## Chart Perimeter as Transmission Line Length

The classical transmission line equation (see Table 1, line 1) clearly illustrates that impedance, and hence VSWR, varies in a repetitive fashion every half-wavelength in distance along a lossless line. On the Smith Chart this is equivalent to repeated values for reflection coefficient with every complete rotation around the chart relative to the center of the chart. The entire perimeter of the Smith Chart calibrates uniformly as a ± quarter-wavelength distance relative to a reference location. Clockwise rotation around the Chart’s periphery is equivalent to moving along the line in a direction toward the source (generator), and counterclockwise rotation around the Chart is equivalent to moving toward the load.

Impedance and Admittance Locus Movement for Discrete Circuit Elements

Electronic circuit impedance matching is easily performed utilizing the Smith Chart. Typically one desires to use only lossless components to accomplish a match. The addition of a discrete circuit element such as a capacitance or an induc­tance in a matching circuit has a well-defined effect on mov­ing the locus of a load impedance vector on the Chart grid. The four key discrete circuit elements commonly used in cir­cuit matching are given as follows along with their effect on motion of an impedance locus (for series elements) or an ad­mittance locus (for shunt elements):

• Series inductance rotates an impedance locus CW on a constant-R circle

• Series capacitance rotates an impedance locus CCW on a constant-R circle

• Shunt inductance rotates an admittance locus CCW on a constant-G circle

• Shunt capacitance rotates an admittance locus CW on a constant-G circle

Here CW and CCW denote clockwise and counterclockwise motion, respectively, on the specified circles.

## THE FUTURE

The utilization of information technology applications in health care is influenced by progress in IT, medicine, clinical practice, and health care delivery. These elements are highly intertwined with one feeding the others. In IT the major trends are the Internet, Web technology, and mobile commu­nication. Web browsers are an easy way to provide uniform user interfaces within an organization. Similarly, Extranets are a way for the organization to be in contact with its clients (citizens, patients) without compromising data confidentiality and security (although there are still doubts about the secu­rity features of Web implementations). Mobile communica­tion, fueled by the explosive growth in cellular phones and value-added services, seems to offer a limitless range of appli­cations.

However, these are just technologies. They need to be ap­plied in a way that results in benefits for the clients/patients, users, and organizations. User organizations should be care­ful not to be too enthusiastic about the possibilities offered by new technologies. New technologies ‘‘obey’’ the life cycle of early adaptation by technology enthusiasts and then early adapters. These provide the testing ground to perfect the technology and to make it available at an affordable price to all. If the technology does not survive the tests of the early adapters it dies (36).

The process approach and the need to manage care jointly are pushing service providers toward collaboration in order to meet the needs of their customers and solve the problems of their patients effectively and efficiently. The scenario of Fig. 7 and Table 4 rests with the idea that IT can integrate data

 Figure 7. A care scenario combining care processes, plans, and clini­cal guidelines, and with quality improvement both at the organiza­tional and medical research levels.

Table 4. Characteristics of a Health Care Environment of

Today and the Future

 Today Future Disease and illness Health promotion and wellness, indepen- management dence and security Hospital-based care Virtual care (front lines and centers of ex- cellence) Authoritarian and pro- Client-centered care fession centered Patient record centered Seamless service chains, logistics, commu- nity health information networks (CHIN)

and make it and medical knowledge available in the right for­mat anywhere and at any time. From the IT viewpoint, health care will become virtual and transparent.

The development of MIS applications that are trans­portable and integratable naturally starts with identifying user needs. User involvement in the development, testing, and evaluation phases is equally important. The concept of a user, however, needs to be viewed as widely as possible. This means that one should include all categories of users from daily end users to management. It also means that efforts should be made to involve more than one health care organi­zation. It also means that when the resulting product is taken into use, its costs are offset by benefits and/or savings in other areas, thus justifying the investment in that specific product. According to Gremy and Sessler the key elements in this are the respect of professional identity and a mutual ef­fort for mutual understanding (37). The medical professions should be empowered by the MIS applications instead of be­ing forced into one working pattern.

## Full-Wave Solutions for the Radar Cross Sections for Multiple-Scale Rough Surfaces

The normalized bistatic radar cross sections aPQ for two-dimensionally rough surfaces are dependent on the polarizations of the scattered (first superscript P = V, H) and incident (second superscript Q = V, H) waves. It is defined as the following dimensionless quantity that depends on the incident and scatter wave-vector directions:

 Fig. 5. Arbitrarily oriented patch of a rough surface.

In Eq. (64) the area Ay is the radar footprint, r is the distance from the rough surface to the far-field observation point. When the rough-surface statistical characteristics are homogeneous though not necessarily isotropic, the (ensemble average) full-wave radar cross section based on the original (denoted by subscript 0) full-wave analysis [Eq. (52)] is expressed as follows:

where SPQ(nf, ni) is the surface element scattering coefficient for incident waves in the direction ni and polarization Q = V (vertical), H (horizontal), and scattered waves in the direction nf and polarization P = V, H. It should be noted that the scattering coefficients SPQ(nf, n1) are not functions of slope. In Eq. (65), Q(nf, n1) is expressed in terms of the surface height joint characteristic function x2 and characteristic function x as follows:

where k0 is the free-space wavenumber and rdt is the projection of rS1 _ rS2 (where rS1 and rS2 are position vectors to two points on the rough surface) on the mean plane (y = 0) of the rough surface y = h(x, z) (see Fig. 3):

and drdt = dxddzd. The vector v is given by Eq. (44). For homogeneous isotropic surfaces with Gaussian joint surface height probability density functions

where vy is they component of v [Eq. (44)], (h2) is the mean-square height andR(rd) is the normalized surface height autocorrelation function [related to the Fourier transform of the surface height spectral density function W(k)]. When the surface is isotropic and homogeneous, R is only a function of the distance

and Q(nf, n1) [Eq. (66)] can be expressed as follows for L, l > lc (the autocorrelation length):

where J0 is the Bessel function of order zero and

Note that Q(nf, n1) remains finite as vy ^ 0.

The above expressions based on the original full-wave solutions are in total agreement with solutions based on Rice’s small perturbation solutions when the height and slopes are of the same order of smallness (3). For these cases

and the integrals in Eq. (66) can be expressed in closed form in terms of the rough-surface height spectral density function [the Fourier transform of the surface height autocorrelation function (hh’) = (h2)R(rd)].

However, the solution [Eq. (66)] based on the original full-wave solution is not restricted to surfaces with small mean-square heights. Since it is based on the first-order single-scatter iterative solution, it is nevertheless restricted to surfaces with small slopes (a2s < 0.1).

When slopes of the rough surface are not small and the scales of roughness are very large compared to wavelength, solutions based on the transformation [Eq. (56)] can be used. Thus, the diffuse scatter cross section

 is expressed as follows:

where the symbol * denotes the complex conjugate and

The (statistical) mean scattering cross section for random rough surfaces is obtained by averaging Eq. (74) over the surface heights and slopes at points rsi and rs2. The coherent component of Eq. (75) is defined as

 17в і

. PQ. WKfff)!* ‘■°c > =

 i|2

AyE?

and the incoherent scattering cross section is defined as

(77)

The above expression for the radar cross sections for two-dimensional random rough surfaces involves integrals over the random rough-surface heights and slopes and the surface variables xsi, xs2, zsi, zs2. This expression can be simplified significantly if the radii of curvature of the large-scale (patch) surface are assumed to be very large compared with the free-space wavelength. In this case, the slope at point 2 may be approximated by the value of the slope at point 1 (hx2 ~ hx1, hz2 ~ hz 1). If, in addition, the rough surfaces are assumed to be statistically homogeneous, the cross section is expressed as follows:

in which the analytical expressions for the conditional joint characteristic functions are

 Furthermore,

/•pQinp, npJ =DPQDPQ, C7^-nl-np)U(nf-np)P2(nf, nl|ii3:i (80)

where P2(n , n1 |ns) is Sancer’s (63) shadow function and ns is the value of np at the specular points.

For random rough surfaces characterized by a four-dimensional Gaussian surface high/slope coherence matrix we obtain

 (82)

X2(a, b) = ежр[-и|(Л£;ц1 — C)]

 dC{h2) ‘ dx. ~ Ux"d
 = ,C 183)

Bx = (h-^h x) — —— ‘

and

 (86)

Cixd, zd> = exp

In Eq. (85), C is the Gaussian surface height autocorrelation function and lcx, lcz are correlation lengths in the x and z directions, respectively.

When the surface is isotropic (lcx = lcz = lc and a2x = a2z = a2s), Eqs. (81), (83), and (84) reduce to

where

and

In this case, the total mean square slope is expressed as

For the assumed isotropic surface with Gaussian statistics, the four-dimensional integral [Eq. (28) with Eqs. (86) and (88)] can be expressed as a three-dimensional integral using a Bessel function identity (4).

The resulting full-wave incoherent diffuse scatter cross section that accounts for surface height/slope correlations is expressed as

where

Furthermore,

 1921
 and

EJ. v, = / V*. + u

(93)

In Eq. (93),

and

In Eq. (90), p(hx, hz) is the probability density function for the slopes (assumed here to be Gaussian).

It is shown that the above results in which the correlations between the surface heights and slopes have been accounted for in the analysis reduce to the small perturbation results when the heights and slopes are of the same order of smallness and reduce to the physical/geometrical results in the high-frequency limit (64). These full-wave results have also been compared with numerical and experimental results for one-dimensionally (3) and two-dimensionally (64) rough surfaces.

When the rough surface consists of multiple scales of roughness as in the case of sea surfaces, two scale models have been introduced to obtain the scatter cross sections. Thus, the surface is assumed to consist of a small-scale surface that is modulated by the slopes of the large-scale surface and the cross section is expressed as a sum of the cross sections for the large — and small-scale surfaces. However, Brown (8) has shown that the hybrid-perturbation-physical-optics results critically depend upon the choice of the spatial wavenumber kd that separates the large-scale surface from the small-scale surface. To apply this hybrid-perturbation-physical — optics approach, the Raleigh rough-surface parameter в = 4k20(h2s) must be chosen to be very small compared to unity. This places a very strict restriction on the choice of kd. As a result, scattering from the remaining surface consisting of the larger-scale spectral components with kl < kd may not be adequately analyzed using physical optics (see Fig. 4).

The above Raleigh rough-surface parameter в does not place any restriction on the choice of kd when the full-wave analysis is used. Furthermore, it is shown (65) that the full-wave solution for these multiple-scale rough surfaces are expressed as weighted sums of two cross sections:

where (ctpqi) is the cross section associated with the surface consisting of the larger spectral components (kl < kd), while (ctpqs) is the cross section associated with the surface consisting of the smaller spectral com­ponents ks > kd. Scattering by the small-scale surface is modulated by the slopes of the large-scale surface, while scattering by the small-scale surface is diminished by a coefficient (less than unity) that is equal to the magnitude of the small-scale characteristic function squared [Eq. (69)].

Thus, using the full-wave approach, extensive use is made here of the full-wave scattering cross-section modulation for arbitrarily oriented composite rough surfaces. Thus, the incoherent diffuse radar cross sections of the composite (multiple scale) rough surface is obtained by regarding the composite rough surface as an ensemble of individual patches (several correlation lengths in the lateral dimension) of arbitrary orientation (see Fig. 5). The cross section per unit area of the composite rough surface is obtained by averaging the cross sections of the individual arbitrarily oriented pixels. It is shown that the (unified full wave) cross section of the composite rough surface is relatively stationary over a broad range of patch sizes. In this broad range of values of patch sizes, the norm of the relative error is minimum.

A patch is assumed to be oriented normal to the vector (see Fig. 5)

Qty = sin £2 COS + COS £2 COS Гй(у + sinro^,

where a x, a y, and a z are the unit vectors in the fixed (reference) coordinate system associated with the mean plane y’ = h0 = 0 and hx = dh/dx, hz = dh/dz. The unit vectors ax and az are tangent to the mean plane of the patch. The angles ^ and т are the tilt angles in and perpendicular to the fixed plane of incidence (the x’, y’ plane).

The cosines of the angles of incidence and scatter in the patch coordinate system can be expressed in terms of the cosines of the angles of incidence and scatter in the fixed reference coordinate system (primed quantities; see Fig. 5) as follows:

—n’ ■ fly = cos 0q = cos(6j + £2) cos r (98)

and

nf • av = cos0Q = [cos 0ц cos £2 + віпбд sin fScos^]

The surface element scattering coefficient for the tilted pixel is expressed as follows (66):

in which SPQp the elements of the 2 x 2 scattering matrix Sp are obtained from SPQ on replacing the angles в1’0 and ef 0 by в10 and ef0, respectively. Furthermore, cos(^f’ — ф1′) and sin(^f’ — ф1′) are replaced by the cosine and the sine of the angle ^f — ф1) between the planes of scatter and incidence (with respect to the pixel coordinate system (see Fig. 5) (62). The matrices Tfp and T1p relate to the vertically and horizontally polarized waves in the reference coordinate system to the vertically and horizontally polarized waves in the local (patch) coordinate system (66). Thus

where

 cos iir{ = [cos r(sin0Q cos £2 — cos0jf cost^ sin £2)
 and

sin ijr* = [sin r cos ф^ — cos r sin £2 sin 4? ]/ sin 0Q (1051

The angles ^ and т can be expressed in terms of the derivatives of h(x, z) as follows:

VI + hl

(107)

t — ——- .—— і aui t — . ^

•Jl + h’i + tii Vl + hi+hi

The radar cross section (per unit area) for the tilted patch can be expressed as follows:

and

where

 11101

a’-a4 = [H-h*±h2J-v2

 і 111)

v = k[ — Ai) = + u’a’ + uX

in which

 ‘ 1121

vv = i> av =v’z sin £2cos r +1. cos £2 cos r ■f u;Bmr1ut = (ua-^)1^

Thus, in Eq. (108) both |.DPQp|2 and Qp are functions of the slopes hx and hz of the tilted patch mean plane (see Fig. 5). For a deterministic composite rough surface, the slopes (that modulate the orientation of the

patch) are known. The radar scatter cross section for this composite surface is given by summing the fields of the individual patches. However, if the composite surface height is random, the tilted pixel cross section (per unit area) [Eq. (108)] for the rough surface is also a random function of the pixel orientation. Thus, in order to determine the cross section per unit area of the composite random rough surface, it is necessary to evaluate the statistical average of aPQp. The cross section of the composite random rough surface is given by

i113j

where (■) denotes the statistical average (over the slope probability density function p(hx, hz) of the tilted patch). The mean-square slope of the tilted patch is given in terms of the surface height spectral density function

 (114)

i=2

p Jo 4

 For the case kp

 PQn

 0 Lp, lp ■

 oo, ap

 0, the cross section (aPQp) reduces to the original full-wave solution (a

[Eq. (65)]. In Eq. (114), the upper limit kp is the wavenumber associated with the patch of lateral dimension

Lp — 2n/kp.

In the expression for Qp(nf, n1) [Eq. (109)], the surface height autocorrelation function for the rough surface associated with the patch is given in terms of the Fourier transform of the surface height spectral density function as follows:

where it is assumed that the surface is homogeneous and isotropic, k = (k2x + k2z)1/2.

Illustrative examples of the results obtained for the scatter cross section using the above procedures have been published (66).

For purposes of comparisons, the generalized telegraphists’ equations [Eqs. (32) and (33)] have also been solved numerically for one-dimensionally rough surfaces (67). The procedures used are outlined here. On extending the range of the wave vector variable u from — to to to, the Eqs. (32) and (33) are combined into one coupled integrodifferential equation for the forward and backward scattered wave amplitudes a(x, u) and a(x, -u), respectively.

On extracting the rapidly changing part exp(-iux), the wave amplitudes are expressed as

ар(ж, ы) = Ар(ж, ы)expf— iux) ‘116j

The total wave amplitude is the sum of the source-dependent primary wave amplitude APp and the diffusely scattered wave amplitude APs due to the surface roughness:

The primary wave amplitude is obtained from Eqs. (32) and (33) on ignoring the coupling terms SaePq. The resulting integrodifferential equation for the diffusely scattered term APs is converted into an integral equation with mixed boundary conditions. This expression is integrated by parts to get rid of the singularity in the scattering coefficient. The resulting integral equation is solved numerically using the standard moments method. Finally the field transforms [Eqs. (17) and (18)] are used to obtain the results for the electromagnetic fields from the wave amplitudes. For the far fields, these expressions can be integrated analytically (over the wavenumber variable) using stationary-phase techniques. These results show that for surfaces with small to moderate slopes the proceeding analytical results are valid (67).

When the observation points are near the surface, it is necessary to account for coupling between the radiation fields, the lateral waves, and the surface waves associated with rough surface scattering (68,69). When the rough surface is assumed to be perfectly conducting, the contribution from the branch cut integral associated with the lateral waves vanishes and there are no residue contributions (associated with surface waves) from the singularities of the reflection coefficients. When the approximate impedance boundary condition is used, the lateral wave contribution is eliminated.

The full-wave method can also be used to determine the fields scattered upon transmission across rough surfaces (70). When scattering from more than one rough interface in an irregular stratified media is considered, in general, it becomes necessary to account for scattering upon reflection and transmission across rough surfaces. This topic is reviewed in the next section.

## BIOLOGICAL EFFECTS OF ELECTROMAGNETIC FIELDS IN HUMANS

This subject is large, and particularly as it relates to possi­ble chronic health effects from low levels of exposure, very contentious. We will first consider the effects that underlie major exposure standards for electromagnetic fields, and then comment about possible effects of chronic exposure to electromagnetic fields in humans.

Static Fields

The strongest DC magnetic field that a human is likely to encounter is in the low-Tesla range (e. g., during imaging by MRI). No biophysical reason exists to anticipate pro­nounced effects in humans at such levels, and limited test­ing with animals has disclosed only subtle effects. One in­vestigator noted mild sensory effects in humans exposed to 4 T fields in an MRI system (32). One group reported a change in the permeability of the blood-brain barrier per­meability in rats from exposure to 1.5-T magnetic fields (33). This effect (which is so far unconfirmed by indepen­dent studies) remains poorly understood and its implica­tions for health and safety are unclear. Blondin et al. re­ported the threshold for human perception of DC electric fields to be 40-45 kV/m (34).

Low Frequency Fields

The threshold for human perception of 50/60-Hz electric fields is in the range of 2 to 10 kV/m, because of the move­ment of the hairs on the subject’s skin. The threshold for perceiving spark discharges corresponds to field strengths outside the body of about 3 kV/m, when a person can per­ceive mild shocks when touching a conductive object lo­cated in the field. At about 8-10 kV/m, painful shocks can be felt by finger contact with vehicles or other large objects in the field (35). Above about 20 kV/m, annoying shocks are felt at the shoe level (36). Exposure to 50/60-Hz elec­tric fields at still higher levels is very unpleasant because of transient shocks. These effects are a result of currents that are passed into the body by touching a conductive object; the fields induced within the body from such exposures, in the absence of contact with conductive objects, is generally far below the thresholds for inducing shock (Fig. 1).

Cardiac Excitation and Fibrillation

Various effects have been reported or can be anticipated from low frequency alternating magnetic fields at sufficient flux densities, which are associated with induced electric currents (Table 2) (37-39). One potentially lethal effect is cardiac fibrillation from induced electric fields in the chest. Reilly estimated that the threshold current density in the human heart for causing electrical stimulation is about 1 A/m2 (60 Hz), with thresholds for inducing fibrillation be­ing about 2-3 times higher. Current densities in excess of2 amp/m2 (60 Hz), if applied directly to the heart, can induce fibrillation in dogs (40). The National Radiological Protec­tion Board (NRPB) estimated the threshold induced cur­rent that would produce cardiac fibrillation in the human to be 3 A/m2 (41). To produce such currents in the human chest would require magnetic flux densities above 100 mT at 60 Hz (42).

Nerve Stimulation by Pulsed Magnetic Fields

Some clinical devices use pulsed magnetic fields to stim­ulate nerve and muscle tissues (43, 44), which typically employ pulsed magnetic fields, usually of millisecond du­ration and with magnetic slew rates (dB/dt) of tens of T/s, and peak magnetic fields ranging from several hundred mT to several T.

Other effects such as headache and general discomfort

(45) have been reported in humans at flux densities > 60 mT (50/60 Hz) and may involve neurological effects. How­ever, the literature on these effects is sparse and variable in quality, and the mechanisms for the effects are not well understood.

Bone Repair Stimulated by Pulsed Magnetic Fields

An often-reported effect of magnetic fields that remains poorly understood is the stimulation of fracture repair in bones. Magnetic bone stimulators have been approved for sale in the United States since the late 1970s. These devices employ a variety of pulsed fields, and they induce electric fields in the body with peak levels of the order of 0.1 V/m (46). The corresponding peak current densities are of the orders of tens of mA/m2 in soft tissue, which are above the level ofnaturally occurring (endogenous) fields but are well below anticipated thresholds for eliciting action potentials in excitable tissue.

Magnetophosphenes

A well-established effect, first observed by d’Arsonval in 1896, is the production of visual sensations, called mag — netophosphenes, when the head is exposed to alternating magnetic fields (10-20 mT, 50 Hz). These effects are caused by small currents (20-200 mA/cm2) that are induced in the retina of the eye (47,48), and are the most sensitive responses observed in humans from exposure to low fre­quency electric or magnetic fields. The effect has not been considered to be a hazard by the expert committees that have examined the literature.

Endogenous Electric Fields

Naturally occurring (endogenous) electric fields exist in the body because of bioelectric phenomena such as the electro­cardiogram, electromyogram, and electroencephalogram. Such fields generally have most of their spectral density below 100 Hz and correspond to current densities of 1-10 mA/m2; but current densities of 1000 mA/m2 can develop during brief periods of electrical activity (action potentials) on the surface of nerve or muscle cells (49). The ubiquitous presence of such fields in body tissues would seem to place a lower limit on the strength of externally induced fields that would be biologically significant.

High-Frequency Fields. As the frequency of the applied field is increased above 1-3 kHz, cell membranes become progressively less sensitive to stimulation, and thermal phenomena predominate. A variety of effects, some haz­ardous, have been reported from high frequency electro­magnetic fields (mostly at radiofrequencies and above).

Perception and Pain

The thresholds for perception of microwave energy have recently been measured by Blick et al. for brief (10-second) exposure to microwave energy over an area of 0.024 m2 on the backs of human volunteers (Table 3) (50). A thermal model, which takes into account the reflection of energy from the skin and heat conduction, shows that the temper­ature rise at the skin surface at the threshold for perception is about 0.07°C over this entire frequency range (51).

The threshold for perception decreases with increasing frequency, because of the shorter penetration depth into tissue (and corresponding increase in SAR near the skin surface), modified by thermal conduction effects.

The threshold for painful stimulation under similar ex­posure conditions would be 50-100 times higher for these exposure conditions. However, the thresholds for percep­tion and pain are likely to vary greatly, depending on the location of the exposed surface, duration of exposure, and other variables.

Burns

At still higher exposure levels, or for longer exposure times at these exposure levels, burns may it result. Despite the many high power sources of radiofrequency and microwave energy that exist in modern society, the incidence of seri­ous burns from radiofrequency energy is low (a handful of incidents have been reported of burns from defective mi­crowave ovens, some of them disputed (52), and occasional industrial accidents occur that involve exposure ofworkers to high levels of radiofrequency fields).

The thresholds for producing thermal damage in tissue depend on the magnitude and duration of the increase in temperature. Tissues can tolerate heating to temperatures below about 43°C almost indefinitely, whereas higher tem­peratures will lead to thermal damage at progressively shorter times at higher temperatures (53). Thus, the mi­crowave exposure needed to produce thermal damage de­pends on several factors, including the time over which ir­radiation persists, the size of the heated region, and the rate at which heat is transported from the heated region. Despite the fact that burns are an unequivocal potential hazard from exposure to RF energy, the incidence of such injuries is very low. Reasons include the general inacces­sibility of high powered sources of RF energy to the gen­eral population and the fact that overexposure will lead to severe pain before thermal damage occurs, forcing the subject to withdraw from exposure. Incidents of serious injury to exposure to RF energy are typically associated with industrial accidents (for example, one case involved a tower climber who was suspended in front of a high pow­ered broadcast transmitter and could not escape) or in mil­itary environments in which a person comes into contact with very intense RF beams.

Thermoregulatory Effects

If the heat load to the body is comparable with, or even below, rates of heat generation by metabolism, biological effects can occur as a result of the normal operation of the thermoregulatory mechanisms. Characteristic thermoreg­ulatory changes include alterations in blood flow, respi­ration, sweating, and many more subtle physiological re­sponses. Various subtle physiological effects observed in animals after moderate exposure to microwaves can be interpreted as normal thermoregulatory responses, and various reported synergistic interactions of drugs and mi­crowave exposure might likewise have a thermoregulatory component (54). The basal metabolic rate in man is about 1 W/kg of body mass, and whole-body exposures somewhat above and below this level can be expected to produce ther­moregulatory responses.

A wide variety of thermal effects have been demonstrated in animals that can be anticipated to occur in humans as well. Some of the more significant include the following:

• Cataract is an established hazard of microwave en­ergy, which has been reported occasionally in humans exposed to high intensity microwaves. Cataracts can be produced in animals at high exposure levels, gen­erally > 1000 W/m2, and are associated with tempera­ture increases of several degrees in the eye. Exposures at such levels would be acutely hazardous to person­nel because of the likelihood of thermal injury to the body (and not just in the eye). Occasional claims of cataract produced by low level microwave exposure have not been substantiated by animal studies (55).

• Reproductive effects (birth defects and other adverse effects) are well established in mammals exposed to microwave energy sufficient to raise body tempera­ture [e. g., (56)]. The exposure required to produce such effects is quite high (tens of W/kg), and the effect can be presumed to be thermal in nature. High exposures, far above present exposure safety limits, would be re­quired to produce such effects.

• Behavioral disruption has been observed in several species of animals exposed to microwaves at whole — body exposures of 4-6 W/kg, at several frequencies above 100 MHz (57). In such studies, the animals are trained to carry out a task (for example, press­ing a lever to obtain food pellets) and exposed to mi­crowave energy. At some exposure level, the animals stop performing the assigned task and begin a differ­ent behavior, typically one associated with thermoreg­ulation (for example, spreading saliva on the tail in rats). Major standards-setting committees have con­sidered behavioral disruption to be the effect of ra­diofrequency energy that has been reliably demon­strated at the lowest whole-body exposure level. Be­havioral disruption can be interpreted as a normal response of the animal to the excessive heat load to its body, and is not, strictly speaking, an adverse ef­fect at all; however the thermal burden to the body in such cases is undoubtedly close to hazardous levels.

Consequences of Long-Term Exposures

All of the scientific results discussed so far pertain to ef­fects produced by short-term exposures to electromagnetic fields, usually at high levels. A very different body of liter­ature has emerged since the late 1970s pertaining to possi­ble health effects from long-term exposures to environmen­tal fields, either at power line (50/60 Hz) or radiofrequen­cies, based on epidemiological studies that focus on possi­ble statistical correlations between exposure and a health endpoint.

The epidemiology literature is far too large to review here. The following paragraphs provide citations to major recent reviews and indicate the nature oftheir conclusions.

Powerline Fields. Most epidemiology studies related to power line fields have focused on a possible link be­tween exposure to 50/60-Hz magnetic fields and childhood leukemia, first suggested in a 1979 paper by Wertheimer and Leeper (58). A variety of other health endpoints have been examined as well.

By now, more than 100 epidemiology studies have been reported related to power frequency fields and human health; for recent reviews, see Kheifets and Shimkhada (59) and Feychting et al. (60). A definitive review of the literature, focusing primarily on epidemiology literature but considering relevant animal studies, was published in 2002 by the International Agency for Research on Cancer (IARC) (61). The IARC review classified power frequency magnetic fields as “possible” human carcinogens (Group 2B in its classification scheme), based on limited epidemiolog­ical evidence together with limited or inadequate animal evidence (other 2B carcinogens, as determined by IARC, in­clude coffee, automobile exhaust, and pickled vegetables). IARC judged the evidence for other health effects to be in­adequate to draw conclusions.

Radiofrequency Fields. Public concerns that use of mo­bile telephones might cause brain cancer were triggered by a story broadcast on a United States television show in 1993 by a man whose wife had used a mobile telephone and subsequently developed brain cancer, which he attributed to the effects of the phone. Such observations have obvi­ous weaknesses for documenting cause-and-effect relation­ships: many millions of people use mobile telephones and an incidence of the disease in the United States is 15-20 new cases per hundred thousand people per year, and con­sequently many users of mobile phones will develop brain cancer every year even if no causal link to the phones ex­ist. In the intervening decade, more than a dozen large — scale epidemiology studies, and numerous animal studies, have been undertaken (for recent reviews, see Ahlbom et al. (62) and Moulder et al. (63). Several massive epidemiol­ogy studies are nearly completed and much more data will become available on this issue in coming years; present results are generally negative but insufficient to persuade most health agencies that no hazards (cancer or otherwise) are associated with use of mobile telephones. The problem is complicated by the largely unknown cause of brain can­cer in its various forms, by the long latency (time between initiation of the tumor and its clinical detection in a pa­tient), and by the rapidly changing technology of wireless communications.

## GRID-BASED FEATURES OF THE SMITH CHART

A number of useful design features result from the final form of the Chart grid as derived by Smith. In addition to the inter-

On the Smith Chart, loci of constant VSWR are concentric circles with all centers located at K = 0, and radii are nonuni — formly distributed between unity and infinity for values of K ranging from 0 to 1.

 90° (a)

 Figure 4. (a) Two-dimensional cylindrical coordinate plot of loci of constant reflection coefficient magnitude and constant reflection coef­ficient angle. (b) Loci of constant-Д circles and constant-X circular arcs scaled to fit on the reflection coefficient loci plot of part (a).