Seybold J.S. Introduction to RF Propagation

Подождите немного. Документ загружается.

monopole) the reactive near-ﬁeld boundary may fall outside of the transition

region, in which case the transition region is not used.

12.5 FCC COMPUTATIONS

The computation equations provided by the FCC are fairly accurate in the far-

ﬁeld and tend to provide conservative (high) estimates of power density in the

near-ﬁeld. The analysis can be performed for the main beam of a direction

antenna, for an omnidirectional antenna, or for a directional antenna when

outside of the main beam. The main beam and omnidirectional case is treated

ﬁrst, and then the application of the antenna radiation pattern is covered in

the following section.

12.5.1 Main Beam and Omnidirectional Antenna Analysis

The estimated power density in the far-ﬁeld as a function of the distance is

given by

(12.5)

where

P is the transmit power (mW)

G is the antenna gain

d is the distance from the center of radiation of the antenna (cm)

The product of the power and the antenna gain, PG, is the EIRP. The effec-

tive isotropic radiated power may be expressed relative to a dipole rather than

an isotropic source. In this case it is called effective radiated power (ERP) and

the value is adjusted by the gain of an ideal dipole in free space.

If the radiator is over a reﬂective surface, the worst case is a doubling of the

electric ﬁeld intensity. This corresponds to a quadrupling of the power density

(12.6)

The EPA has developed models for ground level power density [1], which

suggest a factor of 1.6 rather than 2 for the electric ﬁeld multiplier over a

reﬂective surface. Applying the EPA result produces a scale factor of 2.56

rather than 4.

EIRP

ERP = EIRP or, dB164 23..-

()

mW cm

292 RF SAFETY

(12.7)

Example 12.1. Consider a transmitting system shown in Figure 12.5, with

f = 100 MHz, ERP = 10kW

The antenna is tower-mounted, with a center of radiation at 50 m and is sur-

rounded by a fence that is 20 m from the base of the tower in all directions.

What is the worst-case power density 2m above the ground at a point 20 m

from the base of the tower? Apply the FCC calculations to compute the result.

First, compute the slant distance to the point of interest,

Then, assuming that the ground is reﬂective, the power density is

From Table 12.2, the limit for uncontrolled exposure at 100 MHz is

200 mW/cm

. Thus, even this worst-case analysis shows the site to be compliant

for uncontrolled exposure, and no further analysis is required. 䊐

12.5.2 Antenna Directivity

If a directional antenna is employed, the antenna gain in the direction of expo-

sure may be much less than the peak gain. In this case, (12.7) can be modiﬁed,

◊◊

◊

064 164 105

124

.. .ERP ERP

Wcm

d =+

()

=48 20 52

2.56EIRP EIRP

064

FCC COMPUTATIONS 293

2 m

Figure 12.5 RF exposure geometry.

(12.8)

where F

is the antenna gain reduction in the direction of exposure. For an

omnidirectional antenna, F = 1. The maximum power density at the surface of

an aperture antenna is approximated by

(12.9)

where P is the power to the antenna and A is the physical cross section of the

aperture. The maximum value of the near-ﬁeld, on-axis power density is

approximated by

(12.10)

and

is the maximum near-ﬁeld power density

h is the aperture efﬁciency (0.5–0.75)

P is the power to the antenna

D is the antenna aperture diameter

In the transition region (D

/4l<d < 0.6D

/l), the power density can be com-

puted using

(12.11)

where

is the power density in the transition region

is the maximum near-ﬁeld power density

is the distance from antenna to the outer edge of the near-ﬁeld

d is the distance to the point of interest

This is essentially an inverse distance relationship. The far-ﬁeld computations

use the standard free-space loss equation given by (12.5). The free-space loss

equation computes the main beam (on-axis) power density.The off-axis power

density will, of course, be considerably less.

nf nf

surface

064

. EIRP

294 RF SAFETY

Example 12.2. Consider a system with the following parameters:

f = 40 GHz

P = 20 dBm

30-cm-diameter dish antenna (G = 40 dB if h=0.6)

Perform a station evaluation on this system. The power density at the antenna

surface is

The maximum value of the near-ﬁeld power density is

The transition region is

Within the transition region, the power density is described by

where

nf nf

30 72..m< md <

339 5

m.Wcm

surface

566

mWcm

FCC COMPUTATIONS 295

TABLE 12.3 FCC On-Axis Power Density Equations for Different Antenna

Regions

Region Distance Field Strength Model

Reactive NF 0 < d <l/2

Near-ﬁeld l/2p<d < D

/(4l)

Transition D

/(4l) < d < 0.6D

Far-ﬁeld 0.6D

/l<d

Far-ﬁeld over 0.6D

/l<d

reﬂective surface

064

. EIRP

nf nf

surface

The far-ﬁeld power density is given by

The results are shown in Figure 12.6.

The uncontrolled MPE at 40 GHz is 0.2 mW/cm

, so this system is compli-

ant for uncontrolled exposure beyond about 5 m. From Table 12.1, the con-

trolled MPE at 40 GHz is 1 mW/cm

, so the system is compliant everywhere

for controlled exposure. Note that all calculations are done in consistent, non-

dB units. The results may then be converted to dB (dB mW/cm

) if desired.

By taking the antenna gain pattern into account, the minimum safe distance

would be considerably less than 5 m when outside of the main antenna beam.

If the maximum sidelobe level was -15dB (relative to the peak of the beam),

the power density in the far-ﬁeld would be scaled by

d=>

,.m

= 30.m

296 RF SAFETY

0 5 10 15 20

100

200

300

400

500

600

Power Density versus Distance

d (m)

Power Density in microwatts/sq-cm

Antenna Surface

Beginning of the

Far-Field Region

Transition

Region

Near-Field

Figure 12.6 Predicted power density versus distance for Example 12.2, using FCC

calculations.

which means that once outside of the antenna main lobe, the system would be

safe at any distance up to the antenna surface. Figure 12.7 is a notional diagram

of what the hazard area might look like. The height and width of the hazard

area would depend upon the elevation and azimuth beamwidths of the

antenna and the distance from the antenna center of radiation. 䊐

12.6 STATION EVALUATIONS

All stations are subject to the exposure guidelines, but some installations may

be exempted from having to perform routine evaluations depending upon the

type of service, power levels involved and the applications. For example, the

amateur radio stations that are excluded from the requirement to perform

routine evaluations include mobile and portable push-to-talk devices, mobile

devices below 1.5 GHz and 1.5 W, mobile devices greater than 1.5GHz and less

than 3 W, and stations that can be shown to be below the MPE limits in all

cases. Although some stations are not required to perform routine evaluation

of compliance with exposure limits, compliance is still required and an initial

station evaluation is in order to verify compliance and to be able to demon-

strate compliance if required to do so.

Portable, hand-held consumer products, often with full duty cycle (cellular

and cordless phones), typically must use the uncontrolled exposure standard.

Devices can be either tested or modeled under typical operating conditions to

establish compliance. They should be evaluated based on SAR rather than

MPE limits since the close proximity could yield unsafe levels of localized

tissue heating while still meeting the whole-body requirements. The MPE

limits are based on a whole-body exposure limit of 4 W/kg with safety factors

of 10 and 50 for controlled and uncontrolled environments. Thus the actual

G = 0 0316.

STATION EVALUATIONS 297

5 m

Shaded area is restricted for uncontrolled exposure.

Controlled exposure is OK at any distance from the

antenna, including at the surface

Figure 12.7 Diagram of the directional antenna radiation regions where the FCC

MPE limits are exceeded for Example 12.2.

time-averaged whole-body exposure limits are 0.4 and 0.08 W/kg for con-

trolled and uncontrolled exposure, respectively. For localized exposure,

these levels are increased to 1.6 and 8 W/kg as averaged over any 1 g of tissue

and averaged over the appropriate time interval [11]. If the SAR limits

are met, then it is permissible to exceed MPE limits. In general the MPE is

applied for distances greater than 20 cm; otherwise the SAR limit is used. To

apply the SAR limits, the designer will usually use a modeling package or con-

struct an instrumented mock-up of the human hand and head and measure

the effects.

12.7 SUMMARY

Electromagnetic radiation can be characterized as either ionizing or non-

ionizing. Non-ionizing radiation is generally frequencies from zero up to

beyond visible light and thus is the type of radiation of interest for RF safety.

Presently the only veriﬁed effect of non-ionizing radiation is tissue heating.

Other effects have been postulated, but remain unproven. The FCC maximum

permissible exposure limits were developed based largely on the IEEE/ANSI

RF safety standards.The FCC limits are set to levels signiﬁcantly below where

harmful tissue heating occurs. The FCC limits for RF exposure vary with

frequency and are different for controlled and uncontrolled environments.

The FCC guidelines include computations that can be used to assess com-

pliance with the maximum permissible exposure limits. These computations

are relatively straightforward and provide a conservative estimate of expo-

sure. The computations are only guidelines, however, and if they indicate that

the RF exposure is above the limits, a more detailed analysis should be per-

formed. In addition to the frequency and whether individuals are aware of and

can exercise any control over their exposure, the FCC limits also take the duty

cycle of the transmitted signal and time averaging into account when deter-

mining the exposure level.

Mobile and hand-held devices are handled differently as the actual SAR

limits (per any 1 g of tissue rather than whole body absorption) must be

applied rather than the MPE.This is usually done using measurements or mod-

eling software. The variable nature of hand-held antennas and their position

relative to the body make a general MPE difﬁcult to apply and require that

the potential for excessive localized exposure and tissue heating be addressed.

REFERENCES

1. R. F. Cleveland, Jr., D. M. Sylvar, and J. L. Ulcek, Evaluating Compliance with FCC

Guidelines for Human Exposure to Radiofrequency Electromagnetic Fields,

OET bulletin 65, Edition 97–01, FCC, August 1997. http://www.fcc.gov/oet/info/

documents/bulletins/#65

298

RF SAFETY

2. ETSI TR 101 870 V1.1.1 (2001–11), Fixed Radio Transmitter Site; Exposure to Non-

ionising Electromagnetic Fields; Guidelines for Working Conditions, European

Telecommunications Standards Institute.

3. IEEE Standard for Safety Levels with Respect to Human Exposure to Radio

Frequency Electromagnetic Fields, 3 kHz to 300 GHz (Incorporates IEEE

Std C95.1-1991 and IEEE Std C95.1a-1998), ANSI standard C95.1-1999,

www.ansi.org

4. E. Hare, RF Exposure and You, ARRL, Newington, CT, 1998, p. 4.7.

5. K. R. Foster, and J. E. Moulder, “Are Mobile Phones Safe?”, IEEE Spectrum,

August 2000, pp. 23–28.

6. E. Hare, RF Exposure and You, ARRL, Newington, CT, 1998, p. 3.2.

7. R. F. Cleveland, Jr., and J. L. Ulcek, Questions and Answers about Biological Effects

and Potential Hazards of Radio Frequency, OET bulletin 56, 4th ed., FCC, August

1999, p. 5.

8. R. F. Cleveland, Jr., and J. L. Ulcek, Questions and Answers about Biological Effects

and Potential Hazards of Radio Frequency, OET bulletin 56, 4th ed., FCC, August

1999, p. 8.

9. E. Hare, RF Exposure and You, ARRL, Newington, CT, 1998, p. 4.3.

10. E. Hare, RF Exposure and You, ARRL, Newington, CT, 1998, p. 4.2.

11. IEEE Standard for Safety Levels with Respect to Human Exposure to Radio

Frequency Electromagnetic Fields, 3 kHz to 300 GHz (incorporates IEEE Std

C95.1-1991 and IEEE Std C95.1a-1998), ANSI standard C95.1-1999, p. 17.

www.ansi.org

12. C. Balanis, Antenna Theory Analysis and Design, Wiley, New York, 1997, pp. 32–

33.

EXERCISES

1. What is the primary biological effect of RF exposure that is of concern for

safety?

2. Determine the reactive near-ﬁeld, near-ﬁeld, transition, and far-ﬁeld bound-

aries for the following antennas:

(a) A 200-MHz quarter-wave monopole mounted on a reﬂective surface

(b) A 5-GHz dish antenna with a 1-m diameter

3. In a controlled exposure environment, the E ﬁeld is measured at 0.05 V/m

for 2 min, followed by 0.02V/m for 4 min and then the cycle is repeated.

What is the time-averaged exposure power density in mW/cm

? The aver-

aging time for controlled exposure is 6 min. Is this permissible exposure?

4. Consider an HF station operating at 30 MHz, with a maximum power of

1 kW supplied to a ground-mounted quarter-wave monopole. If the trans-

mitter duty cycle is 50%, what are the minimum safe distances for con-

trolled and uncontrolled exposure?

EXERCISES 299

5. A satellite ground station, located on the roof of a building uses a 30-dB

(directional) antenna pointed upward at 40 degrees to communicate with

the satellite using 100 W of continuous transmit power at 4 GHz.

(a) Is this station governed by controlled or uncontrolled limits? Why?

(b) What is the minimum safe distance from the antenna?

That is, how would it affect the answer given in part b?

6. A 2-m (150-MHz) remote weather station link uses a 15-dB yagi antenna

and 25 W of transmitter power to communicate with its hub. If the antenna

is mounted on a 15-ft tower that is surrounded by a fence, determine the

following:

(a) Is this a controlled or uncontrolled environment?

(b) What is the minimum safe distance from the antenna?

300 RF SAFETY

301

Introduction to RF Propagation, by John S. Seybold

APPENDIX A

Review of Probability for

Propagation Modeling

This appendix serves as a quick introduction or review of probability

theory. While not comprehensive, it does provide the supporting material

for the chapters in this book. Heavy reliance on heuristic argument ensures

that the mathematically sophisticated reader will be disappointed. Neverthe-

less, it is felt that for those needing a refresher or a nuts-and-bolts primer,

this is the most efﬁcient approach. The author offers his apologies to the

purists.

The entire ﬁeld of probability is founded on the three basic axioms of

probability:

0 £ P(A) £ 1 The probability of event A occurring is between

zero and one.

P(r) = 1 If r is a certain event, then the probability of its

occurrence is one.

P(A + B) = P(A) + P(B) If A and B are mutually exclusive events, then the

probability of both occurring is equal to the sum

of their individual probability of occurrence.

Thus probabilities are properly expressed as real numbers between zero and

one inclusive, although sometimes they are written as percentages. At this

point it is also helpful to deﬁne the concept of relative frequency [1–3]. While

not a fundamental axiom of ﬁeld of probability, it is an aid in relating intuition

to probability. Relative frequency is the intuitive concept that the ratio of the

number of times that an event occurs to the number of times that the exper-

iment is run (number of trials) will approach the probability of the event as

the number of trials gets large.

()

Æ•

lim