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J. H. Holland. Adautation in Natural and Artificial Systems. Ann Predictability of Radiation in Vertical Directions Arbor, MI: Universiiy of Michigan, 1975. W. C. Chew, Waves and Fields in Inhomogeneous Media. Van Nostrand Reinhold. 1990.

Based on in Situ Measurements Close to the Ground at Frequencies Above 30 MHz New York:

C. M. Fonseca and P. J. Fleming. “Genetic Algorithms for multiobjective optimization: Formulation, discussion and generalization,” in Proc. Fzph Int. Con$ Genetic Algorithms, 1993, pp. 41H23. S. E. Cieniawski, J. W. Eheart, and S. Ranjithan, “Using genetic algorithms to solve a multiobjective groundwater monitoring problem,” Water Resources Res., vol. 31, no. 2, pp. 399409, 1995. J. D. Shaffer, “Some experiments in machine learning using vector evaluated genetic algorithms,” Ph.D. dissertation, Vanderbilt University, 1984. -, “Multiple objective function optimization with vector evaluated genetic algorithms,” in Proc. First Int. Con$ Genetic Algorithms, 1985, pp. 93-100. N. Srinivas and K. Deb, “Multiobjective optimization using nondom- inated sorting in genetic algorithms,” Evolutionary Computat., vol. 2, no. 3, pp. 221-248, 1995. J. Horn, N. Nafpliotis, and D. E. Goldberg. “A niched Pareto ge- netic algorithm for multiobjective optimization,” in Proc. First ZEEE Con$ Evolutionary Computat., IEEE World Congress on Computational Intelligence, 1994, pp. 82-87. K. A. DeJong, “An analysis of the behavior of a class of genetic adaptive systems,” Ph.D. dissertation, University of Michigan, 1975. D. E. Goldberg and J. J. Richardson, “Genetic algorithms with sharing for multimodal function optimization,” in Genetic Algorithms and Their Applications: Proc. Second Int. Con& Genetic Algorithms, 1987, pp. 4149. C. K. Oei, D. E. Goldberg, and S. J. Chang, “Tournament selection, niching, and the preservation of diversity,” University of Illinois at Urbana-Champaign, 1991. J. Simkin and C. W. Trobridge, “Optimizing electromagnetic devices combining direct search methods with simulated annealing,” IEEE Trans. Magnet., vol. 28, pp. 1343-1348, 1992. S. Kirkpatrick, J. C. D. Gelatt, and M. P. Vechi, “Optimization by simulated annealing,” Science, vol. 220, no. pp. 671480, 1983. L. Davis, Genetic Algorithms and Simulated Annealing. London, Eng- land: Pittman, 1987.

Ian P. Macfarlane

Absfracf-National and international standards specify Limits for the radiated disturbances created by industrial, scientific, and medical (ISM) radio-frequency equipment. The in situ E-field limits they specify above 30 MHz apply at heights above ground of 6 m or less. The international standard CISPR 11 specifies limits at a fixed height of 3 m. The US FCC specifies 1-4 m or 2-6 m height scans, subject to measuring distance. Specified measuring distances vary. For protection of aeronautical safety of life services, CISPR 11 specifies in situ limits 10 m from the exterior wall of the building housing the ISM equipment. The actual distance from the ISM equipment is not specified. This paper considers the predictability of radiation in vertical directions based on in situ measurements using the CISPR and FCC methods. The paper shows that the ISM fields measured by those methods are very poor guides to the fields at elevated angles. In consequence, the specified in situ limits cannot deliver the protection they are assumed to provide for aeronautical safety services. Recommendations are provided to improve the predictability of the fields at elevated angles.

Index Terms- ISM, Numerical Electrnmagnetics Code (NEC), aem- nautical safety of life services, vertical radiation patterns, field strength prediction.

I. INTRODUCTION Limits for radiated disturbances emitted in situ from ISM radio-

frequency (RF) equipment are specified in FCC [l] and CISPR [2] standards. Above 30 MHz, the limits apply to E-fields at heights of 6 m or less. In general, the limits are to protect terrestrial radio and television services. In addition, CISPR 11 Table VI provides

E. F. Kuester and C. L. Holloway, “A low-frequency model for wedge or pyramid absorber mays-I: Theow,” IEEE Trans. Electromag. ComPG vol. 36, pp. 300-306, Nov. 1994. C. L. Holloway and E. F. Kuester, “A low-frequency model for wedge or pyramid absorber arrays-11: Computed and measwed results,” IEEE Trans. Electromag. Compat., vol. 36, pp. 307-313, Nov. 1994.

in situ limits for ‘‘protection of specific safety services ” Table VI lists aeronautical services, including the instrument landing system (ILS). A note to Table VI states: “Many aeronautical communications require the hlkatiOn Of Vertically radiated electromagnetic distur- bances. Work is continuing to determine what provisions may be -

T. Ellam. “An update on the design and synthesis of compact absorbers for EMC chamber applications,” in Proc. 1994 IEEE Int. Symp. EMC, Chicago, Aug. 22-26, 1994, pp. 408412.

necessary to provide protection for such systems.” In cIspR Table the in situ measuring distance above 30

MHz is 10 m “from (the) exterior wall outside the building in which the equipment is situated.” Significantly, the CISPR does not specify the precise measuring distance from the ISM equipment. The FCC specifies in situ measurement distances from the ISM equipment, varying from 30 to 1600 m, or closer distances if the limits are adjusted in inverse proportion to distance.

The CISPR specifies vertically and horizontally polarized E-field measurements at a fixed height of 3 m for Group 2 Class A equipment, and may be interpreted to require a 1-4 m height scan in situ for Group 1 and Group 2 Class B equipment. The FCC specifies height scans of 1 4 m at distances up to 10 m, and 2-6 m at distances greater than 10 m.

By their nature, ISM machines, generating RF powers up to 1 MW or more [3], can radiate high levels of spurious electromagnetic disturbances. To protect aeronautical services, it is important to know whether or not the specified in situ measurements accurately predict the field strengths created at elevated angles. Therefore, some

Manuscript received October 2, 1995; revised April 23, 1996. The author is a consultant with EMC, Victoria 3134, Australia. Publisher Item Identifier S 0018-9375(96)06145-5.

0018-9375/96$05.00 Q 1996 IEEE

526 EEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 38, NO. 3, AUGUST 1996

Excitation frequency, MHZ

15

110

243

interesting questions to be considered are the following: 1) How well can in situ measurements of the vertically and

horizontally polarized E-fields, in height scans of 1-4 m at a known distance of 10 m from the ISM equipment over real ground, predict the field strengths emitted at elevated angles?

2) How predictable are the field strengths at elevated angles when the measuring distance is greater than 10 m but the actual distance is not known (not specified)?

3) How is the predictability affected when the height above ground of the measuring antenna is fixed, e.g., at a nominal 3 m?

Vertically and horizontally polarized E-field vertical plane pattems have been calculated at frequencies above 30 MHz for four kinds of electrically small sources. In this paper, predictability has been judged by how well, or how badly, the calculated patterns show correlation between ground based measurements and the maximum field strengths at elevated angles. The patterns are for the simplest of sources radiating into the half-space above ground. If these patterns identify predictability problems, the problems will increase when real ISM devices are involved. A previous study of ISM vertical radiation at frequencies below 30 MHz used a similar approach [4].

The effects on in situ wave propagation of walls, vegetation cover, and terrain irregularities have not been considered. It is important to note that their effects on predictability have been ignored.

ITU designated bands 74.8-75.2 MHz, Aeronautical Radionavigation (Instrument Landing System (ILS) marker beacons, horizontal polarization). 108-137 MHz, Aeronautical Radionavigation and Aeronautical Mobile (R) (including ILS localizers (108-1 12 MHz), honzontal polarization). 243 MHz is for use by survival craft stations and

11. METHOD OF CALCULATION OF FIELD PATTERNS IN THE VERTICAL PLANE

The source models were four electrically small vertical and hor- izontal balanced electric dipoles and current loops. There is justi- fication for this approach to the study of radiation from electrical equipment. Earlier papers have described simulations of real electrical equipment using arrays of small dipoles and loops [5], [6]. However, they were equivocal about whether the fields created resembled those from single electric dipoles or current loops. In [5] , the authors stated that attenuation of the radiation from electrical equipment could be studied using assemblies of elementary electric dipoles or current loops to simulate the equipment, and that the net field could resemble that from a small dipole or current loop. In a later paper [6], the same authors stated they used arrays to ensure that a simple loop or dipole configuration was not used in the simulation. More recently, airborne measurements of harmonic fields radiated from 27 MHz ISM machines over real ground have been reported in [7]. In [8], data from [7] have been used to show that vertical patterns produced by simple dipoles or loops can match the vertical patterns of horizontally polarized fourth harmonic fields above real 27 MHz ISM machines.

E-field vertical plane patterns in this paper have been calculated using the Numerical Electromagnetics Code (NEC2) [9] which, with SOMNEC, allows the Sommerfeld integral evaluation of fields at the air-ground interface [lo], to include the Sommerfeld-Norton surface wave in the calculated E-fields.

Each small source had a unit dipole moment, and was placed either 1 or 2 m above ground. The two heights help to identify the influence of source height on the vertical radiation patterns, including the creation of additional pattem lobes--called grating lobes-as the electrical spacing between the source and its image in the ground increases beyond A / 2 with increasing frequency [1 I].

330

1000

A. The Frequencies of Interest and the Electrical Constants of the Ground

The five frequencies used to excite the models, in the five ITU designated bands [12] listed in Table VI of CISPR 11, are shown in Table I.

equipment used for survival purposes. 328.6-335.4 MHz, limited to ILS (glide path, horizontal polarization). 960-1215 MHz, reserved on a worldwide basis for

TABLE I FREQUENCIES USED IN THE CALCULATIONS TO EXCITE THE SMALL ELECTRIC

DPOLE AND LOOP MODELS, IN THE ITU FREQUENCY BANDS ABOVE 30 MHz WHICH ARE DESIGNATED FOR AERONAUTICAL SAFETY SERVICES

Frequency, MHz 30

Relative dielectric Conductivity, d

15 1 constant, er mS/m

75

the use and development of airborne electronic aids to air navigation.

15 1.5 110 15 2

1000

The small sources were placed above a “medium dry ground” [13] (CCIR-medium dry ground; rocks; sand; medium sized towns [14]). Studies in [4] and [15] involving “wet ground” and “very dry ground” [13], [14] showed that good general guidance to field behavior over a wide range of ground types is obtained over “medium dry ground.” The electrical constants used for “medium dry ground” at 30 MHz and the other five frequencies are listed in Table 11.

15 35

111. LIMITATIONS OF PRF,DICTABILITY OF RADIATION AT ELEVATED ANGLES

A. Height Scan Measurements at 10 m from the Source Here we can answer the first question posed in the Introduction. The E-field strengths measured in 1-4 m height scans at 10 m

distance make good predictions of the maximum fields, often provid- ing exact guidance to the field strengths to be expected in vertical directions. Overestimates do not occur but some underestimates do. When underestimates occur, they are less than 6 dB.

Some vertical field patterns illustrating these conclusions are discussed in the following sections.

1) Predictability at 75 MHz: Polar plots in Fig. l(a) show hori- zontal E, in the Y-2 plane and vertical E, in the 2-X plane around a small horizontal dipole placed 1 m above ground in the 2-X plane. At a scan radius R of 10 m E, reaches almost 138 dBpV/m at 73” elevation. The plots of E,-the vertical E-field component of the vertically polarized radiation emitted in the plane of a horizontal electric dipole over real ground [lO]-show that vertically polarized measurements near the ground do not give the best predictions of high angle field strengths. Fig. l(b) shows height scan calculations of horizontal E, in the Y-2 plane. E, is almost 133 dBpVlm at a

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Z 1 d

40 IO 60 70 80 90 100 110 120 130 .l.1I,L.t

E-fidd SUUI@L dBpVlm

(a) (b) Fig. 1 . Fields from a small horizontal electric dipole of length 0.2 m, calculated at 75 MHz. Dipole height above the ground 1 m. Dipole moment 1 Am Electrical constants of the ground: er = 15, r = 1.5 mS/m. (a) Vertical polar pattems of horizontally polarized E, and yertically oriented E, fields at scan radii R of 10, 30, and 300 m around the dipole, in the Y-2 plane and the 2-X plane, respectively. (b) Height scan pattems of the horizontally polarized E, fields at horizontal distances d of 10, 30, and 300 m from the dipole, in the Y-2 plane (adapted from [15]).

distance d of 10 m and a height of 4 m-thus a 1 4 m height scan measurement underestimates the maximum field by 5 dB.

2) Predictability at 330 MHz: Fig. 2(a) shows vertical polar plots of E, in the Y-2 plane and E, in the Z-X plane at 330 MHz, around a small vertical loop lying in the 2-X plane at a center height of 1 m above ground. At a scan radius R of 10 m, maximum field strength of almost 167 dBpV/m is reached by E, at an elevation angle of 69" in the Y-2 plane. The calculated E, height scan at 10 m distance in the 2-X plane, in Fig. 2(b), reaches a maximum of almost 163 dBpVlm at a height of 1.45 m. Thus, a height scan of the vertical E, field underestimates the maximum radiation, the horizontal E, field at an elevation angle of 69", by 4.5 dB.

3) Predictability at IO00 MHz: Vertical polar plots of horizon- tally polarized E-field emitted at 1000 MHz by a small horizontal loop located 1 m above ground show the peak of the major grating lobe near ground at an elevation angle near 4", in Fig. 3(a). Height scan pattems in Fig. 3(b) show it at a height of almost 0.75 m at a distance of 10 m. It is not measured in a 1-4 m height scan. The next grating lobe occurs 2.3 m above ground, and underestimates the strength of the major (lower) lobe by less than 0.5 dB.

B. Height Scan Measurements at an Unknown Distance, Greater than 10 m, from the Source

Here we can answer the second question. This situation is anal- ogous to making CISPR measurements in situ at 10 m outside a building containing ISM equipment located at an unknown distance

inside the walls. We ignore complications introduced by the inter- vening building structure.

Field patterns at distances of 30 and 300 m are included in the figures. They show that ground-based measurements will make worse underestimates of the field strengths at elevated angles as the measuring distance increases beyond 10 m, especially at the lower frequencies. The underestimates can exceed 30 dB at a distance of 300 m. They occur even though surface wave contributions can remain significant at frequencies above 30 MHz for vertically polarized fields near ground [16]. However, predictability improves at the higher frequencies when the surface waves become insignificant. Then the field strength measured near ground is the sum of the direct and reflected space waves, the sum sometimes referred to as the "ground wave." Its strength increases at lower elevation angles as more grating lobes form with increasing frequency.

It is particularly important to note that at distances of 30 m and more the worst underestimates occur with horizontally polarized fields. This is most unfortunate. The horizontally polarized signals of the aeronautical ILS (see Table I) require maximum protection from horizontally polarized disturbances.

It is obvious that ground-based in situ measurements at unknown distances greater than 10 m can cause very large underestimates in predictions of the strength of radiation at elevated angles.

1) Rates of Change of Field Strengths with Distance: The reason why underestimates increase with increased measuring distance can be observed in the figures. Near the ground, avoiding nulls, the max-

528 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 38, NO. 3, AUGUST 1996

50'

z

Y

, 330MHr

z

t

WUUNU

6

J

0 SO 90 100 110 120 I10 140 IW I60 170

*I.lleOuL

E-fidd arcngth. dBpVlm

(a) (b)

Fig. 2. Fields from a small vertical loop calculated at 330 MHz. Loop dimensions 0.05 m x 0.05 m. Loop center height above the ground 1 m. Dipole moment of the loop 1 Amz. Electrical constants of the ground: E, = 15, 0 = 7.5 mS/m. (a) Vertical polar pattems of horizontally polarized E, and vertically oriented E, fields at scan radii R of 10, 30, and 300 m around the loop, in the Y-2 plane and the 2-X plane, respectively. (b) Height scan patterns of vertically oriented E, and horizontally oriented E, fields at horizontal distances d of 10,30, and 300 m from the loop, in the 2-X plane (adapted from 1151).

imum rate of change with distance of the "ground wave" approaches a rate inversely proportional to distance squared. A field strength inversely proportional to distance squared is expected in the far field at a constant measuring height, when the surface wave is negligible and reflexion occurs at grazing incidence [16], [17]. However, the field strength of a space wave propagating freely in space at a constant elevation angle is simply proportional to inverse distance. Thus, "ground wave" fields at frequencies above 30 MHz will, in general, attenuate more rapidly with distance than fields propagating in vertical directions from the same sonrce.

C. Predictability Based on Measurements at a Fixed Height The third question posed in the Introduction can now be addressed. CISPR 11 specifies that the antenna height will be 3 m f 0.2 m

(Clause 7.2.4) when measuring fields from Group 2 Class A ISM machines in situ; no height scan is specified.

The obvious risk is that fixed height measurements may be made in a null in the field pattern. With a fixed source height, the risk increases as the frequency increases. At a fixed frequency, the risk also increases if the physical height above ground of the source increases. In both cases, the electrical height to the source increases, increasing the number of grating lobes and nulls.

The effects of nulls on measurements at heights near 3 m can be seen in the figures. At 1000 MHz, Fig. 3(b) shows that at a distance

of 10 m from a small horizontal loop source located 1 m above ground the horizontally polarized field strength varies by more than 12 dB in the antenna height tolerance range from 2.8 to 3.2 m. It also shows how, with fixed height measurements, the field strength can vary with distance in an apparently anomalous manner. At a height of 3 m, the field strengths at 30 m and 10 m distance are the same. At other heights, the field strengths at 30 m distance are greater than those at 10 m. These effects occur at greater horizontal distances and lower frequencies if source heights are increased.

Regardless of practical convenience, fixed height measurements in situ should not be specified. Height scans must be used, especially for field measurements intended to protect aeronautical safety of life services. Note that height scan measurements are unequivocally specified by the FCC in [l].

D. Uncertainty Ranges Bar charts have been constructed in Fig. 4 showing uncertainty

ranges for predictability of the radiation emitted in vertical directions at frequencies above 30 MHz. The bar charts are based upon the vertically and horizontally polarized E-fields calculated in 1-4 m height scans at distances of 10, 30, and 300 m, plotted as the field patterns reproduced in this paper and others, including patterns at 110 MHz and 243 MHz, from [15].

IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 38, NO. 3, AUGUST 1996 529

H 0 W N r . U LOOP

Y

x

2

H O R l Z O M N LOOP SOURCE

HEIGHT SCAN

110 120 I30 140 150 160 170 180 190 I, I m i L

E-fidd mength dBrrVlm

(b)

Fig. 3. Fields from a small honzontal loop calculated at 1000 MHz. Loop height above ground 1 m. Loop dimensions 0.02 m x 0.02 m. Dipole moment of the loop 1 Am2. Electrical constants of the ground: E? = 15, D = 35 mS/m. (a) Vertical polar patterns of the horizontally polarized E, field around the loop at scan radii R of 10, 30, and 300 m, in the 2-3- plane. (b) Height scan patterns of the horizontally polarized E, field at horizontal distances d of 10, 30, and 300 m from the loop, in the 2-X plane (adapted from [15]).

Fig. 4(a) illustrates the ranges of uncertainty in predictability using height scans at a known distance of 10 m. Consider the uncertainty range shown at 75 MHz. The best predictability involves a source behaving as a small vertical dipole (dv). Predicting the maximum E, component of the vertically polarized E, field involves zero error. The poorest predictability at 75 MHz is a 5 dB underestimate of the horizontally polarized Eh field emitted by a source behaving as a small horizontal dipole (dh). At 330 MHz the underestimate of the horizontal Eh field from a small vertical loop (Iv) is almost 5 dB.

The bar chart in Fig. 4(a) indicates that if height scan measnre- ments are made at 10 m distance the predictability of the maximum E-fields in all five aeronautical frequency bands is very good. It must be acknowledged that the small source models cannot reproduce the worst case uncertainties associated with the radiation pattems which may be produced from real ISM equipment. Nevertheless, some justification was given in Section I1 that small sources can provide a good general representation of radiation pattems from real ISM equipment [5]-[SI. Therefore, the small uncertainties demonstrated in Fig. 4(a) indicate it is possible to derive limits to be applied at a 10 m in situ measuring distance from the ISM equipment which will provide, with a high probability, an effective protection ratio for aeronautical systems and other telecommunication systems located high above ground.

When 1 4 m height scans are made at a distance of 30 m, the bar for the uncertainty range at 75 MHz in Fig. 4(b) shows that the poorest predictability involves a larger underestimate of 12 dB for the horizontal Eh field emitted from a small horizontal dipole (dh). The uncertainty range is 11 dB. With a height scan up to 6 m, required by the FCC [l J at distances greater than 10 m, the maximum underestimate is reduced by less than 3 dB (see Fig. 1).

Fig. 4(c) shows the large uncertainties in predictability that can occur when 1-4 m height scans are made at a distance of 300 m. At 75 MHz, the bar shows a 31.5 dB underestimate of the horizontal Eh field emitted from a small horizontal dipole (dh). The smallest underestimate by 16 dB at 75 MHz involves the E, component of the vertically polarized E, field emitted from a small vertical dipole (dv). The uncertainty range i s also almost 16 dB. At higher frequencies the small horizontal loop (Ih) joins the small horizontal dipole (dh) in providing the largest underestimates. Fig. 4(c) strikingly illustrates the very large underestimates which can occur when predicting the strength of radiation in vertical directions based on height scan measurements at unknown distances up to 300 m from the sources. When the height scans extend up to 6 m, as required by the FCC [l], the worst underestimate at 75 MHz remains large, 28 dB (see Fig. 1).

IV. CONCLUSIONS CISPR I1 notes that safety of life services require protection from

vertically radiated electromagnetic disturbances. The conclusions and recommendations below pay particular attention to present measure- ment procedures specified for use above 30 MHz by the US FCC [l] and by the CISPR 121.

In situ field strength limits at a distance of 300 m from many types of ISM equipment (or 1600 m in the case of industrial heaters), specified by the FCC, cannot guarantee protection of aeronautical safety of life services unless, when the limits were set, allowance was made for the existence of much stronger fields at elevated angles. At the aeronautical ILS frequencies ground-based measurements at 300 m distance can underestimate field strengths in vertical directions by up to 30 dB, or more.

In situ measurements specified by the CISPR can also underesti- mate the fields emitted at elevated angles, primarily because of an ill-defined measurement distance. In general, in situ measurements at unknown distances greater than 10 m involve large uncertainties in

530 IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY, VOL. 38, NO. 3, AUGUST 1996

over- estimate

5

Uncatainty dB 0

Under- -5 dimate

75MHz l lOMHz 243- 330MHz 1000 MHz

over- estimate

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S

Uncertainty dB 0

-10

-1s

-20 Under- estimate

-2 5

-30

-3 5

75 MHz 110MHz 24: k 330MHz loo0 MHZ

(c)

Fig. 4. Ranges of uncertainties in the predictability of vertically polarized E, and honzontally polarized EL field strengths radiated in vertical directions from electrically small sources located at a height of 1 or 2 m above ground. The uncertainty ranges are based on calculations of the E-fields at distances of (a) 10 m, (b) 30 m, and (c) 300 m from four electrically small source models [see text in Section 111-D] (adapted from [IS]).

predicting the maximum field strengths at all frequencies from 30 to 1000 MHz. Large underestimates can result. Underestimates decrease at higher frequencies as more grating lobes form.

Underestimates increase if fixed height measurements are made in or near a null. A fixed antenna height should not be specified, especially for measurements intended to protect specific safety ser- vices. Even if the distance from the ISM equipment is known, the unknown height to the radiation center of the source introduces risks of measurements near or in a null, especially at the higher frequencies.

In general, with the measurement procedures specified by the FCC and the CISPR, the largest underestimates will be of the horizontally polarized fields. This gives cause for concern, because

the aeronautical safety of life services requiring greatest protection are the horizontally polarized marker beacon, localizer, and glide path signals of the aeronautical ILS.

To protect aeronautical services in the frequency range from 30 to 1000 MHz, it is recommended that the in situ disturbance limits must be based on height scanned measurements at a well defined horizontal distance from the ISM equipment. Ideally, limits should be based on a 10 m in situ measurement distance from rhe ISM equipment. If, for practical reasons, in situ measurements must be made at a greater distance the limits must be adjusted in inverse proportion with distance squared (see Section 111-Bl). That adjustment is necessary to prevent relaxation of the protection the

IEEE TRANSACTIONS ON ELEC’IROMAGNETIC COMPATLBILITY, VOL. 38, NO. 3, AUGUST 1996 53 1

limits are intended to provide for aeronautical systems and indeed, in general, any telecommunication systems located high above ground.

ACKNOWLEDGMENT

[I51 I. P. Macfarlane, “Predictability of electromagnetic radiation in the vertical plane over real ground at frequencies above 30 MHz,” Telstra Research Laboratories, 770 Blackburn Road, Clayton, Victoria 3168, Australia, Telstra Research Laboratories Report 833 1, 1995.

[I61 -, “Surface waves and near fields over ground planes at frequencies above 30 MHz,” Telstra Res. Lab. 770 Blackburn Road, Clayton, Victoria 3168, Australia, Telstra Res. Lab. Rep. 8329, 1995.

[171 E. C. Jordan and K. G. Balmain, Electromagnetic Waves and Radiating Systems.

The author would like to thank S. I sha for his critical reading and suggestions, and M. Armstrong, R. McKenzie, and S. Hurren for their software assistance. Englewood Cliffs, NJ: Prentice-Hall, 1968, 2nd ed., ch. 16.

REFERENCES

[ 11 US. Code of Federal Regulations (CFR), Chauter I-Federal Commu- nications Commission (FCC), Title 47, Part is, Industrial, scientific, and medical equipment, US Government Printing Office, issue of Oct. 1992. Measurement techniques to determine compliance are, set out in FCC/OST Measurement Procedure MP-5 (1986), “Methods of measurement of radio noise emissions from industrial, scientific, and medical equipment,” U.S. Department of Commerce, National Technical Information Service, Springfield, VA 22161, Feb. 1986. CISPR Publication 11: 1990, “Limits and methods of measurement of electromagnetic disturbance characteristics of industrial, scientific and medical (ISM) radio-frequency equipment,” 2nd ed., International Special Committee on Radio Interference (CISPR), International Elec- trotechnical Commission, Geneva, 1990. ITU-R Study Group 1, Document 1/BL/24-E, Apr. 12, 1994, Draft New Recommendation ITU-R [Doc. 1/64], “Limitation of radiation from industrial, scientific and medical (ISM) equipment,” International Telecommunication Union, Radiocommunication Study Groups, Ques- tion ITU-R 7011, previously CCIR Question 70/1. I. P. Macfarlane, “Predictability of radiation in vertical directions at frequencies up to 30 MHz,” Aiutralian Telecommun. Res., vol. 26, pp.

W. C. Dolle and W. E. Cory, “Measurement of field strength attenuation in the near field,” in Symp. Dig., 8th IEEE Symp. Electromag. Compat., San Francisco, CA, July 1966. -, “Measurements of the attenuation of the electric and magnetic fields at points close to the source,” 1EEE Trans. Electmmag. Compat., vol. EMC-10, pp. 313-319, Sept. 1968. J. D. Nickum and W. Drury, “Measurement of RF fields associ- ated with ISM equipment as it relates to aeronautical services,” Rep. OWAECEER 67- 1, Avionics Engineering Center, Department of Elec- trical and Computer Engineering, Ohio University, Athens, OH 45701. Final Report to the US Federal Aviation Administration, Systems Engineering Service, Washington, DC 20591, Rep. DOT/FAAIES-84/2, May 1985. Document disseminated under sponsorship of the U.S. Department of Transportation, publicly available through the National Technical Information Service, Springfield, VA 22161. I. P. Macfarlane, “Harmonic fields radiated at elevated angles from 27 MHz ISM apparatus over real ground,” Telstra Research Laboratories, 770 Blackbum Road, Clayton, Victoria 3 168, Australia, Telstra Research Laboratories Report 8347, 1995. G. J. Burke and A. J. Poggio, “Numerical electromagnetics code (NECbMethod of moments,” Naval Ocean Systems Center, San Diego, CA 92152, NOSC Technical Document 116, 1981. (Numerical Electromagnetics Code (NEC2) developed at Lawrence Livermore National Laboratory, Livermore, CA, File Created Apr. 11, 1980, Double Precision June 4, 1985). A. Sommerfeld, translated by E. G. Straus, Partial DifSerential Equations in Physics, Lectures on Theoretical Physics. New York: Academic, 1964, vol. VI, ch. VI. W. L. Stutzman and G. A. Thiele, Antenna Theory and Design. New York: Wiley, 1981, p. 123. Radio Regulations, Edition of 1990. International Telecommunication Union (ITU), General Secretariat, Geneva, 1990. CCIR Recommendation 527- 1, Electrical Characteristics of the Surface of the Earth, International Consultative Committee on Radio (CCIR), International Telecommunication Union, Geneva, 1982. CCIR Report 879-1, Methods for Estimating Effective Electrical Charac- teristics of the Surface of the Earth, International Consultative Commit- tee on Radio (CCIR), International Telecommunication Union, Geneva, 1986.

25-39, 1992.

An Approximate Formula for the Calculation of the Horizontal Electric Field from Lightning

at Close, Intermediate, and Long Range

Marcos Ruhinstein

Abstract-We present an approximate formula to calculate the horimn- tal electric field from lightning that is applicable for close, intermediate, and long distances to the lightning, at ground level and at a height above ground. The formula is analytically simple and can he readily implemented for numerical calculations in the frequency and in the time domains. The formula can be particularly useful for lightning induced voltage calculations. A test of the formula by comparison with the results obtained using good approximations to Sommerfeld’s integrals is presented. The results compare favorably for a wide range of dis- tances. Theoretical waveforms obtained with a return stroke model and the formula predict that, for negative ground lightning, the horizontal component of the electric field at close range and at a height of a few meters above the ground starts with a sharp pulse directed toward the lightning channel and is followed by a slower field change of opposite polarity.

I. INTRODUC~ON The importance of the horizontal component of the lightning

electric field in the calculation of induced over-voltages on overhead power and distribution lines in the context of the coupling formulation of Agrawal et al. [I] has been well established [2]-[5]. Several techniques have been developed to compute this field component. The exact solution [6] is computationally inefficient when applied to the lightning case since it requires the evaluation of Sommerfeld integrals for large numbers of elementary dipoles along the lightning channel as well as for a large number of frequencies. An approximate technique known as the wave tilt formula [7] can he employed to find the horizontal electric field from lightning at distances farther than a few kilometers [8]. At intermediate and closer ranges, however, the wave tilt formula is no longer applicable. Cooray [9] has shown that the surface impedance of the ground can be used to calculate the horizontal field at ground level more accurately than with the wave tilt formula. The range of validity of Cooray’s formula is larger than that of the wave tilt formula as it can he applied for distances as short as 200 m [9]. For the calculation of overvoltages by lightning on overhead wires, it is the horizontal electric field at line height that is important. In this paper we present an approximate formula to evaluate the horizontal electric field off the ground, at close, intermediate, and long range. In essence, the formula presented

Manuscript received October 13, 1994; revised January 8, 1996. The author is with Swiss Telecom PTT, R&D, FE 115, Ostermundigen-

Publisher Item Identifier S 0018-9375(96)03853-7. strasse 93, CH-3000 Bern, Switzerland.

0018-9375/96$05.00 0 1996 IEEE