Abstract
The present GPS (global positioning system) is widely used in electric vehicle navigation; it is usually installed in the middle-to-rear position on the car’s roof, near the rear windshield. Since the GPS antenna operating frequency is 1.575 GHz, the health risk of the passengers in the car in this high-frequency electromagnetic exposure is a matter of concern. In this paper, we construct models for a GPS antenna, an electric vehicle, and a human body. Through the multiphysics field coupling calculation in COMSOL Multiphysics, a finite element simulation software, in both frequency domain and transient analysis, we obtain the electric field strength distribution, specific absorption rate, and temperature distribution of the human body at three positions inside the electric vehicle after being exposed to the GPS antenna radiation for 30 minutes. The peak human-induced electric field is 18.4 V/m, and the peak specific absorption rate is 0.193 W/kg. The 30 minute average maximum human-induced electric field is 1.6906 V/m, which is 3.1% of the ICNIRP limit, the 30 minute average whole-body SAR is 0.0036 W/kg, which is 4.5% of the ICNIRP limit, and the 30 minute average human core temperature rise is 0.06°C, which is 6% of the ICNIRP limit. In addition, we simulate the impact of three different vehicle shell materials on the level of electromagnetic exposure to the human body, which can provide reference for electromagnetic shielding design in automobiles. The results indicate that the induced electric field strength, specific absorption rate (SAR), and temperature rise in various parts of the human body did not exceed the standard limits in the latest version of ICNIRP. This suggests that the electromagnetic exposure from the GPS antenna in a typical automotive environment does not pose a threat to human health.
1. Introduction
In recent years, under the strong support and promotion of national policies, new energy electric vehicles have emerged, and antenna is an important part of the radio communication and detection system in electric vehicles. The GPS antenna used in electric vehicles emits high-frequency radiation, which has led to increasing concerns about the biological effects of exposure to high-frequency and radio-frequency electromagnetic fields in the range of 100 kHz to 300 GHz. GPS has 24 satellites, including 21 working satellites and 3 backup satellites, and theoretically GPS receivers should be able to receive signals from 4 to 11 satellites at any location on Earth at any time; therefore, the system can provide accurate and continuous three-dimensional position, velocity, and time information to users with appropriate receivers. The GPS antenna used in electric vehicles operates at a transmission frequency of 1575.42 MHz (L1 band) and 1227.6 MHz (L2 band), providing separate services for civil and military use, respectively. Circularly polarized microstrip antennas are commonly used as GPS antennas due to their lightweight, cost-effectiveness, and ability to provide omnidirectional coverage, making them popular in radar systems and mobile satellite communication as well. These antennas offer the advantage of enabling an omnidirectional orientation between the transmitter and receiver, allowing for efficient signal reception and transmission [1, 2]. In the 1970s, microstrip antennas emerged as a new antenna concept. Subsequently, microstrip antennas studied by R. E. Munson and J. Q. Howell were applied as conformal omnidirectional antennas on rockets and missiles. With further research, microstrip antennas have been widely used in broadband radio devices ranging from 100 MHz to 100 GHz, particularly in aircraft and electric vehicles.
In electric vehicles, where passengers sit very close to the electrical system and antennas, the high currents generated in these vehicles mean that passengers may be exposed to significant electromagnetic fields [3]. In 1990, Tsukahara and Hirano used numerical analysis to calculate the electric field in the passenger compartment for vehicle surface currents and different plane wave exposures [4]. In 2003, Shiraki et al. conducted a study on the electromagnetic radiation generated by electronic devices inside a vehicle. The study employed a hybrid method combining the time-domain finite difference method and transmission line technique. This approach was utilized to determine the optimal placement of the FM radio antenna within the vehicle [5]. In 2015, Vassilev et al. measured the magnetic fields inside eight different electric vehicles (including battery, hybrid, plug-in hybrid, and fuel cell types) with different motor technologies (brush DC, permanent magnet synchronous, and induction) at frequencies of up to 10 MHz [6]. In 2019, Alessandro Arduino examined the accuracy of numerical dosimetric simulations in the context of human exposure to an electric vehicle electrostatic induction charging system. The study focuses on two optional numerical methods: the electric vector potential formulation and the electric scalar potential formulation [7]. In the same year, Gombarska et al. conducted a study using an omnidirectional 8 dBi antenna to measure the electric field intensity generated by in-vehicle communication devices and high-frequency electronic devices within the 500 MHz–3300 MHz frequency range. The study demonstrated that the exposure to the electromagnetic environment in electric vehicles did not exceed the established safe range [8]. In addition, Shah and Yoo et al. conducted measurements to assess the exposure of manikins with implanted pacemakers to electromagnetic fields emitted by electric vehicle wireless power transmission systems. The study revealed that passengers with neurostimulation implants and implanted hip joints with prostheses experienced specific absorption rate (SAR) values exceeding the established safety standard by more than 10 g of human tissue [9]. In 2021, WenTing and Mai conducted an evaluation of the safety of electromagnetic exposure to the human central nervous system from an electric vehicle magnetically coupled resonance wireless charging system. The study demonstrated that the maximum magnetic induction and electric field strengths in the human head were measured as 0.9 μT and 0.18 V/m, respectively. These values were found to be below the public exposure limits set by the International Commission on Non-Ionizing Radiation Protection, which are 27 μT for magnetic induction and 2.97 V/m for electric field strength [10]. In the same year, De Santis et al. conducted an evaluation of external magnetic fields emitted by wireless power transfer (WPT) systems and internal electric fields generated by human models during the charging process of small electric vehicles (EVs). The study revealed that the obtained results exceeded the reference levels set by the International Commission on Non-Ionizing Radiation Protection (ICNIRP) in the driving position [11].
The effects of high-frequency electromagnetic fields generated by antennas on human health have been studied for decades. In 1993, Dimbylow conducted a study where they used the finite difference in time domain (FDTD) method to calculate the radiation emitted by a dipole antenna on a realistic head model. Their analysis led to the conclusion that highly conductive tissues have a greater tendency to absorb the energy preferentially [12]. In 2008, Yu et al. simulated the electromagnetic characteristics of a whip antenna of a car at different positions based on the CST FIT technique [13]. In 2009, Hirata and Ida conducted a simulation study where they exposed a vehicle to a high-frequency electromagnetic environment, including radar and antennas. Their findings revealed that the presence of the human body model led to the suppression of standing waves near the vehicle’s dashboard. This suppression was attributed to the power absorption of the human body, particularly in the frequency range of 100–200 MHz [14]. Wessapan et al. investigated the specific absorption rate (SAR) distribution and temperature field distribution of a real human body model subjected to electromagnetic radiation from antennas operating at 900 MHz and 1800 MHz, respectively, as influenced by the operating frequency and the size of the distance between the antenna and the human head [15]. In 2021, Kumar and Imaculate presented a hybrid half-mode substrate integrated waveguide (HMSIW) diplex antenna for on-body transceiver application with two resonant frequencies of 4 GHz and 4.79 GHz. This literature has simulated the radiation from the antenna to the human head and body and verified the specific absorption rate. Due to the unidirectional nature of the radiation from this antenna, the SAR values are low [16].
At present, investigations have revealed that the research on the impact of high-frequency environments in electric vehicles on the human body is still not very comprehensive, particularly in the context of the effects of onboard antennas on human subjects. And in this paper, multiphysics field coupling calculations are performed. A comprehensive assessment of the safety of human electromagnetic exposure has been carried out in COMSOL software. We simulated not only the EM-induced E-field distribution and SAR distribution of the human body but also the whole-body average induced E-field, SAR, and head temperature field distributions after 30 minutes of EM irradiation environment, and then compared the results with the latest international standard ICNIRP (2020). In addition, I believe that the research methodology used in this study can significantly reduce the computational effort of similar research endeavours, providing a more economical and efficient approach.
2. Model Building and Calculation Method
2.1. GPS Antenna Model
2.1.1. GPS Antenna Design Principle
In this paper, we present the design of a right-handed circularly polarized GPS receiving antenna. The antenna is fed by a coaxial probe, with a center frequency of 1.575 GHz. To achieve circular polarization, an angle cut is employed, ensuring that the antenna radiates circularly polarized waves. The axis ratio of the circularly polarized wave at the center frequency is maintained at less than 2.0 dB. The excitation source of the model is a voltage source, the excitation source is a sinusoidal voltage signal excitation, the amplitude is set to 1 V, the impedance is 50 Ω, the input power is 20 mw, and the excitation source is set at the base of the antenna [17]. There are two ways to feed the rectangular microstrip antenna to obtain circular polarization characteristics, one is single point feed and the other is orthogonal double feed. The GPS antenna model used in this paper is a single-point fed tangential circularly polarized microstrip patch antenna. By a special feeding method, the circularly polarized rectangular patch microstrip antenna can be obtained. The key to circular polarization is to excite a line polarization wave with two polarization directions of equal orthogonal amplitude and 90° phase difference. According to the cavity mode theory, a single rectangular microstrip antenna fed by a point can produce two simple parallel modes with equal polarization orthogonal amplitude but cannot form a 90° phase difference. In order to form a 90° phase difference between the simple and parallel modes, a simple and parallel mode separation unit is introduced in the regular shape of the single microstrip antenna, the most common form of separation unit is to cut the corner on the two diagonals of the rectangular patch, so that the resonant frequency of the simple and orthogonal modes are separated, and the operating frequency is chosen between the two frequencies. When the size of the simple parallel mode separation unit is appropriately selected, it results in the formation of circular polarization radiation. Specifically, at the operating frequency, the equivalent impedance of one mode exhibits a phase angle leading by 45%, while the equivalent impedance of another mode lags by 45%. This phase difference between the modes facilitates the generation of circularly polarized radiation [18].
2.1.2. GPS Antenna Design Steps
Coaxial line feed, also referred to as backfeed, involves a coaxial socket mounted on a grounding plate. The conductor within the coaxial line is connected to the radiation patch through the dielectric substrate. By identifying the correct location for the feed point, a favorable match can be achieved. In order to design a right circularly polarized microstrip antenna, it is necessary to relocate the coaxial line feed point to the position depicted in Figure 1. In addition, two appropriately sized isosceles triangles need to be cut out at the opposite corners of the square metal patch.
Based on the dielectric substrate parameters, we can employ calculations from formulas (1) to (6) to determine the resonant frequency of 1.575 GHz for the initial size of the radiation patch. By adjusting the width W and length L of the radiation patch, as well as the side length of the square dielectric substrate (Length), we can set the distance and the tangent triangle waist length a from the center of the fine-tuned feed point to generate circularly polarized waves [19]. The position of the coaxial feed point with an input impedance of 50 Ω is estimated based on the dielectric substrate parameters and the initial size of the radiating patch. The actual size of the radiating patch and the precise position of the 50 Ω feed point at the resonant frequency of 1.575 GHz are determined through parametric scan analysis. The optimization objective is to achieve a return loss of less than −20 dB, an axial ratio of less than 3 dB, and a radiation patch size and feed point position that meet the design requirements.
For the rectangular microstrip antenna operating at frequency , the width of the high-efficiency radiation patch can be designed using the following equation:where c is the speed of light and is the permittivity of the dielectric substrate.
The length of the radiation patch is taken as /2, where is the wavelength of the guided wave within the medium:
Due to the consideration of the edge-shortening effect, the actual radiation cell length L should bewhere is the effective dielectric constant and is the equivalent radiation gap length. They can be calculated separately by the following equation, i.e.:
The following equation can also be used to directly approximate the location of the feed point when the input impedance is 50 Ω.where
First, the size of the patch is estimated using equation (2). The antenna structure consists of the patch, dielectric substrate, and ground plane, with their material parameters shown in Table 1. The patch, ground plane, inner conductor, and outer conductor of the coaxial cable are assumed to be ideal conductors. An air domain in the shape of a sphere is set outside the antenna and truncated by a perfectly matched layer (PML) to absorb all radiation. To analyze the electromagnetic waves more accurately, all domains are divided into grids, with the maximum grid size not exceeding one-fifth of the wavelength. The antenna is excited by a coaxial collector port with an input voltage of 1 V and a relative dielectric constant of 1. The port is located on the bottom surface of the coaxial-fed outer cylindrical structure. Due to the high input impedance at the edge of the patch and low input impedance at the center, the position of the coaxial feed cable needs to be adjusted to match the 50 Ω reference impedance. In addition, to find the resonance point at 1.575 GHz, a parameterized scan of the chamfer size of the patch is performed. The main process of the parameter scan is shown in Table 2.
Finally, the design results are given, as shown in Table 3. In practice, the shell of the antenna is mostly of shark fin shape. The material is carbon fiber, because it has very little effect on the antenna radiation characteristics, so in order to simplify the calculation, the antenna shell is designed into a square model with side length of 120 mm, as shown in Figure 2.
2.2. Model of Human Body
Based on the internationally common proportions of the human body, a sitting model of an adult with a height of 1.75 meters has been established. The height of the sitting model is 1300 mm, and the shoulder width is 520 mm. The parameters of the simple three-layer head model are: scalp radius is 92 mm, skull radius is 85 mm, and cerebrum radius is 80 mm. As early as 1968, Rush and Driscoll proposed a three-sphere model to replace the real human head model for numerical calculations [20]. They used three concentric spheres with different resistivities to represent the cerebrum, skull, and scalp. The geometry and coordinate system of the three-sphere mathematical model and the nature of its fit to the head were derived from the standard methods of field theory and the potential energy equation (21). The validity of the model was tested by means of an electrolytic bath containing a human skull and compared with in vivo data from the inside of a monkey’s brain and from the surface of the human head, and can be used to calculate equivalently the dielectric parameters of the human head.
The sitting manikin is shown in Figure 3. The dielectric constants and conductivities of human tissues at the corresponding operating frequencies are obtained according to the fourth order Cole-Cole model, where the average values of cerebral white matter, cerebral gray matter, and cerebrospinal fluid are used for the brain, and the average values of four tissues, skin, blood, muscle and bone are taken for the trunk tissues.
2.3. Complete Vehicle Model
Construct a simplified model of a car body based on the design of the Chinese standard car model. The electric car body model, as depicted in Figure 4, primarily utilizes aluminum alloy and glass materials. The dimensions of the body are 4600 mm × 1800 mm × 1500 mm. A three-dimensional Cartesian coordinate system is established, and the left rear endpoint of the electric car was set as the coordinate origin. The positions of the mannequin and the onboard GPS antenna are listed in Table 4.
3. Principles and Methods of Human Electromagnetic Exposure Assessment
3.1. Calculation Method for Electromagnetic Exposure Assessment
When using the RF Module in COMSOL software for simulation, the main electromagnetic wave equations involved are shown in Table 5.
denotes the magnetic flux through the closed equivalent surface of C and Js denotes the surface current density. Deriving the boundary conditions corresponding to the surface integrals in Maxwell-Ampere’s and Faraday’s laws is a process of taking the limit, which requires obtaining the flux perpendicular to the limiting surface. For a surface that tends to be infinitesimal to vanishing, the contribution of this process is zero, so that at rest, the boundary conditions corresponding to Maxwell-Ampere’s and Faraday’s laws are the same.
By combining Maxwell-Ampere’s law and Faraday’s law, a second-order fluctuation equation can be obtained by substituting the rotations of one of the equations into the other, and the system of equations resulting from the union of these two first-order equations represents an electromagnetic wave. Since the conductivity of the antenna material is set to 0, the plane wave equation is
The far field of an antenna can be calculated from the near field using the Stratton-Chu formula. In 3D space, the formula is as follows:
Thus, the relative far-field radiation pattern is given by plotting ||2. The use of a Perfectly Matched Layer (PML) enables the absorption of outgoing radiation over a wide range of frequencies and angles of incidence to improve simulation accuracy.
A major focus of bioelectromagnetic exposure assessment is the dielectric properties of living organisms, as different dispersion phenomena occur in the same biological tissue at different frequency bands, resulting in changes in the relative permittivity and conductivity of biological tissues with frequency [22]. In 1996, Gabriel et al. derived the fourth-order Cole-Cole model based on the results of RHCole and KSCole studies, which can be applied to calculate the dielectric constant of biological tissues in the frequency band of 10 Hz-20 GHz [23]. The fourth-order Cole-Cole model is shown in the following equation:where is the complex relative permittivity, is the real part of the complex relative permittivity, also known as the relative permittivity, is the imaginary part of the complex relative permittivity, also known as the loss factor, is the value of the relative permittivity at the optical frequency, is the angular frequency in rad/s, which can be found from the frequency, and = 8.854187817 × 10−12 is the permittivity in vacuum in F/m. is the increment of dielectric constant, is the central relaxation time, is the relaxation distribution time, which usually takes the value between 0 and 1, and is the conductivity of ions. In this paper, the conductivity of similar tissues is used to simulate various tissues in the head model based on the GPS antenna frequency of 1.575 GHz [24], and the calculated dielectric parameters and the electromagnetic power loss density (emw) heat sources of the three-layer spherical head model and the human trunk are shown in Table 6.
The effect of electromagnetic exposure on the human body in the 1.575 GHz band is dominated by the heating effect on the human body, a physical process expressed in biometrics as SAR. SAR is the electromagnetic power absorbed per unit time mass of human tissue, and the energy increment is absorbed in the time derivative of the mass increment for a given density and volume [25]. The mathematical expression of SAR is
The basic SAR-based equation:where SAR is the specific absorption rate (W/kg), is the electrical conductivity (S/m), is the tissue density (kg/m3), E is the electric field strength (V/m), and c is the specific heat capacity.
Human head tissue absorbs electromagnetic radiation and converts it into joule heat [26]. In this paper, the transient bioheat equation by Pennes [27] is employed in the COMSOL simulation software to describe a series of heat transfer processes occurring when electromagnetic radiation penetrates through the scalp layer and reaches the skull and cerebrum layers. This allows for the analysis of temperature distribution in various tissue layers of the human head model. The heat transfer equation is expressed by the following formula:where is the tissue density (kg/m3); C is the tissue-specific heat capacity (J/(kg·°C)); k is the thermal conductivity (W/(m·°)); is the tissue temperature (°); is the blood temperature (°); is the blood density (kg/m3); is the blood-specific heat capacity (J/(kg·°)); is the blood irrigation rate (s−1); is the metabolic heat source (W/m3); and is the external heat source (W/m3).
The heat transfer between the tissue and the blood stream is approximated by . The external heat source is the heat loss from the absorption of electromagnetic irradiation by the biological tissue. It can be defined as shown in the following equation:.where ; is the relative permittivity of the tissue; and is the (absolute) permittivity in vacuum.
3.2. Electromagnetic Exposure Safety Assessment Criteria
In order to unify the level of protection related to electromagnetic exposure, the World Health Organization (WHO) has recommended the International Commission on Non-Ionizing Radiation Protection (ICNIRP) guidelines and the Institute of Electrical and Electronics Engineers (IEEE) C95.1-2005 as the safety assessment standards for electromagnetic exposure to all countries around the world. In March 2020, ICNIRP published the latest edition of the ICNIRP Guidelines for human protection against exposure to radiofrequency electromagnetic fields (emf) in the range of 100 kHz–300 GHz (referred to as “RF”). According to the latest ICNIRP guidelines (2020), for frequencies ranging from 30 MHz to 2 GHz, in the far-field region, compliance is demonstrated if the incident power density, incident electric field strength, or incident magnetic field strength (only one of them is required) does not exceed the reference levels. The safety limits for public human-induced electric field exposure in electromagnetic fields from 100 kHz to 300 GHz for an average of 30 minutes are shown in Table 7, and the reference levels for whole-body exposures for an average of 30 minutes are shown in Table 8 [28]. Whole-body average SAR values are to be averaged over the entire body and over a 30 minute period. The 30 minute averaging time is intended to take into account the time required to reach a steady-state temperature, while requiring that the whole-body human body warming value does not exceed 1°C.
The frequency of the GPS antenna is 1.575 GHz. Corresponding to the data in the table, the safety limit of the human body–induced electric field at this frequency is 54.57 V/m, and the safety limit of the whole body average SAR is 0.08 W/kg.
3.3. Computational Validation
In order to test the accuracy of the research modelling and methodology, this paper is compared with the findings in the literature [29]. In the literature, there are studies that focus on the use of UHF Radio Frequency Identification (UHF RFID) passive tagged fixed multiantenna readers for performing SAR assessments in the human body. As depicted in Figure 5, the dimensions of the antenna patch are 122.5 mm in width and 99.6 mm in length. The substrate measures 138.3 mm in width and 131.5 mm in length, with a thickness of 1.52 mm. The copper patch utilized for the antenna possesses a conductivity of 5.813 × 107 S/m, and a relative dielectric constant of 1. The substrate material employed is RO3003, which has a conductivity of 2.2 × 10−4 S/m. The ground surface is set as PEC (perfect electrical conductor). The UHF RFID antennas were located at a distance of 5 cm to the closest surface of the human body. In the exposed scenario, there are three antennas. The center height of the lower antenna is 626 mm, that of the middle antenna is 1018 mm, and that of the upper antenna is 1410 mm, as shown in Figure 6. In this paper, the corresponding microstrip patch antenna is modelled using COMSOL simulation software, the input power of the excitation source is 1 W, and the operating frequency is 866 MHz. The electrical parameters of the organisation in the human body model at 866 MHz are calculated from the fourth order Cole-Cole model, as shown in Table 9.
After performing numerical analysis using the COMSOL software, the human body’s 30 minute whole-body average specific absorption rate (SAR) value was calculated. The distribution of these simulated values is depicted in Figure 7. In order to assess the accuracy of the simulation, the obtained SAR values were compared with the corresponding values reported in the literature. The results of this comparison are presented in Table 10.
The simulation results show that the 30 minute whole-body average SAR value of the human body is 0.0118 W/kg, compared with the results obtained from the simulation in the literature of the 30 minute whole-body average SAR value of 0.012 W/kg. The error ratio of 1.67%, which is within the permissible range of error, due to the different selection of the mesh sectioning fineness of the COMSOL software as well as the computational differences between different software, will inevitably result in the existence of errors. The validation is primarily aimed at confirming the accuracy of the theories, methods, and COMSOL software employed in this study. This paper constructed a microstrip patch antenna model of the same type as described in the literature. The model was utilized to simulate the electromagnetic field distribution when a human body is exposed to the electromagnetic environment of the antenna. A comparison of the results revealed errors of less than 5%, indicating that the methods and software utilized in this study are suitable for electromagnetic simulation calculations involving human subjects.
4. Safety Assessment of Human Electromagnetic Exposure in Electric Vehicles under GPS Antenna Operating Conditions
4.1. GPS Antenna Radiation Characteristics Simulation
For high-frequency electromagnetic fields, the characterization of the system requires defining scattering parameters (S-parameters) based on the electric field. To achieve this, an eigenmode expansion of the electromagnetic fields on the ports is necessary. This expansion allows for the conversion of an electric field pattern on a port into a scalar complex number representing the voltage in transmission line theory. Assume that an eigenmode analysis has been performed on the ports 1, 2, 3, …, and that the electric field patterns E1, E2, E3, …, of the fundamental modes on these ports are known. Further, assume that the fields are normalized with respect to the integral of the power flow across each port cross section, respectively. The port excitation is applied using the fundamental eigenmode, the mode with subscript 1. The computed electric field on the port consists of the excitation plus the reflected field. That is, on the port boundary where there is an incident wave, the computed field can be expanded in terms of the mode fields aswhere as on all other port boundaries, the computed field is given by
The S-parameter for the mode with index k is given by multiplying with the conjugate of the mode field for mode k and integrating over the port boundary. Since the mode fields for the different modes are orthogonal, the following relations are obtained for the S-parameters.
To get S22 and S12, excite port number 2 in the same way.
In this paper, the radiation performance of the antenna is simulated in COMSOL software, and the electromagnetic wave reflection capability is analyzed. As Figure 8 gives the GPS antenna ideal case S11 parameter curve, the horizontal coordinate is frequency, the vertical coordinate is return loss, its resonance point is located at 1.575 GHz, and the return loss at this point is −20 dB. Therefore, the antenna exhibits good return loss. Figure 9 shows the polar plot of antenna axis ratio, all of which are in line with the design principle of GPS antenna. Figure 10 shows the antenna surface electric field distribution; the maximum electric field is 3110 V/m. The four corners of the patch exhibit high electric field, which is consistent with the characteristics of circularly polarized antennas. Figure 11 shows the antenna three-dimensional far field gain; the maximum gain is 6.83 dBi. Figure 12 represents the antenna voltage standing wave ratio (VSWR), and the VSWR values near the resonance points are all below 2, indicating that the antenna has good input matching. The characteristics of the GPS antenna in this work are compared with other literature, as shown in Table 11.
4.2. Electric Field Intensity Distribution in Space of Electric Vehicles
Figure 13 shows the three-dimensional distribution of the induced electric field intensity in the electric car body, wherein the radiation energy it receives is more uniformly spread throughout the car, which is due to the omnidirectional nature of the radiation of the circularly polarized antenna. The maximum value of the induced electric field on the car body is 61.9 V/m, which is located on the rear window glass of the car.
4.3. Human Electric Field Intensity Distribution
Figures 14–16 show the induced electric field intensity distributions of the whole human body and head at the middle rear seat position, the rear window seat position, and the driver’s seat position, respectively, as well as the XY and YZ plane slices of the head. Table 12 gives the details of the maximum values and distributions of the induced electric field intensity of the human body model and the ball head model under the operating frequency of 1.575 GHz of the GPS antenna, respectively.
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As can be seen from Figures 14–16, the distribution of electric field intensity in the whole human body has no obvious rule, which shows that the direction of the electric field generated by the GPS antenna is scattered and not concentrated, and the maximum value does not exceed the ICNIRP guideline of the public exposure safety limit of 54.57 V/m. From the head slices, it can be seen that the electric field gradually decreases from outside to inside the head, and all of them are within the safety standard.
4.4. Human SAR Distribution
For high-frequency electromagnetic radiation, the applied electric field will produce an induced electric field in the human body, and human tissues are lossy media, so there will be a current generated by the electric field, absorbing and dissipating electromagnetic energy, thus the electric field causes a heating effect on human tissues. According to the safety guidelines of ICNIRP, the exposure threshold for the general public is generally 0.08 W/kg, which has been widely used in recent years in bioelectromagnetic exposure studies. Figures 17–19 show the distribution of the specific absorption rate of the antenna on the human body in the middle rear seat position, the rear window seat position, and the driver seat position, respectively.
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The SAR values of the human head model and the three-layer spherical head model consisting of the scalp layer, the skull layer, and the cerebrum layer at the operating frequency of 1.575 GHz of the GPS antenna are given in detail in Table 13. Comparing with Table 13, it can be seen that as the electromagnetic wave generated by the antenna penetrates the human head model, the SAR value is highest in the scalp layer of the human head model, decreases after passing through the skull layer, and is lowest after entering the cerebrum layer. This is determined by the electrical characteristics of the skull layer, where a large amount of electromagnetic waves are absorbed by the skull layer, thus reducing the number of electromagnetic waves entering the cerebrum layer.
4.5. Whole-Body Average of 30 Minute Exposure to GPS Antenna Electromagnetic Fields
The electromagnetic waves generated by the vehicle GPS antenna penetrate the human body. Due to the electromagnetic coupling effect and the cumulative effect of radiation over time, each tissue layer of the human body absorbs the electromagnetic radiation energy and converts it into heat loss. The space averaged induced electric field strength values, whole body averaged SAR, temperature rise values, and ICNIRP limit comparisons for the human body model when the vehicle GPS antenna is operated continuously for 30 minutes at an operating frequency of 1.575 GHz are given in detail in Table 14. A cutaway view of the temperature distribution of the three-layer spherical head model after 30 minutes of irradiation is shown in Figure 20.
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The peak human body temperature over time is derived in the COMSOL results, as shown in Figure 21.
As can be seen, after 30 minutes of irradiation time under the operating condition of the onboard GPS antenna, the average value of the human-induced electric field, the average SAR of the whole human body, and the temperature rise of the body core of the human model at the three positions inside the electric vehicle do not exceed the ICNIRP limits. Therefore, the 30 minute exposure to the human body produced by the car GPS antenna does not produce physiological damage.
From the distribution of temperature field in the head, it can be observed that the scalp layer with the highest electromagnetic power dissipation density has the highest temperature rise, while the skull layer with the lowest power dissipation has the smallest temperature rise. According to Figure 21, the temperature increases rapidly during the early stage of radiation and then gradually slows down after reaching a certain value.
From Table 15, it can be observed that the SAR value and temperature rise caused by GPS antenna radiation on the human body are the lowest compared to medical antennas and mobile phone antennas. This is because GPS antennas typically have lower power levels and are located at a certain distance from the human body. However, due to the prolonged exposure of the body to vehicle-mounted antennas, further research is needed to assess the potential effects of long-term exposure.
4.6. The Impact of Different Vehicle Shell Materials on Human Exposure to Electromagnetic Radiation
Considering that different vehicle body materials can affect the radiation performance of antennas, this study simulated the electromagnetic impact on the human body caused by three typical car shell materials [35–38]. The shell materials were set as PEC, aluminum alloy, and carbon fiber, with their respective dielectric parameters shown in Table 16. Table 17 provides a detailed comparison of the spatial average induced electric field strength, whole-body average SAR value, temperature rise, and ICNIRP limit when the vehicle-mounted GPS antenna operates continuously for 30 minutes at a frequency of 1.575 GHz.
The data indicate that the average whole-body exposure level of the human body is significantly below the ICNIRP standard limits. Among the different vehicle shell materials, carbon fiber material results in the highest exposure to electromagnetic radiation. At a frequency of 1.575 GHz, materials with higher relative permittivity and electrical conductivity exhibit better electromagnetic radiation shielding capabilities. Materials with higher relative permittivity cause a slowdown in the propagation of electromagnetic waves within the material, providing better electromagnetic radiation shielding. Materials with high electrical conductivity can effectively absorb and conduct electromagnetic radiation energy, reducing its propagation. However, carbon fiber materials exhibit relatively weaker absorption capabilities in the high-frequency range. The data presented in this study can provide some reference for the electromagnetic shielding design of vehicles. However, the optimal choice of shielding materials still depends on specific application requirements and design needs, necessitating practical testing and evaluation to determine the most suitable materials.
5. Conclusion
In this paper, we investigate the electromagnetic exposure generated by the GPS antenna of an electric vehicle. Specifically, we focus on evaluating the induced electric field and the specific absorption rate (SAR) in various tissues of the adult human torso, as well as the three layers of tissues in the scalp, skull, and cerebrum. Our simulations were conducted for three different seating positions: the rear middle seat, the rear window seat, and the driver’s seat. To perform these simulations, we employed a multiphysics field approach, utilizing both frequency domain and transient coupling techniques in the COMSOL software.
The purpose is to comprehensively analyze the potential harm caused by the electromagnetic field generated by the GPS antenna. We can also see that the electromagnetic field generated by the GPS is unevenly and unconcentratedly distributed everywhere in the EV. The peak value of human-induced electric field is 18.4 V/m, and the peak value of specific absorption rate is 0.193 W/kg. The average maximum value of human-induced electric field in 30 minutes is 1.6906 V/m, which is 3.1% of the ICNIRP limit; the 30 minute average whole-body SAR maximum is 0.0036 W/kg, which is 4.5% of the ICNIRP limit; and the 30 minute maximum body core temperature rise is 0.06°C, which is 6% of the ICNIRP limit.
Based on the literature review, the advantages of this paper compared to previous similar works are summarized in Table 18.
According to the simulations conducted in this study under specific conditions, the radiation levels of the GPS antenna are considered safe and within the limits set by the International Commission on Non-Ionizing Radiation Protection (ICNIRP). However, in real-world situations, the electromagnetic radiation from in-vehicle GPS antennas is subject to various limitations. For instance, from a material perspective, different materials used for the GPS antenna and vehicle shell exhibit different dielectric properties, which can affect the propagation of electromagnetic waves in and around the antenna, thus influencing the intensity and range of electromagnetic radiation. In terms of time, prolonged operation of the GPS antenna can increase the amount of electromagnetic radiation exposure to the human body. Therefore, when designing and using GPS systems, it is important to consider multiple factors for control and limitation to ensure that human exposure remains within safe levels.
The induced electric field strength, specific absorption rate (SAR) value, and temperature rise in the human body resulting from exposure to the EV GPS antenna are influenced by numerous complex factors. These factors include the operating frequency of the antenna, dielectric properties of the tissues, thermal properties, blood irrigation rate, and more. Further research will focus on developing more realistic human body and antenna models to provide detailed explanations regarding the potential safety risks associated with electromagnetic irradiation from the EV GPS antenna. Ongoing investigations and research into the effects of EV GPS antenna radiation will enhance our understanding of potential risks and help ensure that electromagnetic exposure remains within acceptable limits to protect human health.
Data Availability
All data are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This work was supported in part by the National Nature Science Foundation of China (no. 51867014) and the Department of Education of Gansu Province (Grant number 2024CXPT-11).