1: We thank the referee for the positive evaluation of our manuscript and the insightful remarks. We respond to each specific comment below.
Comment 2: Fig. 3: All parameters, pointed in the figures, must be deciphered.
Response 2: All the parameters in Fig 3 (now Fig 4) have now been deciphered, see line 103.
Comment 3: Equations of other authors must be accompanied by corresponding references in the whole paper text. For example, (2), (3).
Response 3: We think that the phase-shift for a first-order, and second order, all-pass band-stop filter, as given in Eq (2) and (3) does not require a reference as these are standard equations. We have added an additional sentence which clarifies how the equation is conceived, see line 108
Comment 4: Arctan and atan in the same designation of this geometric function must be used in the whole paper. Compare (2) and (4).
Response 4: We unified all appearances and solely use ‘atan’ now.
Comment 5: (Line 112): Correct subscript in w0.
Response 5: We corrected this as suggested, line 125.
Comment 6: How can we receive Fig. 6 from Fig. 5?
Response 6: The function shown in Fig. 6 (now Fig.7) is the difference of the two functions shown in Fig. 5 (now Fig. 6). We now comment on this in the caption of Fig. 6 (now Fig 7.), line 193.
Comment 7: Figs. 5, 6 must be displaced from P. 5 to P. 4.
Response 7: We thank the referee for this comment but would like to finalize such formatting issues during the proof stage, as the journal editing would most probably slightly reformat parts of the paper anyway.
Comment 8: (Line 133): How was received the formula for c2?
Response 8: This is a generally utilized definition for chi-square; to make this more clear we added an equation to the manuscript, line 155.
Comment 9: Figs. 7, 8 must be displaced from P. 6 to P. 4.
Response 9: We thank the referee for this comment regarding Fig 7 & 8 (now Fig 8 & 9) but would like to finalize such formatting issues during the proof stage, as the journal editing would most probably slightly reformat parts of the paper anyway.
Comment 10: Comparing (4) and (7), the plus before second term in (7) must be replaced by minus.
Response 10: We thank the referee for pointing this out, it is corrected in the new version, line 185.
Comment 11: (Lines 171 – 174): How were received these formulae?
Response 11: This was found by simple mathematical analysis, through calculating a first-order series in the relevant terms. We added specific wording to make this more clear, line 186.
Comment 12: In all text: Designations f and F must be the same.
Response 12: We unified the appearance of frequencies to be denoted by f everywhere.
Comment 13: How was received formula (11)?
Response 13: This was found by analytically integrating the chi-square function defined earlier.
Comment 14: (Lines 211 – 212): The average does not depend on variable d, but depend on constants ???? and ???x, see (12).
Response 14: In fact the average indeed depends on D (the second derivative with respect to delta is 2D). The phi(delta) function is expressed in Eq. (8), and that’s where this result comes from. We modified the text to make this more clear, line 238.
Comment 15: Comparing (12) and (13), where is it right: ????/???x or ???x/?????
Response 15: The two are actually equivalent, since then the logarithm of this is taken (so a factor of -1 is at stake), which is then squared (so the factor disappears). For the sake of aesthetics, this was given as max/min for Delta phi - we modified the paper to make it more clear, line 247.
Comment 16: (Lines 330 – 332): How can be justified the optimal choice, pointed in Line 332?
Response 16: This is optimal in terms of simplicity and symmetry of the formulas. We modified the paper to make this more clear, line 360.
Comment 17: (Line 334): How was it empirically justified that the three parameters (?1, ?2, ?0,1) can be fixed almost arbitrarily?
Response 17: It was found that the constantness does not depend on their choice; in other words, out of the five parameters only two represent strong modes. We modified the paper to make this more clear, line 364 - 366.
Comment 18: (Lines 337 – 340): What are the grounds for the pointed optimal choice of the parameters.
Response 18: This was found in a chi-square analysis, similarly to the other numerical values in this section (now lines 367-369).
Comment 19: (Line 340): Why the minus sign states before X3?
Response 19: We defined it in such a way that all parameters are positive, (now line 371).
Comment 20: How was received representation (24) on the base of (15) and (16)?
Response 20: This was found via a second-order investigation, if any such shift of phi0, substituted in the formulas for Q2 and xi1, creates a more constant phi(omega).
Comment 21: Summary should be extended for account of the results obtained.
Response 21: We thank the referee for this comment and have added an additional sentence to clarify the results, line 424-425.
Reviewer 3 Report
Comments and Suggestions for AuthorsThis article is a significant contribution to the field of all-pole phase shifters and numerical optimization. With a few minor improvements, it deserves to be published in the journal. Therefore, I recommend acceptance with minor revisions.
The title accurately reflects the content and contributions of the article, highlighting the focus on the synthesis of all-pole phase shifters and the use of numerical optimization. The abstract is concise and informative, clearly summarizing the study's purpose, methods, results, and conclusions. It allows readers to quickly grasp the main contributions of the article.
The introduction provides good context and clearly explains the importance of phase shifters in modern applications. The motivation for the study is well established. The literature review is comprehensive and well-referenced, but adding more recent references would enhance the study's relevance. The research problem is well identified, and the article's contribution to addressing this gap is well articulated.
The methods used are appropriate for the research question posed. The explanations provided on all-pole phase shifters and numerical optimization methods are detailed and justified. The implementation details for both numerical and analog approaches are clear. A diagram could help summarize the numerical optimization process for better understanding. The article is technically sound. However, additional verification might be necessary to ensure all technical aspects are adequately covered.
The results are well presented and easy to understand. Figures and tables are effectively used to illustrate key points. The results are adequately compared with previous studies, clearly showing the improvements made by this study. The study's limitations are addressed but could be further elaborated. Suggestions for future research are provided and well-grounded in the study's findings.
Author Response
Comment 1: This article is a significant contribution to the field of all-pole phase shifters and numerical optimization. With a few minor improvements, it deserves to be published in the journal. Therefore, I recommend acceptance with minor revisions.
The title accurately reflects the content and contributions of the article, highlighting the focus on the synthesis of all-pole phase shifters and the use of numerical optimization. The abstract is concise and informative, clearly summarizing the study's purpose, methods, results, and conclusions. It allows readers to quickly grasp the main contributions of the article.
The introduction provides good context and clearly explains the importance of phase shifters in modern applications. The motivation for the study is well established. The literature review is comprehensive and well-referenced, but adding more recent references would enhance the study's relevance. The research problem is well identified, and the article's contribution to addressing this gap is well articulated.
Response 1: We thank the referee for the positive evaluation of our manuscript and the insightful remarks. We respond to each specific comment below.
Comment 2: The methods used are appropriate for the research question posed. The explanations provided on all-pole phase shifters and numerical optimization methods are detailed and justified. The implementation details for both numerical and analog approaches are clear. A diagram could help summarize the numerical optimization process for better understanding.
Response 2: We thank the referee for the comment. The main process in numerical optimization is to define a chi-square (“penalty function”) and then find its minimum as a function of the parameters. We added a comment to make it more clear (line 148-159 & line 152-155), but we do not find that a diagram would be particularly helpful in this case.
Comment 3: The article is technically sound. However, additional verification might be necessary to ensure all technical aspects are adequately covered.
Response 3: We thank the referee for the comment. We find that the apparent constant phase-shift as a function of frequency shows the adequacy of the model. In a subsequent analysis, a digital circuit implementation can indeed be accessible, but this is out of scope for this manuscript.
Comment 4: The results are well presented and easy to understand. Figures and tables are effectively used to illustrate key points. The results are adequately compared with previous studies, clearly showing the improvements made by this study. The study's limitations are addressed but could be further elaborated. Suggestions for future research are provided and well-grounded in the study's findings.
Response 4: We again thank the referee for the insightful remarks and the positive evaluation.
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsThe authors have satisfactorily responded to the reviewers' suggestions.
Author Response
Comment 1: The authors have satisfactorily responded to the reviewers' suggestions.
Response 1: We thank the referee for the positive evaluation of our responses, as well as that of the manuscript.
Reviewer 2 Report
Comments and Suggestions for AuthorsThe authors have introduced certain revision into text and the paper could be accepted for publication with change of the places of several figures into text.
Author Response
Comment 1: The authors have introduced certain revision into text and the paper could be accepted for publication with change of the places of several figures into text.
Response 1: We thank the referee for the comment, and updated the placement of several
figures in the manuscript, to have them close to where they are referred to in the text. We also thank the referee for the positive evaluation of our previous responses and the new version of the manuscript.
