Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Authors present interesting and valuable work on ultra-wideband baluns. However, the manuscript suggest that the presented work has been published in the US Patent 9,312,815 B2 and successfully implemented as commercial product LTC5549 approximately 10 years ago. The authors should indicate clearly what is novel in this manuscript and how does this contribute to scientific understanding of their previously work.

The impedances A, B, and C used in the equation (2) should be written out in the their own equation block for the sake of completes of derivation. In the following paragraph (l.70-72) it is explained that equation (2) is used for calculation of high-frequency performance and results are shown in Figure 2. However, Figure 2 includes two pairs of curves. It is not obvious which corresponds to equation (2) and how the other pair is obtained. What kind of simulation? Caption of Figure 2 also states some values of used parameters. How were they chosen?

 

In paragraph lines 93-96 a balun were r₂=r₃ is mentioned in one sentence. It would be beneficial if the statement could be supported with equations showing phase difference of 180 degrees.

Section 3 is titled Balun Design, Simulation and Measurement, however, it gives little in information on design process. Instead it just reports the technology in which the prototype was fabricated. If the authors could outline the design process of the proposed balun the manuscript would gain a strong scientific value. By that it is meant the process of getting from the desired bandwidth to the values of inductors and capacitors. The reader should be at least directed to other literature regarding the on-chip layout of balun (floating metal strips are mentioned in line 163). Little comment is given on obtaining the measurements.

Section 4 solely describes the technical specifications of the commercial product where the ultra-wideband balun is incorporated. It this form it contributes little to overall manuscript. This section could be easily dropped out in favor of more in-depth analysis of the balun structure itself. From a model to physical implementation.

Comments on the Quality of English Language

Throughout the manuscript the balun is written capitalized as Balun. This is not seen in other literature and also doesn’t have any grammar value. The word pad is also capitalized in line 194. Same can be observed in captions of Figure 4 and 5, where “Ultra Wideband balun” is used. The inconsistent use of capitalization should be corrected.

Words are unnecessarily hyphenated which suggests that the text was copied from other source. See for example: perform-ance (l.19), capacit-ance (l.28), trans-former (l.33, l.76, l.158), main-taining (l.36), envir-onment (l.188), appro-ximately (l.195), match-ing (l.215), linear-ity (l.216)

For transformers an unusual convention is used: transformer voltage and transformer current, where it contexts dictates that voltage and current are adjectives thus should come before transformer. So in the text should be voltage transformer and current transformer.

Author Response

Comments and Suggestions for Authors: 

1. Authors present interesting and valuable work on ultra-wideband baluns. However, the manuscript suggest that the presented work has been published in the US Patent 9,312,815 B2 and successfully implemented as commercial product LTC5549 approximately 10 years ago. The authors should indicate clearly what is novel in this manuscript and how does this contribute to scientific understanding of their previously work.

Reply:  

We sincerely appreciate your positive evaluation of our work. As you noted, the inventor listed in the cited patent is indeed the corresponding author of this manuscript. The patent was filed primarily to protect the intellectual property of the invention and to secure time for further theoretical investigation of the structure, as the patent itself does not elaborate on the operational mechanisms or underlying principles of the circuit topology.

The corresponding author was also involved in the design and development of the LTC5549. While the successful commercialization of this structure demonstrates its significant practical potential, its academic exploration and analysis remained lacking. This study builds upon those prior achievements, providing a focused theoretical examination of its high-frequency performance, supported by dedicated experimental validation.

We have carefully incorporated your suggestions by further clarifying the novel contributions of this work in the Introduction section, emphasizing its role in complementing prior research with theoretical insights.

Thank you again for your valuable feedback.

 

2. The impedances A, B, and C used in the equation (2) should be written out in the their own equation block for the sake of completes of derivation. In the following paragraph (l.70-72) it is explained that equation (2) is used for calculation of high-frequency performance and results are shown in Figure 2. However, Figure 2 includes two pairs of curves. It is not obvious which corresponds to equation (2) and how the other pair is obtained. What kind of simulation? Caption of Figure 2 also states some values of used parameters. How were they chosen?

Reply:  

We sincerely appreciate your constructive suggestions, which have greatly improved our work.

1. Equation (2):

We have added a new Equation (2) to provide a clearer description of impedances A, B, and C, addressing the gap in the original manuscript.

1. Figure 2 Clarifications:

The "Simulation Curve" illustrates the frequency-dependent insertion loss of an ideal transformer under both positive and negative coupling conditions, accounting for inter-winding parasitic capacitance at high frequencies.

The "High-Frequency Equivalent Model Curve" validates the effectiveness of the transformer’s high-frequency equivalent circuit shown in Figure 1(c). When the model parameters (listed in Figure 2’s caption) were applied—selected based on empirical fitting—the close alignment between the two curves at high frequencies confirms the model’s accuracy.

1. Purpose of Figure 2:

This figure serves two key purposes:

• Demonstrating the validity of the proposed high-frequency model.
• Highlighting the impact of positive/negative coupling on the transformer’s high-frequency behavior.

As per your suggestions, we have expanded the discussion in Lines 75–81 to better explain these points, enhancing the clarity of our methodology and findings.

Thank you once again for your invaluable feedback, which has significantly strengthened the rigor and readability of our paper.

 

3. In paragraph lines 93-96 a balun were r₂=r₃is mentioned in one sentence. It would be beneficial if the statement could be supported with equations showing phase difference of 180 degrees.

Reply:  

We sincerely appreciate your insightful suggestion regarding the phase difference discussion. After careful consideration, we have incorporated the explanation of the "180° phase difference" into Section 2.2 of the manuscript. This adjustment serves two important purposes:

1. It provides a unified discussion of phase characteristics for the balun throughout the paper
2. It enriches the technical content of Section 2.2 while maintaining optimal paper organization

Your thoughtful comment has significantly contributed to improving the completeness and clarity of our study. We believe this modification has strengthened both the logical flow and technical rigor of the manuscript.

Thank you once again for your valuable input, which has helped enhance the quality of our work.

 

4. Section 3 is titled Balun Design, Simulation and Measurement, however, it gives little in information on design process. Instead it just reports the technology in which the prototype was fabricated. If the authors could outline the design process of the proposed balun the manuscript would gain a strong scientific value. By that it is meant the process of getting from the desired bandwidth to the values of inductors and capacitors. The reader should be at least directed to other literature regarding the on-chip layout of balun (floating metal strips are mentioned in line 163). Little comment is given on obtaining the measurements.

Reply:  

We sincerely appreciate your insightful comments, which remarkably align with our ongoing research direction. In our subsequent studies, we plan to develop both qualitative and quantitative design methodologies for this circuit based on specific target performance metrics. While we have made preliminary progress in this area, comprehensively explaining the practical implementation would require substantial space, as the current design process relies on iterative simulations (typically 2-3 cycles) that cannot yet be clearly systematized.

The present paper primarily focuses on elucidating the fundamental principles behind the proposed broadband balun's operation. Regarding design optimization and parameter extraction, we currently depend on simulation software iterations. Nevertheless, in response to your valuable suggestion, we have added a new Figure 8 to illustrate the key process technology information and the general layout configuration of the floating metal strips.

Your constructive feedback has significantly enriched the content of our paper. We greatly appreciate your thoughtful comments, which have helped improve our work.

 

5. Section 4 solely describes the technical specifications of the commercial product where the ultra-wideband balun is incorporated. It this form it contributes little to overall manuscript. This section could be easily dropped out in favor of more in-depth analysis of the balun structure itself. From a model to physical implementation.

Reply:  

We sincerely appreciate your valuable suggestions. Following your guidance, we have streamlined Section 4 by removing excessive technical specifications about the mixer. Recognizing that these product performance metrics are already documented in the published datasheet, we have eliminated the comparative performance table (original Table II).

However, we have retained Figure 11 for the following reasons:

1. The corresponding author was directly involved in developing this product
2. The figure presents previously unpublished measurement data of the mixer employing our proposed balun structure
3. These unique results provide concrete experimental validation of the ultra-wideband balun's contributions as presented in this work

Your thoughtful comments have helped us focus the paper more effectively on its core scientific contributions. We believe these modifications have significantly improved the manuscript's conciseness and academic value.

Thank you once again for your expert guidance.

 

Comments on the Quality of English Language:

1. Throughout the manuscript the balun is written capitalized as Balun. This is not seen in other literature and also doesn’t have any grammar value. The word pad is also capitalized in line 194. Same can be observed in captions of Figure 4 and 5, where “Ultra Wideband balun” is used. The inconsistent use of capitalization should be corrected.

Reply:  

Thank you for your valuable feedback. We have carefully reviewed and revised the manuscript to address the capitalization issue you emphasized.

Your suggestion has greatly improved the clarity and professionalism of our work. If you have any further questions or require additional modifications, please feel free to let us know.

 

2. Words are unnecessarily hyphenated which suggests that the text was copied from other source. See for example: perform-ance (l.19), capacit-ance (l.28), trans-former (l.33, l.76, l.158), main-taining (l.36), envir-onment (l.188), appro-ximately (l.195), match-ing (l.215), linear-ity (l.216)

Reply:  

Thank you for your valuable feedback. We have carefully reviewed and revised the manuscript to address the issue you highlighted regarding the use of hyphens.

Your suggestion has greatly improved the clarity and professionalism of our work. If you have any further questions or require additional modifications, please feel free to let us know.

 

3. For transformers an unusual convention is used: transformer voltage and transformer current, where it contexts dictates that voltage and current are adjectives thus should come before transformer. So in the text should be voltage transformer and current transformer.

Reply:  

Thank you for your valuable feedback. We have carefully reviewed and revised the manuscript to address the grammar issues you emphasized.

Your suggestion has greatly improved the clarity and professionalism of our work. If you have any further questions or require additional modifications, please feel free to let us know.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The integrated balun is important componet of most design in RF, in this paper, it presents the toplogy which is relative interesting and useful, and it achieves large bandwidth. For the propsoed design, it is mainly based on the transfomer, thus I would like to know of the transform ratio  k, kn, is designed for the planar coils on the substrate used.  Also, do the transformer coils whcih illustrated in Fig. 8(b) are designed for specific substrate?  

Author Response

1. The integrated balun is important componet of most design in RF, in this paper, it presents the toplogy which is relative interesting and useful, and it achieves large bandwidth. For the propsoed design, it is mainly based on the transfomer, thus I would like to know of the transform ratio  k, kn, is designed for the planar coils on the substrate used.  Also, do the transformer coils whcih illustrated in Fig. 8(b) are designed for specific substrate?  

Reply:  

We sincerely appreciate your valuable feedback on our work. In response to your comments, we have made the following improvements to the manuscript:

2. Equation (5) in Section 2.2:

We have added a new equation (Equation 5) to explicitly present the relationship between n and k. The specific parameters for k and n used in our study are detailed in Figure 9(a) and line 220 of the manuscript.

1. Process Technology Clarification:

While this work is implemented in a 45nm CMOS process (with the simplified architecture and circuit schematic now illustrated in new Figure 8), we would like to emphasize that the proposed topology is not substrate-specific. Our additional simulations demonstrate its broadband performance across various substrates including Si, GaAs, and IPD.

Thank you for your support of this research. Your insightful comments have significantly strengthened our manuscript. Please don't hesitate to let us know if any additional clarifications would be helpful.

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

Review Opinion, 1st Round Review

 

electronics-3588383:

 

Authors presented a design of an integrated balun for increased bandwidth. They presented the theory, design, simulation, and experiment. They compared the proposed design with representative existing works. The manuscript is well written and can be accepted after minor revisions.

 

My comments and suggestions are as follows.

 

1. 'Balun' is capitalized in many places. Please consider uncapitalizing it conforming to journal standards.

2. Figure 1b: 'Ideal Transformer' notation fonts are too small. Please increase it for better readability.

3. There needs to be a sentence after Line 87, which will describe Equation 1.

4. Figure 1b: In passive baluns, unbalanced currents are due to asymmetries in physical geometry or in circuit elements. In this respect, Figure 1b can be improved. Figure 1b is used to obtain S21 of Equation 2, not to explain the balanced current in the positive (+) and negative (−) terminals in Figure 1b. So consider dividing (1-k^2) Ls by two and place them in the positive line and in the negative line, which results in a symmetry in the circuit.

5. Figure 3: Please explain what r1, r2 and r3 stand for.

6. In the same vein as in 2, consider dividing Rp, (1-k^2)Lp, Rs by two, and placing them symmetrically.

7. Lines 120 to 126 explain the concept of the proposed design. The operating principles of the proposed balun can be explained in a more intuitive way as follows.

In Figure 1b, we transfer r2 to the primary side. Since r2 = r3 and Lm = L3, we have a balanced condition in the resulting bridge circuit: (j*omega*L3)r2 = (j*omega*Lm)r3. Thus no current flows from the top of r3 to the top of L3, which proves I_r2 = I_r3.

Please consider revising the principles of operation for reader's convenience.

8. The proposed balun assumes Lm = L3. Lm is magnetizing inductance while L3 is a lumped element inductance. The frequency dependency of Lm and L3 should be different so that the condition Lm = L3 cannot be met at all frequencies. Please add some comments on this issue while explaining Figure 4b or Figure 6.

9. Equations 7 and 8 correspond to Figure 6. Z0's in Ports 1, 2, and 3 need to be replaced with r1, r2, and r3 respectively.

10. Figures 10a and 10b: Vertical axis title 'Transmission Coefficient' needs to be corrected to 'Magnitude (dB)'.

 

Comments for author File: Comments.pdf

Author Response

Comments and Suggestions for Authors: 

My comments and suggestions are as follows.

 

1. 'Balun' is capitalized in many places. Please consider uncapitalizing it conforming to journal standards.

Reply:  

We sincerely appreciate your valuable feedback. We have carefully standardized all letter cases for variables, abbreviations, and technical terms throughout the manuscript to ensure consistency. Your suggestion has significantly improved the clarity and professionalism of our work. Should any further refinements be needed, we would be happy to address them.

Thank you again for your time and expertise.

 

2. Figure 1b: 'Ideal Transformer' notation fonts are too small. Please increase it for better readability.

Reply:  

Thank you for your valuable suggestion. We have improved the readability of Figure 1(b) by enlarging the "Ideal Transformer" label.

We appreciate your helpful feedback.

 

3. There needs to be a sentence after Line 87, which will describe Equation 1.

Reply:  

Thank you for your valuable suggestion. We have enhanced the contextual description of Equation (1) to improve the logical flow of the manuscript. Your insightful comment has significantly improved the clarity of our work.

We appreciate your professional guidance and welcome any further suggestions.

 

4. Figure 1b: In passive baluns, unbalanced currents are due to asymmetries in physical geometry or in circuit elements. In this respect, Figure 1b can be improved. Figure 1b is used to obtain S21 of Equation 2, not to explain the balanced current in the positive (+) and negative (−) terminals in Figure 1b. So consider dividing (1-k^2) Ls by two and place them in the positive line and in the negative line, which results in a symmetry in the circuit.

Reply:  

Thank you for your insightful suggestion. We have revised Figure 1(b) to optimize circuit symmetry through improved content arrangement. This modification has significantly enhanced the clarity of our presentation.

We appreciate your expert guidance and welcome any additional feedback.

 

5. Figure 3: Please explain what r1, r2 and r3 stand for.

Reply:  

Thank you for your valuable suggestion. We have added detailed descriptions of r1, r2, and r3 in Section 2.3 (Line 112) to clarify their definitions earlier in the text.

Your feedback has significantly improved the manuscript's clarity. We appreciate your expertise and welcome any further suggestions.

 

6. In the same vein as in 2, consider dividing Rp, (1-k^2)Lp, Rs by two, and placing them symmetrically.

Reply:  

Thank you for your thoughtful suggestion regarding circuit symmetry in Figure 6. While we agree this modification could improve aesthetic balance, we found it would:

1. Introduce excessive complexity in the schematic layout
2. Potentially hinder reader comprehension

However, we successfully applied similar optimization to Figure 2, demonstrating the value of your suggestion. The current Figure 6 retains its original form as it:

1. Preserves clarity of key components (Rp, (1-k^2)Lp, Rs)
2. Does not affect theoretical conclusions

We appreciate your expertise and welcome further discussion on this matter.

 

7. Lines 120 to 126 explain the concept of the proposed design. The operating principles of the proposed balun can be explained in a more intuitive way as follows.

In Figure 1b, we transfer r2 to the primary side. Since r2 = r3 and Lm = L3, we have a balanced condition in the resulting bridge circuit: (j*omega*L3)r2 = (j*omega*Lm)r3. Thus no current flows from the top of r3 to the top of L3, which proves I_r2 = I_r3.

Please consider revising the principles of operation for reader's convenience.

Reply:  

Thank you for your constructive suggestion. We have incorporated your proposed explanatory content into Lines 146-153, which has significantly improved the clarity of this section.

We appreciate your valuable input that enhanced our manuscript's quality, and remain open to any additional feedback you may have.

 

8. The proposed balun assumes Lm = L3. Lm is magnetizing inductance while L3 is a lumped element inductance. The frequency dependency of Lm and L3 should be different so that the condition Lm = L3 cannot be met at all frequencies. Please add some comments on this issue while explaining Figure 4b or Figure 6.

Reply:  

Thank you for your insightful observation regarding the frequency-dependent nature of inductances (Lm, L3) and coupling coefficient (k). We fully agree this introduces complexity in circuit analysis.

In response:

1. Added Figure 8 showing the floating metal strip configuration used for fine-tuning
2. This compensation method partially mitigates frequency-dependent effects (Lines 182-188)
3. The adjustment helps maintain analysis validity within target frequency ranges

Your suggestion has significantly strengthened our discussion of practical implementation challenges. We appreciate your valuable perspective.

 

9. Equations 7 and 8 correspond to Figure 6. Z0's in Ports 1, 2, and 3 need to be replaced with r1, r2, and r3 respectively.

Reply:  

Thank you for your valuable feedback. We have carefully modified the characteristic impedance identification names of the three ports in Figure 6 to prevent confusion for readers when reading.

Your suggestion has greatly improved the clarity and professionalism of our work. If you have any further questions or require additional modifications, please feel free to let us know.

 

10. Figures 10a and 10b: Vertical axis title 'Transmission Coefficient' needs to be corrected to 'Magnitude (dB)'.

Reply:  

Thank you for your valuable feedback. We believe that your suggestion regarding the coordinate axis title is very scientific and accurate, and it has been revised accordingly.

Your suggestion has greatly improved the clarity and professionalism of our work. If you have any further questions or require additional modifications, please feel free to let us know.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Most of the comments from the first round of review were addressed. Minor comment before publication:

• From equations (8) and (9) I would assume that r₂ and r₃ in line 150 should be exchanged so that it would be written: (jωL₃)r₃ = (jωL_m)r₂

Author Response

Most of the comments from the first round of review were addressed. Minor comment before publication:

1. From equations (8) and (9) I would assume that r2 and r3 in line 150 should be exchanged so that it would be written: (jωL3)r3 = (jωLm)r2.

Reply:  

We sincerely appreciate

Thank you for identifying this important technical correction. We have revised the parallel relationship between the components to accurately reflect: (jωL₃)∥r₃ = (jωLₘ)∥r₂

This correction has been implemented in the manuscript to properly represent the balanced output configuration.

Your rigorous review has been invaluable in ensuring the technical accuracy of our work. We sincerely appreciate your expertise and welcome any additional feedback.

Author Response File: Author Response.pdf