Interactions of Electrostatic Discharge With the Human ... - IEEE Xplore

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IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 52, NO. 8, AUGUST 2004

Interactions of Electrostatic Discharge With the Human Body E. Okoniewska, M. A. Stuchly, Fellow, IEEE, and M. Okoniewski, Senior Member, IEEE

Abstract—Electrostatic discharge (ESD) pulses comprise frequencies up to approximately 1 GHz. These pulses have been reported to be associated with health effects. Human exposure standards also set limits on the specific absorption (SA) in tissue. Electric fields and SA are computed using the finite-difference time-domain method and heterogeneous model of the human body. The average SA values in all organs and tissues are below the limits in the IEEE Standard for typical and realistically high ESD pulses. Index Terms—Electrostatic discharge (ESD), finite difference time domain (FDTD), human body, specific absorption (SA).

I. INTRODUCTION

E

LECTROSTATIC discharges (ESDs) occur when two objects at different electric potentials come close enough to arc (spark) in the gap between the objects. In electric utilities or under high-voltage transmission lines, spark discharges occur between an ungrounded or grounded person and an isolated or grounded conducting object in the electric (or magnetic) field. Discharges associated with a static field (as in the case of walking on a carpet) are usually nonrepetitive, however, for time-varying fields (50 or 60 Hz), the discharges can be repetitive due to the recharging of the bodies (provided that the gap between the bodies is maintained sufficiently small). The main concern with ESD relates to its effects on sensitive electronic equipment, consequently, numerous investigations have been performed to evaluate coupling of the ESD to devices or their models. Only limited research has been devoted to interactions of ESD with the human body, and most of the analyses have been limited to low frequencies within the pulse and highly simplified models. The most advanced modeling to date has involved a human model consisting of 11 inter-connected spheres representing basic anatomical parts (head, upper and lower torso, and upper and lower limbs) [1]. On the other hand, previous laboratory studies and analyses of blood samples from electric-power employees have suggested that chromosomal anomalies may result from exposure to spark discharge [2], [3]. ESD consists of two phases: a relatively slow buildup of charges on objects (resulting in a voltage differential) and a rapid transfer of the charges due to the breakdown of air. In the case of 50 or 60 Hz, the buildup of charges of opposite polarity Manuscript received August 12, 2003; revised December 22, 2004. This work was supported by the National Sciences and Engineering Research Council of Canada under grants and by the EPRI under a contract. E. Okoniewska and M. A. Stuchly are with the Department of Electrical and Computer Engineering, University of Victoria, Victoria, BC, Canada V8W 3P6. M. Okoniewski is with the Department of Electrical and Computer Engineering, University of Calgary, Calgary, AB, Canada T2N 1N4. Digital Object Identifier 10.1109/TMTT.2004.831971

occurs every half cycle; i.e., 100 or 120 times per second. In alternating (ac) fields, ESD is defined in terms of the current peak value, wave shape (frequency spectrum), and repetition rate. These parameters depend on many factors and can vary widely. The electrical properties of the body, its shape and posture, and, more specifically, capacitances between the body and ground, and the characteristics of the spark determine the waveform of ESD events. Actual waveform may vary considerably, as it depends on many factors related to the charged object and human body, and perhaps most importantly, the geometry associated with the direct discharge. A specific waveform has been agreed upon in the compatibility test standards [4]–[6]. This form captures typical representative features of practical discharges. The rise time of the pulse is 0.7–1 ns, and its spectrum extends from 0 to approximately 1 GHz. However, most of the pulse energy is limited to frequencies below approximately 4 MHz [5]. Electromagnetic fields interact with the human tissue by producing fields inside the body. From the health-protection perspective, the limits of exposure are based on the specific absorption rate (SAR) for fields continuous in time and the specific absorption (SA) for pulses (single and repetitive) [7]. Previously, the finite-difference time-domain (FDTD) technique has been used to compute currents in the human body resulting from a uniform plane-wave exposure to a prescribed pulse [8], [9]. A heterogeneous model of the human body had a resolution of 1.31 cm, and the typical electromagnetic pulse (EMP) of a rise time of 10–30 ns was represented by an idealized sine wave with duration of a half-cycle at 40 MHz [8]. Alternatively, a convolution procedure was used to obtain the same data for EMP from the incident impulse response [9]. In this paper, we compute the electric fields and SA in various organs and tissues of a high-resolution magnetic resonance imaging (MRI)-based model of an average man with an ESD standard pulse applied to a finger. The FDTD technique is used with appropriate modifications to inject electric charges on the model of the body and a metallic object, and to allow for local application of current of a prescribed waveform. The method is verified against a known solution for a capacitor. The SA data are compared to the IEEE Standard [7]. II. MODELS AND COMPUTATIONAL METHOD A. ESD Scenario Model The configuration modeled consists of a heterogeneous model of the human body with a finger pointing toward a metallic right angle parallelepiped, as illustrated in Fig. 1.

0018-9480/04$20.00 © 2004 IEEE

OKONIEWSKA et al.: INTERACTIONS OF ESD WITH HUMAN BODY

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Fig. 2. Standard ESD current waveform as prescribed in the CENELEC Standard.

B. Computational Method

Fig. 1. Scenario representing ESD between an isolated metallic object (blue) and the human body in contact with the ground plane via both feet. The red outline shows the placement of computational boundaries. The man stands along the z -axis and points in the y -direction.

The human body model (1.76 m, 76 kg) is derived from MRI scans with a resolution of 3.6 mm, and has approximately 80 organs and tissues identified, as described elsewhere [10]. For the computations presented, the model has been re-sampled to consist of 5.4-mm voxels. The model is placed in contact with an infinite perfect electric conductor (PEC) simulating ground. The right-hand finger is extended, aligned with one Cartesian coordinate, and points to the parallelepiped box made of the perfect conductor. The distance between the finger and box is 10.8 mm (two cells). Computational space, outlined in red in Fig. 1, has dimensions of 126.36 135.54 210.06 cm. The distance between each absorbing boundary condition (ABC) and the body model or metallic box is 36 cm. The metal box is 8.1 cm above the perfect conductor on which the human model is placed, and has dimensions of 54 cm width 18.36 cm thickness 167.94 cm height . A standard waveform, as defined by the Federal Office for Scientific, Technical, and Cultural Affairs (CENELEC) [4], is illustrated in Fig. 2. The shape of the pulse reflects nonlinear phenomena of the discharge, and typical impedance of the human body including capacitances to the ground for various body parts. The peak current depends mainly on the potential difference between the two bodies (human and metallic box) in Fig. 1. The shape of the curve is invariant with the potential difference. The ESD is a two-step process. Initially, an electric (surface) charge has to be established on one of the objects, while the other remains grounded. In the second stage, a spark (pulse in Fig. 2) results in the charge transfer and elimination of the potential difference between the objects.

An FDTD code previously developed and extensively tested in our laboratory is used. Before this code could be used for ESD modeling, additional algorithms had to be added, and verification, as well as numerous tests (outlined in Section III), had to be performed. A straightforward addition was an ideal current source. In a manner consistent with standard procedures based on Ampere’s Law [11], the current source (the ESD current between the finger and metal box) is simulated by enforcing four components of the surrounding magnetic field in neighboring Yee cells with each component equal to the prescribed current (where is the mesh size). The electric field divided by is forced to zero along the line of the discharge, thus effectively creating a wire. In the simulations of the ESD, the CENELEC waveform is used for excitation. Other code modifications are charge computation (also used for verification) and retarded excitation (which allows for activation of selected excitation tasks at an arbitrary time of the stimulation). Additionally, an introduction of electric- and magnetic-field uploads/downloads allows for substantial savings in run time. In the simulations performed (and many others), there are two distinct stages of computations, namely, a common initial stage, and then a variety of secondary runs. Here, the initial stage data are uploaded into a disk, and can be downloaded prior to each secondary task. Computational space is terminated with a first-order Mur boundary condition, sufficiently distanced from the active simulation region. The first-order Mur was selected after the perfectly matched layer (PML), GPML, and second-order Mur proved to provide unsatisfactory performance (see Section III). The computational domain comprises a total number of nearly 23 million voxels of 5.4-mm side. The time step is 10.3 ps for a total duration of simulation of 154.485 ns, corresponding to 15 000 steps. Voxels occupied by various tissues of the human body have their values of the average dielectric constant and conductivity, which are summarized in Table I, based on the recent measurements [12]. Dielectric properties of tissues vary as a function of frequency from 0–1 GHz. Their dispersive nature can be modeled in our FDTD code, however, simplified modeling without the dispersion was chosen as it introduces errors whose magnitude is limited for the following reasons. The ESD pulse energy is predominantly contained within frequencies below ap-

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Similar addition is performed for the conductivity, e.g.,

TABLE I AVERAGE TISSUE PROPERTIES USED IN THE MODELING

(2) Energy in the voxel integrated over a pulse duration (in steps) is Energy

(3)

The SA in a voxel is proximately 40 MHz. Up to a few megahertz, the displacement current in tissues is a very small function (less than 1%) of the conduction current. Therefore, at these frequencies, there is no need to assign correct values of the dielectric constant. The selected values of the dielectric constant and conductivity (Table I) are close to the actual values in the 10–100-MHz range. The conductivity values are higher than actual below 10 MHz and lower above 100 MHz, but differences are relatively small. and For instance, for muscle, the values used are S/m, while at 100 Hz, the actual S/m and, at 500 MHz, and S/m [12]. Numerical experiments with different permittivity values, which were performed with a model of the human body of a lower resolution, indicated that errors associated with the assumed nondispersive “average” tissue properties are below 10%, and typically less. The dielectric constant at higher frequencies is greater than actual, but conductivity lower. The errors introduced by neglecting the dispersion will likely overestimate the electric fields in the tissue. Additionally, at frequencies below 10 MHz, the computed SA values will be greater than actual as a direct result of higher conductivity values assigned. Errors at high frequencies are additionally mitigated by the human body acting as a low-pass filler, where the high-frequency spectrum is practically confined to the finger, as shown earlier [6] and in Section IV. C. Data Processing and Scaling Calculation of energy in a voxel over time and the SA proceed in the following manner. The mass of the voxel is computed as a weighted average of the masses of tissues comprising the voxel, based on the original 3.6-mm model. Electric fields computed by the FDTD code on the voxel edges are interpolated to the center of the voxel (using standard FDTD notation)

(1)

Energy voxel mass

(4)

Reported organ and tissue average SA values are computed with exclusion of voxels in which air occupies more than 30% of their volume. If only voxels with no air were taken into account, it was found that the SA values were approximately 10% lower. All computations were performed for the scenario shown in Fig. 1 corresponding to the potential difference of 2.6 kV, capacitance of 850 pF, and peak ESD current (Fig. 2 of 7.5 A). The relationships that need to be used for scaling to different voltage difference ( ) and capacitances ( ) are (5) (6) Energy where

is the charge and

(7) is the ESD current.

III. PRELIMINARY MODELING AND VERIFICATION A. Charge Injection Before modeling the ESD through a heterogeneous model of the human body, several preliminary investigations were performed for simpler models such as a spherical or hemispherical metal object (electrode) over an infinite PEC, and spherical lossy dielectric over an infinite PEC (structure shown in Fig. 3), a spherical lossy dielectric with a small cylindrical extension (simulating the finger) over an infinite PEC. The test objects do not represent the geometry of the actual problem (illustrated in Fig. 1), however, they are adequate representations for the tests of the code performance, while simple enough to introduce to the FDTD code. The main purpose of these tests was to: 1) determine if the code can establish correct charge distribution and 2) how to set up the critical parameters in the code for reliable and accurate simulations. These preliminary tests resulted in development of the additions to the FDTD code and guided selection of the parameters used in the numerical computations, as outlined in Section II. A desired charge is injected into an object (electrode) either by: 1) imposing the displacement vector onto selected points on the electrode or by 2) injecting the current into the object using an ideal current source. After a relatively short transient, a steady state is achieved and the charge distributes itself on the


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TABLE II INJECTED CHARGE VERSUS GAUSSIAN PULSE SPECTRAL CONTENTS

Fig. 3. Structures used to compute static charge on two electrodes and to examine performance of ABCs. The electrodes are formed by the PEC boundary. (a) Hemisphere touching ABC (overall structure dimensions 4 4 1 m). (b) Isolated sphere positioned in the center of the structure 4 2 m). The radius of the hemisphere (overall structure dimensions 4 and the sphere is 50 cm; discretization is 10 cm in each direction. Excitation utilizes Gaussian pulse in time, and spans 50 cm in the z -direction between the electrodes.

2 2

2 2

conductive object surface. A CENELEC waveform of 1-A peak amplitude is found to carry a charge of nC

(8)

If method 1) is used, the charge is transferred by applying the normal electric field to one FDTD cell on each electrode (spherical and PEC), using a soft electric source, where the electric field is found as (9) is the area of the voxel side. where Both delta function (Dirac delta) and Gaussian pulse excitations were tested. With the Gaussian excitation and the applied source of infinite impedance (soft source), the amplitude of the exciting pulse is adjusted at each time step as (10) where is the Gaussian pulse envelope. The radius of the hemisphere and the sphere is 50 cm; discretization is 10 cm in

Fig. 4. Charge on the PEC electrode as a function of time. Note the oscillatory character and long time to the steady state for the delta pulse (grey).

each direction. Excitation utilizes Gaussian pulse in time, and spans 50 cm in the -direction between the electrodes. Table II shows the magnitudes of the injected charges on the two electrodes for various spectral content of the Gaussian pulses. The small difference in the charges on two electrodes is due to the integration (summation) of charges performed only over the finite surface of the PEC within the computational domain bounded by the ABC. This was confirmed numerically, whereby with the increasing computational domain, the difference was disappearing. As expected, Dirac delta results in slower convergence rate, as shown in Fig. 4. Additionally, Dirac excitation results in a large radiated transient in free space, as shown in Fig. 5. The optimal excitation is achieved with the Gaussian of 200 MHz, where the fastest convergence occurs. This pulse is subsequently used in the final simulations for charging stage of the simulations. In summary, these tests indicate that the implemented charge injection using a Gaussian pulse (200 MHz) can be used to establish potential difference between the objects prior to ESD event. B. Absorbing Boundaries Different ABCs were tested in conjunction with the charge injection. Both the lossy sphere and hemisphere terminating on the ABC were evaluated (for the structure, see Fig. 3). Fig. 6 shows the time history of charging the hemisphere [see Fig. 6(a)] and flat PEC [see Fig. 6(b)]. It is apparent that the

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Fig. 5. Radiated electric field in the vertical direction 1.2 m from the charge excitation. Note the strong radiated fields for delta excitation (grey) compared with the Gaussian excitation pulses (various colors).

Fig. 7. (a) Charging of the spherical PEC electrode and (b) the flat PEC electrode for different ABCs terminating in the computational space.

Fig. 6. (a) Charging of the hemispherical PEC electrode and (b) the flat PEC electrode for different ABCs terminating in the computational space.

first-order Mur performs well in both cases for both electrodes. The PML and GPML show satisfactory performance only for the isolated sphere [see Fig. 7(a)]. It should be noted that the hemisphere and PEC are in “physical” contact with the PML or GPML. The following consideration may explain the lack of proper performance of the PML and GPML for charged electrodes in contact with the boundaries. Both boundaries consist of lossy dielectric layers (with anisotropic properties) terminated by the PEC and, as such, they provide a conductive path for static charge. Thus, the charge is simply leaking through the PML/GPML layers to the ground. Terminating PML layers with magnetic walls rather then electric walls does not change the charge behavior, confirming that the leakage is due to conductivities of PML/GPML layers. Thus, if a charged electrode is connected to such an ABC, an exponential RC discharge takes place. This is best illustrated in Fig. 6(b) for the hemisphere. Furthermore, increasing the number of layers in either termination did not result in any improvement. Application of a second-order Mur boundary did not result in


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TABLE III COMPUTED CAPACITANCES OF PARALLEL-PLATE AIR-FILLED CAPACITOR

expected static behavior of fields and was not used in the final simulations. C. Computation of Capacitance A possibility of using the FDTD method to successfully compute electrostatic problems is not widely recognized. Thus, an additional test involving a parallel-plate capacitor was performed. The goal here was to compute static capacitance, and compare it with known solutions. The structure consisted of two PEC square plates of 40 40 cm, separated by air gaps of 2 cm. A relatively coarse mesh with the highest density of 1 1 0.5 cm was used. Two cases were studied, which were: 1) the ideal parallel-plate capacitor and 2) the capacitor with fringing fields. The first case was evaluated by computing voltage and charge contents at the surface of an inner section of the capacitor, cut out from the entire parallel-plate capacitor in such a way that it did not include the conductor edges (thus removing fringing effects). The following observations, characteristic of electrostatics, were made: the voltage remained constant, regardless of location over the capacitor surface, and the magnetic field diminished to noise level. The results, shown in Table III, indicate excellent performance of the FDTD code.

Fig. 8. Simplified model of the scenario for ESD modeling used in the preliminary investigations.

D. Additional Tests To further verify the performance of the code, the electric and magnetic fields around the sphere during charging and in the steady state were evaluated. As expected, after approximately 300 time steps, the electric field attained constant values, while the magnetic field became negligible (noise level), manifesting electrostatic properties of the solution. Tests of time course of discharges with ESD waveforms of spheres of various conductivities confirmed the expected behavior dependence on the conductivity. The lower the conductivity, the longer the time to attain the steady state. In the limit, for a lossless (nonconductive) sphere, the injected charge remains in the point of injection. A series of further tests were performed with a simplified model of the human body consisting of blocks representing head, neck, torso, both legs, one arm, and a finger, as shown in Fig. 8. With this model, tests were performed to determine the minimum distance between the boundary conditions and objects, the length of the spark, the effect of the tissue dielectric constant and conductivity, differences between charging and discharging, and another evaluation of the performance of three ABCs with the human model grounded and separated from the ground.

Fig. 9. Voltage on various objects measured with respect to ground (0 V) during ESD.

IV. MODELING RESULTS A. ESD Characteristics Figs. 9–12 show voltage, charges on objects, energy transfer, and currents flowing through various parts of the human body as functions of time. Fig. 9 presents voltage on various parts of the right arm and the metal object computed with respect to ground (0 V) during the ESD. The voltage decreases with distance from the ESD site. Fig. 10 clearly illustrates the existence of equal and opposite polarity charges on two bodies in Fig. 1, i.e., the metal object and human model plus the ground PEC. It also illustrates that the charges on the grounded human model

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Fig. 10. ground.


Charges on the metal box and anatomical model of the human and

are on both parts of the model, which correctly reflects the actual physical behavior. Over a half of the energy transformed to the human body during the ESD is in the hand-making contact with the spark, and approximately 90% is contained in the arm (Fig. 11). This behavior is consistent with current to the ground via the capacitance between the arm and ground. The “short circuiting” of the discharge current to ground by distributed capacitances of the body parts is further illustrated in Fig. 12. This behavior is consistent with earlier simplified modeling [6]. It can also be noted from Fig. 12 that human body acts as a low-pass filter. The high-frequency content of the pulse is only partly retained in the finger tissues. The rise time of the current pulses increases progressively further away from the location of the ESD spark. Also, as expected, there is no current flowing through the head, and only short low amplitude transient flows through the top part of the shoulders. Overall, the simple global characteristics of the ESD in human body model attest to the proper modeling of the ESD. B. Energy Deposition in Tissue

Fig. 11.

Energy transferred to some body parts during the ESD.

Fig. 12. Current in various body parts during the ESD; also the applied ESD current is shown (excitation).

Spatial variations of the current density tissue in selected body cross sections are shown in Fig. 13 at time snapshots during the ESD discharge. These spatial patterns illustrate the superimposed effect of the ESD current through various surface areas of the body as it flows from the finger to the feet on the ground plane and the differences in the conductivity of tissues. Thus, in the finger, there is very high current density, up to 7.5 kA/m [see Fig. 13(d)]. It decreases to approximately 0.8 kA/m in the upper arm [see Fig. 13(a)], and to 0.12 kA/m in the lower torso [see Fig. 13(c)], but increases to over 0.4 kA/m in the feet, which have smaller cross sections [see Fig. 13(d)]. Additionally, it can be noted that in the torso [see Fig. 13(b) and (c)] and feet, the current is highly concentrated in the large blood vessels (the human body model used maintains continuity of the major blood vessels [10]. The spatial distribution of the SA is illustrated in Fig. 14 and summarized in Table IV. While the maximum SA in the finger [see Fig. 14(b) and (e)] exhibits the same behavior as the current density [see Fig. 13(a) and (d)], the SA patterns in other cross sections depend less drastically than the current density on the conductivity. This is a reasonable behavior, as the electric field is typically lower in high-conductivity tissues. The SA values in Table IV can be compared to the limits imposed by an IEEE Standard established for health protection from RF fields [7]. The IEEE Standard gives a limit of 28.8 J/kg for the whole body average, and 576 J/kg for 1-g spatial peak for single pulses. The limits are based on the equivalency to 0.4 W/kg and 6-min averaging time for exposures to continuous electromagnetic fields and an additional safety factor of five. These limits according to the IEEE Standard [7] are conservative with respect to the auditory effect observed in humans and the loss of consciousness observed in rats, in addition to the protection against harmful biological effects considered by the standard in establishing the limits for continuous radiation. Results presented in Table IV can be extrapolated to higher voltages and capacitances. For example, with capacitance of 850 pF, typical of a car, and voltage of 20 kV, the whole body


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Fig. 13. Current density A/m in various cross sections of the human body during ESD. (a) Through the center of the body at y = 47 cm and at t = 37:1 ns. (b) Through the center of the body at x = 61 cm and at t = 30:9 ns. (c) Through the hips at z = 86 cm and at t = 31:2 ns. (d) Through the right arm at x = 86:2 cm and at t = 35:6 ns. (e) Through the knees at z = 45 cm and at t = 33:9 ns.

and hand SA would be 4.6 mJ/kg and 5.23 J/kg, respectively. In the case of the repeated ESD discharges, as it may occur under

a high voltage transmission line, the SA values in Table IV need to be multiplied by the number of pulses. It is rather unlikely

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Fig. 14. Spatial distribution of SA (normalized to max) in decibels in various cross sections of the human body at the end of ESD. (a) Through the center of the body at x = 61:02 cm. (b) Through the right arm at x = 86:2 cm. (c) Through the center of the body at y = 46:44 cm. (d) Through the shoulders at z = 130:14 cm. (e) Through the torso at z = 95:58. (f) Through the feet at z = 1:62 cm.

that a person would not avoid ESD discharges after a few occurrences. Assuming, however, persistent repetitive discharges, in

the 60-Hz field, there are 120 pulses per second, or 43 200 pulses in 6 min. For the whole body and ESD parameters in Table IV,


TABLE IV AVERAGE SA AND ENERGY IN THE PULSE IN SELECTED ORGAN FOR THE ESD = 7:5 A, WITH BODY-METAL BOX POTENTIAL V = 2:6 kV, I CAPACITANCE TO GROUND OF A MODEL OBJECT 850 pF

this repetitive discharges would result in J/kg and, for J/kg. In the case of repetitive ESD occurthe hand, ring where the potential difference between the human body and J/kg [from (7)] an object is 20 kV, the body-average J/kg. In this case, both limits of and, for the hand, the standard are significantly exceeded. V. CONCLUSIONS Modeling of interactions of the ESD with the human body has been performed with the FDTD technique and heterogeneous model of the body. It has been shown that a properly modified FDTD code can be used to inject charges on conductive objects and to obtain their distribution in the steady state. Deposition of the charges is accomplished either by application of Gauss law and imposition of the displacement vector normal to the surface or by injecting controlled amount of charges using current source. While a Dirac function can be used for this purpose, its application results in long lasting transients and strong radiation fields. Much more effective is to use a Gaussian pulse with a bandwidth of approximately 200 MHz. Computations have indicated that human body capacitances to the ground limit the spectral contents of the ESD in most body parts to frequencies of tens of megahertz. Only very close to the finger through which the ESD spark event takes place, some fraction of the energy is present at higher frequencies of the ESD (up to approximately 1 GHz). Overall, a human body with its distributed capacitance to ground acts similarly to a low-pass filter. Thus, the data obtained in this study confirm earlier predictions based on simplified circuit models and quasi-static analyses [4], [6]. From the health protection perspective, the modeling indicates that, for single discharges, the SA values in organs and tissues are below the limits prescribed in [7], even for ESD pulses of relatively high energy. For instance, if a capacitance of the isolated object is 850 pF (corresponding to, e.g., a large car under a high-voltage transmission line) and the potential differmJ/kg and, in ence is 20 kV, the human body average the hand where ESD occurs, J/kg. These values can J/kg, specified in the IEEE Standard be compared to [7]. On the other hand, it has also been shown that, for repeti-

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tive pulses and a high potential difference of 20 kV, SA in the body exceeds the limits. In practice, it is unlikely that a person will experience repetitive ESD pulses at the rates corresponding to 50- or 60-Hz electric-field charging an isolated object, unless working in close proximity to a high-voltage transmission line. Computations presented give SA values representative of typical ESD discharges, which are lower than the IEEE limits. In practical situations, ESD pulse shape and duration may be quite different, nevertheless, at least qualitative and likely quantitative evaluation can extrapolated from the data presented to the other waveforms. To address the question of chromosomal aberrations and possible other biological effects, this numerical investigation is not sufficient and additional evaluation of biophysical interaction mechanisms, as well as relevant biological experiments, need to be performed. REFERENCES [1] V. Amoruso, M. Helali, and F. Lattarulo, “An improved model of man for ESD applications,” J. Electrostat., vol. 49, pp. 225–244, 2000. [2] I. K. Nordenson, K. H. Mild, S. Nordstrom, A. Swein, and E. Birke, “Clastrogenic effects in human lymphocytes of power frequency electric fields: In vivo and in vitro studies,” Radiat. Environ. Biophys., vol. 23, pp. 191–2001, 1984. [3] I. Nordenson, K. H. Mild, U. Ostman, and H. Ljungberg, “Chromosomal effects in lymphocytes of 400 kV-substation workers,” Radiat. Environ. Biophys., vol. 27, pp. 39–47, 1988. [4] W. Rhoades and J. Maas, “New ANSI ESD standard overcoming the deficiencies of the worldwide ESD standards,” in IEEE Electromagnetic Compatibility Symp., Denver, CO, August 24–28, 1998, pp. 1078–1082. [5] Electromagnetic Compatibility (EMC), Part 4, Testing and Measurement Techniques—Section 2: Electrostatic Discharge Immunity Test, IEC Standard 61 000-4-2, 1995. [6] M. Angeli and E. Cardelli, “Numerical modeling of electromagnetic fields generated by electrostatic discharges,” IEEE Trans. Magn., vol. 33, pp. 2199–2202, Mar. 1997. [7] IEEE Standard for Safety Levels with Respect to Human Exposure to Radio Frequency Electromagnetic Fields, 3 kHz to 300 GHz, IEEE Standard C95.1-1991, 1991. [8] J.-Y. Chen and O. P. Gandhi, “Currents induced in an anatomically based model of a human for exposure to vertically polarized electromagnetic pulses,” IEEE Trans. Microwave Theory Tech., vol. 39, pp. 31–39, Jan. 1991. [9] J.-Y. Chen, C. M. Furse, and O. P. Gandhi, “A simple convolution procedure for calculating currents induced in the human body for exposure to electromagnetic pulses,” IEEE Trans. Microwave Theory Tech., vol. 42, pp. 1172–1175, July 1994. [10] T. W. Dawson and M. A. Stuchly, “High-resolution organ dosimetry for human exposure to low-frequency magnetic fields,” IEEE Trans. Magn., vol. 34, pp. 708–718, May 1998. [11] A. Taflove, Advances in Computational Electrodynamics: The FiniteDifference Time-Domain Method Artech House Norwood, MA, 1998. [12] S. Gabriel, R. W. Lau, and C. Gabriel, “The dielectric properties of biological tissues: III. Parametric models of the dielectric spectrum of tissues,” Phys. Med. Biol., vol. 41, pp. 2271–2293, 1996.

E. Okoniewska, photograph and biography not available at time of publication.

M. A. Stuchly (S’71–SM’76–F’91), photograph and biography not available at time of publication.

M. Okoniewski (S’88–M’89–SM’97), photograph and biography not available at time of publication.