Theoretical Study of the Input Impedance and Electromagnetic Field Distribution of a Dipole Antenna Printed on an Electrical/Magnetic Uniaxial Anisotropic Substrate

Round 1

Reviewer 1 Report

This paper presented a theoretical study for the investigation of the electromagnetic field distributions and the input impedance of a printed dipole antenna structure loaded on a uniaxial anisotropic medium. 
The motivation of the paper is convincing, the organization of the letter is good.

There are some issues that need to be addressed. Detailed comments and suggestions follow below.

Introduction: Many studies have been performed to characterize microwave structures printed on complex media, ferrites, metamaterials, chiral by employing numerical and analytical methods [11]-[24].
The references are simply listed as [11]-[24]. It is better to introduce the works presented in the reference.  

Figure 1 is not clear. Please plot it in a more clear way.

Writing and English usage should be improved in some places. Please proofreads the manuscript to improve the quality.  

There are some errors in the reference. I suggest the authors list all the references in a consistent format.

Author Response

Response to Editor and Reviewers

Dear Editor,

The authors would like to thank the editor and the reviewers for their precious time and valuable recommendations. We also greatly appreciate the reviewers’ constructive criticisms and appreciated comments and suggestions.

 We have carefully addressed all the reviewers’ comments. A point-by-point response to reviewers’ comments and the corresponding changes and refinements made in the revised paper are denoted below.

The changes are highlighted in red color marked using in the new version.

Sincerely,

Dr Issa Elfergani

Senior Research Engineer

Instituto de Telecomunicações

Campus Universitário de Santiago

3810-193 Aveiro.

Portugal

Answers to Reviewer 1

We are grateful to the reviewer for his positive and encouraging comments. We sincerely thank the reviewer for his constructive criticisms and we also appreciate his insightful comments on revising the paper.

This paper presented a theoretical study for the investigation of the electromagnetic field distributions and the input impedance of a printed dipole antenna structure loaded on a uniaxial anisotropic medium. 

The motivation of the paper is convincing; the organization of the letter is good.

There are some issues that need to be addressed. Detailed comments and suggestions follow below.

Comment #1

• Introduction: Many studies have been performed to characterize microwave structures printed on complex media, ferrites, metamaterials, chiral by employing numerical and analytical methods [11]-[24].

The references are simply listed as [11]-[24]. It is better to introduce the works presented in the reference.

Response:

Thanks for pointing this out.

We detailed on the above-mentioned references and the following paragraph is added to the text:

“In [11], a detailed analytical model is derived for the circularly polarized slot antenna, built on a ferrite substrate. This model is based on an integral equation for the radial electric field on the slot. In [12], a patch antenna model is fabricated on a multiple-ferrite-cored substrate and simulated using the finite element method-based HFSS software.  Recently, in [13], Karma et al. studied microstrip transmission lines with anisotropic and uniaxial anisotropic substrates using the discrete mode matching method. A technique for the calculation of the input impedance of a microstrip antenna printed on chiral substrate based on the integral equation with the Cauchy singularity is derived in [14]. This technique is used, in [15], to investigate the dependences of the input impedance and the magnitude and phase of the electric-field components on the radiator length for different types of chiral substrates. In [16], a method based on the volume integral equation (VIE) is used to evaluate the electromagnetic (EM) fields scattered by general anisotropic multilayer structures. In [17] and [18], for a microstrip patch antenna, the effect of a bianisotropic gyro-chiral substrate on the complex resonant frequency, half-power bandwidth and input impedance, and on the surface waves, respectively, is presented. The analysis is based on the full-wave spectral method of moments using sinusoidal basis functions. In [19], the far field radiation of a Hertzian dipole for two-layered uniaxial anisotropic medium is investigated using the spectral method of moments based on the derivation of the spectral dyadic Green’s functions (DGFs) to examine the effect of anisotropy, effect of layer thickness and effect of dipole location on the radiation fields. The effect of the dielectric constitutive parameters on the input impedance and resonance lengths of a dipole antenna based on stratified electrical anisotropic and chiral substrates and a microstrip patch have been analyzed in [20-23] using the spectral method of moments [24].”

Comment #2

• Figure 1 is not clear. Please plot it in a more clear way.

Response:

Thanks for the remark,

the figure is replaced with a clear one

Comment #3

• Writing and English usage should be improved in some places. Please proofreads the manuscript to improve the quality.  

Response:

The manuscript has been proofread, rectifications are highlighted in yellow in the text.

Comment #4

4. There are some errors in the reference. I suggest the authors list all the references in a consistent format.

Response:

Thanks for the remark.

The format of all references is updated.

Author Response File: Author Response.pdf

Reviewer 2 Report

In this paper, the authors have proposed the theoretical study of the input impedance and electromagnetic field distribution of a dipole antenna printed on an electromagnetic uniaxial anisotropic substrate. The article is well organized, and the study is interesting. However, minor concerns needed to be addressed before the acceptance for publish.
1. The author should add more discussion on the motivation of the proposed method, compared with other analysis of electromagnetic field methods?

2. There are massive literatures on the electromagnetic forward problem computation via the FEM. For examples, the A-V Galerkins equations is the main governing theory on the EM eddy current computations. Lots of approaches have been proposed and believed has its novelty since it has improved the performance of the eddy current computations based on the Galerkin equations. E.g., the conjugate gradients squared (CGS) method with an optimized initial guess-the final solution from the previous frequency can significantly speed up the convergence of the CGS solving process particularly the multi-frequency mode.
3. More discussions on the effects of dipole lift-off on the impedance. The lift-off of the dipole could significantly affect the inspection result, which is a great research interest in the field of NDT. The generated field from dipole is similar to that from coils with AC exciting currents. For example, the corrosion or the coating may influence the lift-off of the sensor during the monitoring. More explanations are suggested to make the paper compelling. For example, literatures for compensating the lift-off errors using eddy current sensors could be highlighted, as some advanced method such as novel compensation algorithms (directly inversion of lift-off distance; lift-off insensitive algorithms; and dual linearity feature), novel sensor designs such as planar triple-coil sensor, and the modified Newton-Raphson method for multi-frequency electromagnetic sensing system.
4. In addition to concern 3, both the 'conductivity lift-off invariance phenomenon' for the non-magnetic metallic plates and the 'permeability invariance phenomenon' for the ferromagnetic plates have already proposed before for the lift-off compensating and addressing the influence of other parameters, in which the optimized Transmitter-Receiver sensor configurations and controlled lift-off have been proposed for the lift-off compensations.

5.To make the manuscript self-contained and more readable, make sure all the variables have been fully specified after each equation.

6. It would be great to see the limitations of the scheme? Overall, the article is quite interesting and technically sound particularly for readers of ECT.

Author Response

Response to Editor and Reviewers

Dear Editor,

The authors would like to thank the editor and the reviewers for their precious time and valuable recommendations. We also greatly appreciate the reviewers’ constructive criticisms and appreciated comments and suggestions.

 We have carefully addressed all the reviewers’ comments. A point-by-point response to reviewers’ comments and the corresponding changes and refinements made in the revised paper are denoted below.

The changes are highlighted in red color marked using in the new version.

Sincerely,

Dr Issa Elfergani

Senior Research Engineer

Instituto de Telecomunicações

Campus Universitário de Santiago

3810-193 Aveiro.

Portugal

Answers to Reviewer 2

We sincerely thank the reviewer for the constructive criticisms and we also appreciate his insightful comments on revising the paper.

In this paper, the authors have proposed the theoretical study of the input impedance and electromagnetic field distribution of a dipole antenna printed on an electromagnetic uniaxial anisotropic substrate. The article is well organized, and the study is interesting. However, minor concerns needed to be addressed before the acceptance for publish.

Comment #1

1. The author should add more discussion on the motivation of the proposed method, compared with other analysis of electromagnetic field methods?

Response:

The following paragraph is added in the Introduction

“….. functions derivation [35]-[38]. The Method of Moments in the spectral domain is found to be a powerful numerical technique to solve integral equations [39], and considered as rigorous and full-wave numerical technique for solving electromagnetic problems and the employing of this method becomes an increasingly important research issue [4-10,17-24,28-31,34-38]. To accurately predict the electromagnetic behavior of microwave components, the method of the moment is widely used in the spectral domain [8-10] [17-18] [20]. The efficient spectral Galerkin-based method of moments (SGMoM) is extensively used to analyze microwave planar structures [34], such as microstrip line and antenna structures, with perfect conductors, it was first applied in the microwave field by Harrington in 1968 [39,40]. To accelerate convergence and improve the computation efficient of this method several procedures have been introduced [10,34,41]. Resolving…”

Comment #2

2. There are massive literatures on the electromagnetic forward problem computation via the FEM. For examples, the A-V Galerkins equations is the main governing theory on the EM eddy current computations. Lots of approaches have been proposed and believed has its novelty since it has improved the performance of the eddy current computations based on the Galerkin equations. E.g., the conjugate gradients squared (CGS) method with an optimized initial guess-the final solution from the previous frequency can significantly speed up the convergence of the CGS solving process particularly the multi-frequency mode.

Response:

In our considered structure, the eddy current is negligible and is not taken into consideration in this study, because the dipole consists of a narrow conducting strip with negligible thickness and is supposed to be printed on a non-metallic perfect dielectric (σ=0).

Comment #3

3. More discussions on the effects of dipole lift-off on the impedance. The lift-off of the dipole could significantly affect the inspection result, which is a great research interest in the field of NDT. The generated field from dipole is similar to that from coils with AC exciting currents. For example, the corrosion or the coating may influence the lift-off of the sensor during the monitoring. More explanations are suggested to make the paper compelling. For example, literatures for compensating the lift-off errors using eddy current sensors could be highlighted, as some advanced method such as novel compensation algorithms (directly inversion of lift-off distance; lift-off insensitive algorithms; and dual linearity feature), novel sensor designs such as planar triple-coil sensor, and the modified Newton-Raphson method for multi-frequency electromagnetic sensing system.

Response:

The present work deals with the distribution of electric and magnetic fields of a dipole printed directly on the upper surface of the anisotropic substrate. Indeed, the lift-off of the dipole affects in one way or another the input impedance and the EM field distribution, and may be of interest for research, this parameter may be taken into consideration in future works.

Comment #4

4. In addition to concern 3, both the 'conductivity lift-off invariance phenomenon' for the non-magnetic metallic plates and the 'permeability invariance phenomenon' for the ferromagnetic plates have already proposed before for the lift-off compensating and addressing the influence of other parameters, in which the optimized Transmitter-Receiver sensor configurations and controlled lift-off have been proposed for the lift-off compensations.

Response:

Thanks for drawing our attention to this phenomenon, however, we think that this is out of the scope of the present work. This phenomenon will be dealt with in future works.

Comment #5

5. To make the manuscript self-contained and more readable, make sure all the variables have been fully specified after each equation.

Response:

Thanks for the remark

All variables are now defined. The following passage is added

 is the free space wavenumber and  is the angular frequency.  and  are the Fourier variables corresponding to the space domain wavenumbers  and .

Comment #6

6. It would be great to see the limitations of the scheme?

Overall, the article is quite interesting and technically sound particularly for readers of ECT.

Response:

We apologize, we could not quite understand the point of the question, and we thank you for the compliment.

Author Response File: Author Response.pdf

Reviewer 3 Report

In the paper under review, the investigation of the electromagnetic field distributions and the input impedance of a printed dipole antenna structure loaded on a uniaxial anisotropic medium is carried out. The results how the magnetic uniaxial anisotropy influences on the input impedance and the evaluated electromagnetic field are presented and discussed. The recommendations how to improve the dipole radiation using the uniaxial anisotropy, are given. The electric and magnetic field distributions in a dipole antenna structure based on media with uniaxial anisotropy of the constitutive parameters have been calculated.

1. It seems to be much more interesting that the cases of ENG, MNG and DNG materials present much more interest but they do not studied in the paper.
2. The frequency dispersion of permittivity and permeability does not taken into consideration, although the influence of dispersion can essentially distort the images in Fig.14 and Fig.15. The authors are offered to introduce some comments in the text about possible influence of frequency dispersion.
3. Figures 8 and 9 are absent.
4. In line 157 the point after the end of the sentence is omitted.

Author Response

Response to Editor and Reviewers

Dear Editor,

The authors would like to thank the editor and the reviewers for their precious time and valuable recommendations. We also greatly appreciate the reviewers’ constructive criticisms and appreciated comments and suggestions.

 We have carefully addressed all the reviewers’ comments. A point-by-point response to reviewers’ comments and the corresponding changes and refinements made in the revised paper are denoted below.

The changes are highlighted in red color marked using in the new version.

Sincerely,

Dr Issa Elfergani

Senior Research Engineer

Instituto de Telecomunicações

Campus Universitário de Santiago

3810-193 Aveiro.

Portugal

Answers to Reviewer 3

The authors sincerely thank the reviewer for the constructive criticisms and we also appreciate his insightful comments on revising the paper.

In the paper under review, the investigation of the electromagnetic field distributions and the input impedance of a printed dipole antenna structure loaded on a uniaxial anisotropic medium is carried out. The results how the magnetic uniaxial anisotropy influences on the input impedance and the evaluated electromagnetic field are presented and discussed. The recommendations how to improve the dipole radiation using the uniaxial anisotropy, are given. The electric and magnetic field distributions in a dipole antenna structure based on media with uniaxial anisotropy of the constitutive parameters have been calculated.

Comment #1

1. It seems to be much more interesting that the cases of ENG, MNG and DNG materials present much more interest but they do not studied in the paper.

Response:

The effect of the magnetic/electrical uniaxial anisotropy substrate on the distribution of the electromagnetic field has given several results that cannot be ignored. Certainly, the ENG, MNG and DNG case studies will yield more results which may disperse the reader (Overload results that distracts the reader). The results obtained in this paper are original and can be considered as a platform for ENG, MNG and DNG cases which will be treated, separately, in future works.

Comment # 2

2. The frequency dispersion of permittivity and permeability does not taken into consideration, although the influence of dispersion can essentially distort the images in Fig.14 and Fig.15. The authors are offered to introduce some comments in the text about possible influence of frequency dispersion.

Response:

Indeed, the dispersion phenomenon is not taken into account and it would certainly affect the obtained results. However, in this work, the dispersion is supposed to be negligible i.e. the permittivity and the permeability are frequency-independent in the microwave frequency band. The following note is added to the text. 

“which are assumed to be less frequency dispersive in the microwave frequency band”.

Comment #3

3. Figures 8 and 9 are absent.

Response:

Thanks for this valuable remark

Numbering of figures is corrected

Comment #4

4. In line 157 the point after the end of the sentence is omitted.

Response:

Thanks, corrected

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors have addressed all my concerns and therefore I support publication without further changes.

Reviewer 3 Report

The revised version of the paper is suitable for publication in presented view.