Abstract

The aim of this work is to present a preliminary investigation on the propagation of electromagnetic fields generated by wireless technologies inside a nuclear facility or power plant. First, a survey of currently proposed wireless technologies for nuclear facilities and plants has been carried out. Then, for selected scenarios, the electromagnetic field propagation has been studied by means of electromagnetic simulation tools, and the presence of the nuclear environment has been simulated by properly modeling environmental parameters and engineered barriers. The choice of the proper simulation techniques and tools is mandatory in order to simulate the effect of the realistic environment on the propagation. Accordingly, the feasibility of wireless technologies application at nuclear facilities can be assessed on the basis of results achieved from simulated scenarios. The goal is to analyze, for selected scenarios, possible issues due to the propagation of an electromagnetic field in the presence of simplified barriers mimicking the real nuclear environment. This approach can provide indications on how to deploy potential benefits of wireless technologies in a nuclear environment, evaluating pros and cons of the investigated technologies.

1 Introduction

It is well known that the nuclear industry is a conservative one. As a consequence, while new technologies are immediately implemented in the conventional industry, as they may offer promising improvements in term of performance and costs, they undergo a slower, more difficult acceptance process when one tries to apply to the nuclear field.

Such an approach is perfectly understandable in consideration of the strict rules and conditions that the nuclear industry must respect in order to guarantee safety and security everywhere and at all time. This is the case for the application of wireless technologies in a nuclear power plant, in a research reactor or in a nuclear facility for the waste management, e.g., for improving sensor or network capabilities. The potential benefits of implementing wireless technology are evident and increase as the technology rapidly evolves.

However, as in every enterprise, and in the nuclear industry a fortiori, the impact of such an implementation should be considered as a major decision.

During the last years, some reports have been proposed in order to analyze the deployment of wireless technology in a nuclear plant setting from a systematic approach, with the aim to provide an overview of the available technology, to support the decision making, and to offer templates for business cases to managers and operators [1,2] as well as to support the assessment of wireless systems implementation from a safety perspective [3]. “Wireless technology is ideally suited for replacement of wire and cable from instrument or control device to the data acquisition system, programmable logic controller, distributed control system, or network node access point. With low power, small size, and ease of circuit integration advantages, wireless process control signal transmission has applications for installations where it can reduce maintenance, and provide signaling where not previously possible or practical” [1].

What is still lacking, to the authors' knowledge, is a detailed analysis of the effects of the specific environment (i.e., the nuclear plant with its piping, vessels, tubes, tanks, and so on) on the electromagnetic field propagation.

Nuclear environments are not as simple as domestic and working environments: they present complex structures and components, which could lead to operational issues for wireless devices if not properly addressed. In fact, they are characterized by extreme temperature and humidity variations, high noise levels as well as potential exposures to chemicals and ionizing radiation. On the other hand, some sensors and instruments may be sensitive to the electromagnetic radiation emitted by the wireless devices. Finally, the presence of the metallic and concrete structures together with a wide variety of sensors, instruments, and systems of different material and shape contributes to the overall nonuniformity of the nuclear environment.

This is widely recognized as a crucial point: “The locations of wireless transmitters must be given adequate thought and planning. The desired coverage area needs to be defined and a site analysis developed. If possible, a propagation analysis should be conducted” [3].

The main motivation of this paper (an augmented and revised edition of [4]) is indeed to start investigating the propagation of electromagnetic fields generated by wireless technologies inside a nuclear facility or power plant.

1.1 Candidate Wireless Technologies for Nuclear Power Plants.

A detailed discussion of key features of a wireless communication system is out of the scope of this paper. There is a huge variety of books and papers dealing with such a highly developed and widespread technology. The interested reader can easily refer to the reference literature for a comprehensive overview of the underlying principles, implementation issues, and key enhancing features [5,6]. Here, only the main elements essential for the core discussion will be briefly recalled. A wireless communication is mainly composed by a transmitter, which processes the input signal so that it is suitable for the transmission in the communication medium, and a receiver, which is able to recover the transmitted signal after the propagation through the noisy medium. Digital wireless networks, widely diffused in industrial environments, are the most suitable wireless technology to be applied in nuclear facilities because of the data types encountered [3]. The most important wireless networks follow the Institute of Electrical and Electronics Engineers (IEEE) 802 family of standards [7], maintained by the IEEE 802 LAN/MAN Standards Committee (LMSC). In particular, wireless local area networks, which operate over a coverage area of hundreds of meters, are covered by the IEEE 802.11 series of standards: 802.11a, 802.11 b, 802.11 g, 802.11n, 802.11ac (also called Wireless Fidelity or WiFi standards). Wireless personal area networks (PANs) operate over a range of a few tens of meters and are covered by the IEEE 802.15 series of standards: 802.15.1 refers to Bluetooth certification, 802.15.2 refers to IEEE 802.15 and IEEE 802.11 coexistence, and 802.15.4 refers to low-rate wireless PAN (e.g., ZigBee, WirelessHART, MiWi, etc.). Services and protocols specified in IEEE 802 map to the data link and physical layers of the ISO-OSI model. IEEE 802 splits the data link layer into two sublayers named logical link control and media access control.

The coverage area typically required in a nuclear facility ranges from few meters to hundreds of meters. As a consequence, in order to realize a facility wireless sensor network, PANs and local area networks standards seem to be the reference standards to be used in a nuclear facility. For an optimal design, the main features of such a wireless sensor network (Fig. 1) should be [5,6]:

  • compliant to a wireless standard

  • low power consumption

  • limited range (multihop)

  • self-organizing

  • low cost

  • easy maintainable

It should be observed that all the features are well fit by the 802.15 standard. In particular, 802.15.4 [8] implements the lowest power consumption protocol for ubiquitous communication between devices. Important features include provisions for supporting time and rate sensitive applications and integrated support for secure communications. Devices also include power management functions such as link quality and energy detection. The basic framework conceives a 10-m communications range with a transfer rate of 250 kbit/s and three possible frequency bands for operation (868/915/2450 MHz). In particular, the 2.4 GHz industrial, scientific, and medical frequency band has got 16 channels with typical transmitting power in the range 1–100 mW and a receiver sensitivity equal to −85 dBm (at 2.4 GHz).

On the basis of the aforementioned considerations, in this paper, the central frequency of 2.4 GHz is adopted in what follows as the frequency range for the simulation model.

2 Simulation Methods

Numerical simulations can probably represent the best approach to carry out preliminary investigations on the propagation of electromagnetic fields from wireless technologies within a nuclear facility, as well as to study possible effects on the quality of service of wireless signals transmission owing to the presence of complex geometries (packed with equipment and concrete or concrete/steel barriers) in the simulated scenario.

The simulation approach offers several advantages. First of all, it allows overcoming all the practical difficulties in performing experimental activities inside a reactor. Moreover, it permits to realize feasibility studies and to create predictive models useful for understanding the expected behavior of the sensor network once deployed. This can be achieved thanks to its intrinsic modular approach, the readiness of results, and the possibility to develop customized simulations exploiting realistic computer-aided design models. Of course, a rigorous V&V phase on real cases is required to achieve reliable models for simulation analysis.

In this paper, a bottom-up approach has been defined to address possible issues related to wireless signals propagation from sensors for monitoring process and environmental parameters (e.g., temperature, pressure, humidity, radiation…) deployed in a nuclear facility. Specifically, the following reference scenarios have been considered to simulate the presence of simplified barriers mimicking the real environment of a nuclear plant:

  • line of sight (LOS) propagation

  • propagation in the presence of engineered barriers

  • propagation in realistic scenarios

A critical point of such an approach is the choice of a numerical method appropriate to simulate the considered scenarios. To this end, analytic approximation techniques—which, in principle, are easy to manipulate and to be interpreted—could be exploited to infer approximate solutions. As a main drawback, however, they provide low simulation accuracy especially when considering scenarios characterized by complex geometries or nonhomogeneous materials.

Computational electromagnetics (CEM) provides far better accuracy, for it exploits a wide range of numerical methods to achieve different tradeoffs between simulation accuracy and calculation speed: of course, this is paid in terms of computational cost [5,10]. CEM tools are widely available both as commercial tools and as custom codes. Different simulation techniques have been implemented over the years, to address problems characterized by different levels of complexity in terms of electrical size and of materials included in the model. Full-wave techniques are usually exploited for low electric size problems, as they allow achieving high accuracy of simulation, e.g., finite difference time domain (FDTD), finite element method (FEM), method of moments (MoM), multilevel fast multiple method (MLFMM) for large structures [1114]. Conversely, asymptotic techniques are typically exploited to solve large electric size problems with acceptable computational cost, e.g., physical optics (PO), geometrical optics (GO), geometrical theory of diffraction (GTD), and uniform theory of diffraction (UTD) [1519]. The aforementioned full-wave and asymptotic techniques can be also exploited in combination to implement hybrid approaches [19,20], able to solve large electromagnetic problems with increased simulation accuracy.

For the scenarios addressed in this study, possible simulation approaches might consider the so-called indoor propagation models [5]. Indoor propagation models include International Telecommunication Union (ITU) models and log-distance path loss models. ITU models estimate the path loss inside a room or a closed area inside a building delimited by walls of any form [9].

In particular, the ITU model estimates the path loss inside a room or a closed area inside a building delimited by walls of any form. Suitable for appliances designed for indoor use, this model approximates the total path loss an indoor link may experience:  
L=20log(f)+Nlog(d)+Pf(n)28

where L is the path loss (in decibels), f is the frequency of transmission (in MHz), d is the distance (in meters), N is the distance power loss coefficient, n is the number of floors between transmitter and receiver, and Pf(n) is the floor loss penetration factor.

The log-distance path loss model is a radio propagation model predicting the path loss a signal encounters inside a building or densely populated areas over distance:  
L=L0+10γlog(d/d0)+N0

where L0 is the path loss (in decibels) at the reference distance d0 (in meters), γ is the path loss exponent, and N0 is a normal random variable with zero mean corresponding to the attenuation (in decibels) caused by flat fading (γ and N0 must be experimentally characterized).

This approach, suitable for appliances designed for indoor use, approximates the total path loss that an indoor link may experience. Log-distance path loss models are radio propagation models predicting the path loss that a signal encounters inside a building or inside densely populated areas over distance.

However, the above-mentioned approaches are not suitable for application to the scenarios considered in this study, because they usually refer to uniform indoor environments, not to a complex environment like a nuclear plant, that is, characterized by a large electrical size as well as by in-homogeneous structures.

As a consequence, the CEM approach appears to be mandatory in order to properly simulate wireless signals propagation in such nuclear facility environments.

In this work, different CEM methods have been investigated. The CEM techniques have had an enormous success after numerical analysis like FDTD, FEM and MoM have been merged with computational power. The interested reader can refer to a wide variety of literature both for theory and applications [10,15].

Due to the very large electrical size involved in a nuclear plant, pure full-wave methods like FDTD, FEM, and MoM have been excluded. Conversely, asymptotic methods like UTD, PO, and GO have been taken into account, both individually or combined in a hybrid approach (e.g., PO/MoM). Among the available commercial electromagnetic simulation tools ([2225]), FEKO® has been used in this study, as it includes all the aforementioned methods with a number of extensions implemented also according to hybrid approaches [22].

2.1 Asymptotic Methods.

In this paragraph, the main features of the three asymptotic methods considered above will be recalled for the sake of clarity in the following discussion and only for the aspects that are relevant for the considered problem. For a comprehensive and detailed treatment, the reader can refer to the vast literature [10,15,21,22].

Physical optics is based on a known radiating current distribution, or the radiation pattern of an antenna. When a scatterer is placed in the radiated field, PO uses a physical approximation to compute the induced currents on the surface. The scattered field is obtained by numerical integration of the surface currents. The main advantage in the considered case is its easiness to be hybridized with MoM. On the other hand, effects of diffractions, multiple bounces, and creeping waves are neglected. As a matter of fact, as it can be seen later, FEKO® implements a number of extensions to the PO

  • fock currents to account for the effect of creeping waves over the shadow boundary region into “unlit” areas;

  • correction terms to achieve more accurate current representation close to edges and wedges.

Geometrical optics is based on the following postulates: (1) wavefronts are locally plane and waves are TEM; (2) rays are normal to the equiphase planes; (3) homogeneous medium; (4) no spatial variation of the dielectric constant, so the rays travel in straight lines.

Geometrical optics is only valid in lit regions because edge diffraction gives a nonzero field in shadows. Edge effects are not taken into account by GO. In order to consider diffraction effects, the GTD has been proposed. This method considers the case of an incident ray at the diffraction point. Yet, GTD is only valid in deep shadow regions since it exhibits singular behavior near the shadow boundary solutions present discontinuities at the shadow boundaries. To predict a continuous total field, in 1974, Kouyoumjian and Pathak introduced UTD [19], as an extension of the geometrical theory of diffraction, multiplying the GTD formula by a canonical transition function, which is unitary inside the deep-shadow region.

3 Simulation Results

The following specifications have been defined to set the numerical simulation models considered in the study [26]:

  • continuous wave wireless signal at the frequency of 2.4 GHz—being one of the most used frequencies for wireless applications in the industrial, scientific, and medical frequency band, it may represent an ideal frequency to be candidate for application of wireless technology in nuclear power plants and facilities

  • indoor propagation in an electrically large environment (about 2 orders of magnitude larger than the wavelength)

  • different materials (e.g., perfect electric conductor (PEC), concrete, etc.) representing various structures present in the environment

  • multiple TX antennas to be excited at the same time representing different sensors deployed in the simulated scenario.

Simulation results obtained with FEKO in different propagation conditions are here presented and compared referring to three asymptotic solvers (namely, UTD, PO, and GO). The objective is to evaluate the three asymptotic solvers available in FEKO® considering two conditions for wireless signal propagation inside a room with the walls made of PEC material, i.e., ideal LOS propagation and nonline-of-sight (NLOS) propagation in the presence of simplified engineered barriers.

Accordingly, three simulation scenarios have been investigated as follows:

  1. Simple PEC room

  2. PEC room without sidewalls

  3. PEC room slice

In Fig. 2, the comparison between LOS and NLOS propagation is considered in the general case of a transmitting (TX) dipole centered on the edge of the irradiation plane.

In Fig. 3, a TX dipole is located inside a PEC room, emitting 1 W of radiated power. A PEC wall separates the room in two half-spaces, one of which contains the dipole. The wall occludes the LOS but its width and height are slightly smaller than the room; thus, it does not cover the entire room section. The calculation of the EM field distribution is required in order to evaluate the electromagnetic field transmitted or scattered in the other half-space of the room.

In Fig. 4, the E-field distribution from the side of a wall opposite to the TX dipole is reported by using different CEM methods.

As expected, GO gives no field in the deep-shadow region, while the effect of the propagation can be seen on the lit regions (see Figs. 4(e), 4(g), 4(h)). On the contrary, both PO (Figs. 4(a), 4(b), 4(c)) and UTD (Fig. 4(e)) are able to evaluate the scattered E-field in the side of the PEC wall opposite from dicetion of incidence of the EM field.

In Fig. 5, a different configuration is considered in order to study the contribution only from ceiling and front/back wall (no floor and side walls). The objective is here to compare asymptotic methods and the full-wave MLFMM, which is specific for large structure. PEC room slice (0.5 m thick) without floor is here considered. In particular, three setups are considered, for a wall thickness equal to 0.01 m and with three different environments

  • both ceiling and front wall present;

  • ceiling present, front wall absent;

  • ceiling absent, front wall present.

Results are summarized in Fig. 6 (in the presence of both wall and ceiling), Fig. 7 (no ceiling), and Fig. 8 (no front wall).

From Figs. 68, it can be observed that PO works better near the wall, even if this result can be affected by the solver implementation. On the other hand, UTD and to some extent GO correctly predict these interference figures. It can also be noted that the interference figure vanishes once the ceiling is removed. Results also show that GO could be the best method for composite structures, PO for a single medium, UTD for PEC structures. It can be underlined that PO generally over-estimates the actual power, while UTD generally under-estimates the actual power. Moreover, near the surface of the PEC wall, PO seems to provide a better accuracy. It also models some interference figures due to rays that are reflected by the ceiling and reach the other side of the PEC wall. These effects are modeled with reasonable accuracy as far as 1.5 m away from the PEC wall. UTD is able to model multiple reflections, edge, and corner diffraction when applied to large polygonal plate, but it is not well suited to the analysis of complex objects with curved surfaces. Accordingly, as the distance from the PEC wall increases, UTD seems to model the effects of constructive/destructive interference with much more accuracy. These interference figures are not modeled by PO, whereas GO seems to capture some of them.

It can also be argued that GO remains the only method capable of handling composite structure, although not suitable for accurate modeling of scattering phenomena from complex geometries. PO is more accurate to model the scattering region near complex-geometry objects, but can only handle a single medium at a time. UTD works only with polygonal PEC structures.

4 Conclusions

The application of wireless communication in a nuclear facility requires a preliminary evaluation of the propagation characteristics of the environment. In this paper, the overall environment geometry has been modeled such that both diffraction and reflection paths play an important role, the LOS path being occluded by a PEC wall. It has been shown that asymptotic methods give results that have a different accuracy when compared with a full-wave method, the degree of accuracy depending on the particular method and varying along the computed near field. It is then of primary importance choosing the proper numerical method for the specific problem in order to come to reasonable, reliable conclusions.

From these preliminary results, it can be argued that UTD would be the best asymptotic method to simulate wireless propagation in the presence of PEC structures, as it approximates near-field electromagnetic fields as quasi-optical and uses ray diffraction to determine diffraction coefficients for each diffracting object-source combination.

On the other hand, GO—being an asymptotic method intended for simulation of electrically large dielectric structures—would be most suitable for applications including composite materials, provided that local wave effects could be ignored.

Physical optics is an intermediate method between GO and full-wave electromagnetic solutions: it is able to model single-medium large structures as well as scattering (nondiffractive) effects. Therefore, PO is particularly suited for hybridization with other CEM methods (e.g., MoM) to simulate wireless propagation in scenarios including large structures as well as complex geometries.

Further work is needed in order to expand this result to different frequencies and different environment configurations.

New research is ongoing in order to include in the simulation framework a realistic plant, so as to study the propagation problem in the presence of real barriers. An analytical method is then required in order to evaluate a performance parameter that can summarize the overall communication quality.

Nomenclature

     
  • d =

    distance, m

  •  
  • d0 =

    reference distance, m

  •  
  • f =

    frequency, MHz

  •  
  • L =

    path loss, dB

  •  
  • L0 =

    path loss at the reference distance d0 , dB

  •  
  • N0 =

    normal random variable with zero mean corresponding to the attenuation (in decibels) caused by flat fading

Greek Symbol

    Greek Symbol
     
  • γ =

    path loss exponent

Nondimensional Numbers

    Nondimensional Numbers
     
  • n =

    number of floors between transmitter and receiver

  •  
  • N =

    distance power loss coefficient

  •  
  • Pf(n) =

    floor loss penetration factor

Acronyms

    Acronyms
     
  • CEM =

    computational electromagnetics

  •  
  • FDTD =

    finite difference time domain

  •  
  • FEKO® =

    Altair Feko™ , a computational electromagnetics (CEM) code

  •  
  • FEM =

    finite element method

  •  
  • GO =

    geometrical optics

  •  
  • GTD =

    geometrical theory of diffraction

  •  
  • IEEE =

    Institute of Electrical and Electronics Engineers

  •  
  • ISO-OSI =

    International Organization for Standardization - Open Systems Interconnection

  •  
  • ITU =

    International Telecommunication Union

  •  
  • LAN =

    local area networks

  •  
  • LMSC =

    LAN/MAN Standards Committee

  •  
  • LOS =

    line of sight

  •  
  • MAN =

    metropolitan area networks

  •  
  • MLFMM =

    multilevel fast multiple method

  •  
  • MoM =

    method of moments

  •  
  • NLOS =

    nonline-of-sight

  •  
  • PAN =

    personal area networks

  •  
  • PEC =

    perfect electric conductor

  •  
  • PO =

    physical optics

  •  
  • QoS =

    quality of service

  •  
  • RX =

    receiving/receiver

  •  
  • TX =

    transmitting/transmitter

  •  
  • UTD =

    uniform theory of diffraction

  •  
  • V&V =

    verification and validation

References

References
1.
EPRI
,
2002
, “Guidelines for Wireless Technology in Power Plants—I: Benefits and Considerations,” accessed July 24, 2019, https://www.epri.com/#/pages/product/1003584/
2.
EPRI
,
2002
, “
Guidelines for Wireless Technology in Power Plants—II: Implementation and Regulatory Issues
,” accessed July 24, 2019, https://www.epri.com/#/pages/product/1007448/
3.
ORNL
,
2006
, “
Assessment of Wireless Technologies and Their Application at Nuclear Facilities
,” accessed July 24, 2019, https://www.nrc.gov/docs/ML0621/ML062140045.pdf
4.
Cappelli
,
M.
,
Lopresto
,
V.
,
Cecchi
,
R.
, and
Marrocco
,
G.
,
2018
, “
Evaluation of Electromagnetic Fields From Wireless Technologies in a Nuclear Plant
,”
26th International Conference on Nuclear Engineering (ICONE)
, London, July 22–26, Paper No. 82290.
5.
Peraia
,
E.
, and
Stacey
,
R.
,
2013
,
Next Generation Wireless LANs: 802.11n and 802.11ac
,
Cambridge Press
,
Cambridge, UK
, p.
478
.
6.
Smith
,
C.
, and
Collins
,
D.
,
2014
,
Wireless Networks
,
McGraw-Hill Professional
,
Toronto, ON, Canada
, p.
752
. pages.
7.
IEEE 802 Working Groups and Study Groups, 2019, “The IEEE 802 LAN/MAN Standards Committee,” accessed July 24, 2019, https://standards.ieee.org
8.
IEEE 802.15 WPANTM Task Group 4 Report
,
2019
, “IEEE 802.15 WPAN™ Task Group 4,” accessed July 24, 2019, http://www.ieee802.org/15/pub/TG4.html
9.
Pechac
,
P.
, and
Klepal
,
M.
,
2000
, “
Empirical Models for Indoor Propagation in CTU Prague Buildings
,”
Radioengineering
,
9
(
1
), pp.
31
36
.
10.
Bondeson
,
A.
,
Rylander
,
T.
, and
Ingelström
,
P.
,
2005
,
Computational Electromagnetics
,
Springer Science
,
New York
.
11.
Kunz
,
A. S.
, and
Lubbers
,
R. J.
,
1993
,
The Finite Difference Time-Domain Method for Electromagnetics
,
CRC Press
,
Boca Raton, FL
.
12.
Jin
,
J.
,
1993
,
The Finite Element Method in Electromagnetics
,
Wiley-IEEE Press
,
New York
.
13.
Harrington
,
R. F.
,
1993
,
Field Computation by Moment Methods
,
Wiley-IEEE Press
,
New York
.
14.
Song
,
J. M.
, and
Chew
,
W. C.
,
1995
, “
Multilevel Fast Multiple Algorithm for Solving Combined Field Integral Equations of Electromagnetic Scattering
,”
Microwave Opt. Technol. Lett.
,
10
(
1
), pp.
14
19
.10.1002/mop.4650100107
15.
Deschamps
,
G. A.
,
1972
, “
Ray Techniques in Electromagnetics
,”
Proc. IEEE
,
60
(
9
), pp.
1022
1035
.10.1109/PROC.1972.8850
16.
Boag
,
A.
, and
Michielssen
,
E.
,
2004
, “
A Fast Physical Optics (FPO) Algorithm for High Frequency Scattering
,”
IEEE Trans. Antenna Propag.
,
52
(
1
), pp.
205
212
.10.1109/TAP.2003.822428
17.
Sun
,
E. Y.
, and
Rusch
,
W. V. T.
,
1994
, “
Time-Domain Physical-Optics
,”
IEEE Trans. Antennas Propag.
,
42
(
1
), pp.
9
15
.10.1109/8.272295
18.
Keller
,
J. B.
,
1962
, “
Geometrical Theory of Diffraction
,”
J. Opt. Soc. Am.
,
52
(
2
), pp.
116
130
.10.1364/JOSA.52.000116
19.
Kouyoumjian
,
R. G.
, and
Pathak
,
P. H.
,
1974
, “
A Uniform Geometrical Theory of Diffraction for an Edge in a Perfectly Conducting Surface
,”
Proc. IEEE
,
62
(
11
), pp.
1448
1461
.10.1109/PROC.1974.9651
20.
Bouche
,
D. P.
,
Molinet
,
F. A.
, and
Mittra
,
R.
,
1993
, “
Asymptotic and Hybrid Techniques for Electromagnetic Scattering
,”
Proc. IEEE
,
81
(
12
), pp.
1658
1684
.10.1109/5.248956
21.
Davidson
,
D. B.
,
2011
,
Computational Electromagnetics for RF and Microwave Engineering
, 2nd ed.,
Cambridge University Press
,
Cambridge, UK
, p.
530
. pages.
22.
Sumithra
,
P.
, and
Thiripurasundari
,
D.
,
2017
, “
A Review Comput. Electromagnetics Methods,” Adv. Electromagn.
,
6
(
1
), pp.
42
55
.
23.
Altair Feko™
,
2019
, “
Altair Feko™ Overview
,” accessed July 24, 2019, www.feko.info
24.
CST Studio Suite
,
2019
, “Electromagnetic Field Simulation Software”, accessed July 24, 2019, www.CST.com
25.
ANSYS HFSS
,
2019
, “3D Electromagnetic Field Simulator for RF and Wireless Design”, accessed July 24, 2019, http://www.ansys.com/Products/Electronics/ANSYS-HFSS
26.
Balanis
,
C. A.
,
2005
,
Antenna Theory Analysis and Design
, 3rd ed.,
Wiley
,
Hoboken, NJ
, p.
1136
.