The Development of a Cellular Phone Antenna with Small Irradiation of Human-Organism Tissues 2 Michael Bank' and Boris Levin 1Kaf Tet

Benovember St., 6/8, Ashdod, 77450, Israel Tel:/Fax: 972 8 8640565; E-mail: michaelbank~bezeqint.net 2

Tlamim St., 5/23, Lod, 71338, Israel Tel:/Fax: 972 8 9246996; E-mail: [email protected]

Abstract The method put forward here is to reduce undesirable irradiation using an auxiliary radiator of low power. Calculations show that an arrangement with an additional radiator reduces irradiation by a factor of three to four. The structure and magnitude of the field in the far zone preserve their quality of communication with the correspondents (base stations) in all directions. Keywords: Antenna theory; antenna radiation patterns; biological effects of electromagnetic radiation; electromagnetic compatibility; Land mobile radio cellular systems; Land mobile radio equipment; mobile antennas; telephone equipment; auxiliary radiator

1. Introduction

2. Known Methods

an electromagne of the basic aims of EM theory is to create netic field with a predetermined structure. In the case under study, a predetermined field structure is to be created near an antenna (radiator). The significance of this goal should be clear. For example, to a considerable extent, a fundamental electromagnetic problem regarding compatibility is caused by the mutual effect of radiation sources located at close proximity to each other.

Today, extensive research has been done on the creation of new antenna types for portable cellular phones [5-13]. Some methods of reducing the interaction level between the phone's antenna and the human head are possible. These methods are presented on Table 1, together with methods of reducing the deformation of the antenna's pattern.

O

In the vicinity of power radio transmitting centers, the field strength is so great that one may become anxious over the health of neighboring citizens. The dangerous-zone radius increases as the wavelength grows. Over the VHF range, the near-field-region radius is small. However, because of the close proximity of a portable cellular phone to the user's head during a phone conversation, sensitive human organs (for example, the brain or eyeball) are in the radiator's near field. This causes irradiation of human-organism tissues, leading to a health risk [1-4]. In addition, the radiator's proximity to the user's head distorts the antenna pattern, and results in power losses. It is necessary to reduce the irradiation of human tissue. At the same time, the structure and magnitude of the field in the far zone should not change. This is to preserve the quality of commnunication with the correspondents (base stations) in any direction. The methods of achieving the stated goals are different; however, all of them require investigation of the features of the field structure, as well as the field behavior in the near-field regions of various radiators. IEEE Antennas and Propagation Magazine, Vol. 49, No. 4, August 2007

The first method removes the antenna from the most sensitive part of human tissues. For example, this method was utilized in US Patents 5950116 and 5513318, and also in the international patent WO 9944346. The antennas that are produced according to this method are bulky, are not aesthetic, and are also not very practical for use. The second method is antenna screening or radiation absorption on the human side of the antenna. For instance, antenna screening was utilized in US Patents 5784032, 5826201, and 5657386, among others. Radiation absorption was utilized in US Patent 5666125. However, in order to shield a user's head, it is necessary to employ a screen that is substantially larger in size than the lateral dimension of the phone housing. This results in changes in the field magnitude in the far zone. Figure 1 shows the pattern distortion caused by a screen. For similar reasons, one must reject an absorber application. Therefore, numerous suggestions (patents) based on shielding the human head or on reducing radiation in its direction are unacceptable. ISSN 1045-9243/2007/$25 @2007 IEE

E

65

Table 1. Known methods. 1. Decrease in Head Irradiation 1.1 Removing the Antenna from Sensitive Human Tissues J. Baro, US Patent N59501 16 Mobile Telephone with Off-Center Antenna N. O'Badia, international patent WO 9944346 Reduced Radiation in Hand C. A. Tsao, US Patent N55 13383 Mobile Communication Terminal having Extendable Antenna 1.2 Screening and Absorption E. A. EI-Sharawy, international patent WO 9747054 Dual Resonance Antenna for Portable Telephone" R. H. Johnston and L. G. Levesque, US Patent N5784032 Compact Diversity Antenna with Weak Back Near Fields G. Gratias, US Patent N5826201 Antenna Microwave Shieldfor Cellular Telephone J. H. Schwanke, US Patent N5657386 Electromagnetic Shieldfor Cellular Telephone N. N. Luxon, K. A. Luxon, and R. J. Milelli, US Patent N5666125 Radiation Shielding and Range Extending Antenna Assembly C. E. Combest, international patent WO 9426000 AntiElectromagnetic FieldAntenna for Cellular Telephone

antenna with reduced field strength in the near region (the field in the far region must not be changed). One approach is to design an omnidirectional. antenna with a field that is decreased in the near region. A horizontal magnetic dipole is such an antenna. Actually, the electric field strength of an elementary electrical dipole (a Hertz dipole), located vertically along an axis z (.9 = 0), is equal to (see, for example, [14])

El =ij3 Okl 1+l

2

2

Je

sin 9.

(1)

Here, k is the propagation constant, 1 is the dipole length, and J is the electrical current along it. The spherical coordinate frame (R, S,q(p) is used. The electric field strength of an elementary magnetic dipole, located horizontally along an axis x ((p = 0) is equal to

E jklJM (1

47r

jkR)

-jkR sinp,,

R

(2)

1.3 Null Zone International patent WO 0876688 Directive Antenna with Null Zone 2. Reduction of Antenna Pattern Deformations 2.1 Mechanical Methods S. K. Kivela, US Patent Accessory RF Unitfor Hand-Held Wireless Telephone Systems 2.2 Diversity Reception M. R. Pye and S. A. Williams, US Patent N5337061 High PerformanceAntenna for Hand-Held and PortableEquipment Y. Okamnoto, 1. Horikawa, and S. Komaki, US Patent N4710975 Space Diversity Reception System having CompensationMeans of Multipath Effect

Figure 1. The distortion of an antenna pattern. E E(O,01)

T. Fukuda, S. Nakamnura, and M. Sakuma, international patent WO 0030267 Cellular Phone, Flip and Hinge M. Ottelin and H. Ryhaenen, international patent WO 9744911 Method and Device for Local Elimination or Restriction of a Radio-Frequency Radiation Field

The third known method is to use a directive antenna with a null zone in the given direction. This method was used in international patent 0876688, for example. This method also degrades the quality of communication. Thus, the stated problems are not solvable via known methods. R,m In order to attenuate the interaction between a portable cellular-phone antenna and the human head, one has to develop an 66

Figure 2. The electric (1) and magnetic (2) dipole fields. IEEE Antennas and Propagation Magazine, Vol. 49, No. 4, August 2007

where JM is the magnetic current along the dipole. Hence, the electrical field strength of a magnetic dipole -in contrast to the same field of an electric dipole -does not contain the term that is the reciprocal to the cube of a distance R from a radiator. In other words, as the distance R is reduced, the field of a magnetic dipole increases much more slowly than the field of an electric dipole (Figure 2). Since the irradiation power (the power that is absorbed in the portion of the human head adjacent to the telephone) is proportional to E , the thermal losses are

2 a-dy, P fJE1

(3)

where ai is the conductivity of the head tissues and V is the volume of the head. Then, if the radiation powers of electric and magnetic dipoles are equal (the field magnitudes in the far region are the same), the irradiation power of the magnetic dipole is reduced substantially. Such an antenna is described in the papers of Ruoss and Landstorfer [15, 16]. It is the direct slot antenna with loads on both ends: in other words, it is made of two slots in the form of the letter T connected in a foundation. As the authors explain, the application of such a dipole enables the reduction of the irradiation power in a human head from 30% up to 5.7% of the total power, which is approximately a six-time reduction. Such a slot antenna has an essential disadvantage: it has no circular pattern in the horizontal plane. First, the antenna has a direct axis, and thus the pattern is shaped like a figure eight. Secondly, the slot is implemented as a one-sided slot, i.e., it is closed on the head side by the metal housing of the cellular telephone.

3. The Proposed Method Another method to reduce the unfavorable irradiation is to equip a telephone unit with an auxiliary radiator of low power, and to drive it approximately in anti-phase to the main radiator. The action principle of the antenna is based on the field interference of two radiators spaced at a distance (Figure 3). In addition to the main radiating monopole, 1, the antenna contains another (auxiliary) monopole, 2, of a smaller length (with lower dipole moment), which is situated in the plane spanning the head center and the main monopole. Its position is between the head and the main monopole. It is excited approximately in anti-phase to the main monopole ("approximately" is attributable to the field's phase incursion across the interval between the monopoles). A schematic diagram of a telephone unit with an auxiliary radiator is shown in Figure 4a. The auxiliary radiator is placed between the user's head and the main radiator, a small distance from the main radiator, alongside of the head. This allows compensation of the fields of both radiators at a specific (compensation) point inside the head, creating around the head an area with a weak field. If both radiators are placed rationally, and if the amplitude and phase of the auxiliary radiator's electromotive force are selected correctly, the overall field that is transmitted will weaken in a predetermined part of the head, and, from a practical standpoint, will not vary in the far region in comparison to the main radiator's field. This enables a substantial reduction of the power that is absorbed in the predetermined part of the head, provided that the far-region field does not change. At the same time, the total irradiation of the human head is substantially reduced. IEEE Antennas and Propagation Magazine, Vol. 49, No. 4, August 2007

Figure 3. A two-radiator antenna: the placement of the main (1) and auxiliary (2) radiators near the user's head.

convetiina) redietnsmttotw

newradiotranhtniter mainanntenna

I-

--eo -t---

I auxiliary antenna

- -- --

-- --

atteuahtor and network)

Figure 4. A schematic diagram of a telephoae unit with an auxiliary radiator of low power.

The proposed method produces a minimum field at a selected point in space, rather than at a given far-field angle, i.e., it does not distort the antenna pattern. Besides resulting in a phone antenna designed to decrease the irradiation of the head, this also improves the overall performance by recovering power that would otherwise be absorbed in the head. During reception, an electronic changeover switch hooks the receiver only to the main antenna. A similar method was offered in reference [ 17]. There, it was shown by a concrete example that a two-element phased-array phone antenna can be designed to greatly reduce the radiofrequency irradiation of the user. Unfortunately, the method described in this reference was not obvious (not easy to interpret), and did not allow generalization of the results obtained. Besides this, the authors of [17] choose the field null to lie on the head's surface, and the auxiliary radiator was placed remotely from the user's head. 67

hIn [18], the variation of the placement of two dipoles (one of which was passive) near to the user's head was considered. The application of only a passive radiator as the auxiliary radiator limits the possibilities for changing the structure of a near-zone field.

E(R,)IE,(0. 01)

Since the distances between both the antennas and the compensation point are small, the calculation of the fields of the antenna in the near zone should be realized by taking into consideration the finite sizes of the radiators. The direct measurement of a field (for example, by using a dummy) represents a difficult task, so there is a need for exact solutions and accurate calculations. The equations for the electromagnetic fields of electrical and magnetic dipoles of fintite length were obtained in [19], and the results of these field calculation for these antennas were also presented there. The electromagnetic field components of an electrical dipole with finite length are

E(RP(

Figure 5c. The field strength of the radiators as a function of the distance between the monopole antennas: R1 =0 m, R2 = 0.01lm, R, = 0.03 m, E2 = 0.2797E~e-3 0 .

1

E(R)/E,(O.01)

Figure 5a. The field strength of the radiators as a function of the distance between the mnonopole antennas: R, = 0 m, R2=

0.02 m, R,,

=

0.06 m, E2

=

0.397E~ej3 5 .

Figure 5d. The field strength of the radiators as a function of the distance between the monopole antennas: R1 =0m, R2 =0.01 m, R, =O0.02 m, E2 '=0.1l92E~ej'3 1725

ER

#'l+.I

= 6 OheJA [Fl30

[

Es= I3okheJA I~-

)_ke-jRCs

P-2Rj]kR

2

JR2 cs

R

2

f'3+(l _I?)(1_1) ~4R 2 sin 2 9)YkRkOR

2

e-k sin 9 R

(4) HVjkheJA(I L2 )(I +e j H(,j4)~r 4R sin' ,9) 1 kR)

Figure 5b. The field strength of the radiators as a function of the distance between the mnonopole antennas: R, =0 mn, R2 = 0.01 in, R, = 0.06 mn,E2 = 0.71 Ollej3. 31 6 . 68

-ý

HR

=

kl sn Rsn

H, 9 = 0

Herein a system of spherical coordinates (R, ~9, (p) is used, he is the antenna's effective length [20], JA is the current in antenna's base, IEEE Antennas and Propagation Magazine, Vol. 49, No. 4, August 2007

L is the dipole arm length, k

=

2ris the propagation constant of

the wave in air, and A is the wavelength. The dipole is located at the coordinate origin along the z axis. The fact that quantities z and L are small in comparison with R sin 3 was taken into account. Equation (4) generalizes the known formulas for the field components of an elementary electric dipole (Hertz dipole) to the case of a dipole with finite length. The length of the Hertz dipole is much less than the wavelength and than the distance to the observation point, while the current amplitude and phase along the dipole are the same along its length. The symmetric dipole-arm length is comparable to the wavelength, and the current along it follows a sine distribution law. Equation (4), as well as the known formulas for the fields of a Hertz dipole, takes into account the terms inversely proportional to the first, second, and third powers of the distance R to the observation point, i.e., they are valid both in the far-field and near zones. Similarly, for a horizontal circular loop of a finite radius a,

___

[

22

3 )sin 2Slsin,9 -3 k2.2 (±+2a+Sa2+5a j ~) 3 8 (5) ER Here, s

0.2ana

= ;ra , an.=jR

where R0 is the distance from the

center of the loop to an integration point. The loop of radius a lies in the plane xOy, and the center coincides with the origin of the coordinates. The fact that the loop radius is small (a «2A, R0 ) and that the amplitude and phase of the current J along the loop's wire do not vary are taken into account.

4. Numerical and Experimental Results In Figure 5a, the results of calculations for two monopole antennas are presented as a function of the distance from the main radiator. The dimensions in the figure are given in meters. The distance between the antennas was 0.02 mn.The auxiliary radiator was placed alofig the tangent to the head, i.e., the area occupied by the head was to the right of the point R = 0.02 m. The main antenna's field strength (curve E1 ), the auxiliary antenna's field strength (curve E2 ), and the overall field strength (curve E, + E 2 ) are all displayed in the figure. The calculations were performed at a frequency 900 MIHz. The magnitudes of the fields were normalized to the main antenna's field magnitude, E1 (0.01), at a distance of 0.01 m from its axis. The compensation distance (the distance between the compensation point and the main radiator) was R,=0.06 m. In order to ensure the mutual compensation of the antenna fields at this distance, it was necessary that the dipole moment, E02 , of the auxiliary radiator be equal to E2= 0.397E01 ej 3 53 , where E0 , was the dipole moment of the main radiator. From the figure, one can see that for a distance of up to 0.2 mn(the area of the user's head), the overall field was reduced. At a large distance from the radiators, the field magnitude was smaller by a factor of 1.31 compared with the original field. If the IEEE Antennas and Propagation Magazine, Vol. 49, No. 4, August 2007

fields of both antennas field were increased 1.31 times, then the overall field strength at a large distance would be the same as the original field strength. However, one must increase the overall feeding power approximately by a factor of two. The calculated results for two monopole antennas located at a distance of 1 cm from each other are presented in Figure 5b. Here, the overall field was reduced by a greater amount. However, with a reduction of the distance to the compensation point, the difference between the main antenna's field and the total field of the two antennas in the far zone decreased (see Figure 5c, where R, = 0.03 m, and Figure 5d, where R, = 0.02 in). For the case corresponding to Figure 5d, the overall feeding power would be increased approximately by 20%, i.e., the battery life would be slightly reduced. This increase would be smaller if the compensation distance was smaller. When two antennas -such as monopoles - are put close to each other, their performance will be significantly affected. The total radiation field is not the simple addition of the fields radiated by the two individual antennas. Account must be taken that when mutual compensation of the fields of the basic and auxiliary antennas is made, the relationship of their dipole moments, rather than the mutual coupling of the antennas, serves as the main criterion. The current distribution along the antennas is automatically taken into account by means of the effective lengths of the radiators. A loop placed on a phone housing can also be used as an auxiliary antenna. The loop should be placed on a side surface of the phone unit, in order for the polarizations of the fields of the main and auxiliary antennas to coincide. The results of calculations for monopole and loop antennas are presented in Figure 6a. The main antenna (a monopole) was located at the origin of the coordinates. The center of the auxiliary antenna (a loop with radius a = 0.3 mn) was at a distance R2 = 0.015 m from the main antenna. The compensation distance was R, = 0.06mi. In Figure 6b, similar curves are given for R?2 = 0.01lm, R, = 0.03mi, and a =0.05 m. However, the greater dimensions of these loops render these antennas bulky and unusable. The calculations showed that the fields of the two antennas in the direction of the head and in the opposite direction at a distance greater than 0.2 m were almost the same: in other words, the pattern was omnidirectional. The effect of the second antenna on the pattern of the first antenna was negligible, since the second antenna was an obstacle in the form of an isolated conductor of small radius. For the same reason, the second antenna produced a small effect on the tuning of the transmitter's output stage (the tuning can be performed by a slight change of the length of an antenna). On the other hand, one can see from the figures that the power dissipated in the user's head was reduced substantially, since it was a function of the square of the area under the field curve. Figure 7 displays the circuit of the amplifier used for an experimental check of the calculated results. The dependence of the total field on thc distance R and the essential field attenuation in the given area (in the compensation zone) that was obtained by the calculations was also verified experimentally by means of instruments for the measurement of the field in near zone. The results of the experimental check of the total field are presented in Figure Sd (by the closed circles). The experimental procedure was analogous with the procedure that was described in [21]. The experiment showed agreement with the calculation. 69

5. Decrease of Irradiation Let K be an irradiation-decrease factor (the magnitude of the decrease in the power irradiating the human head) caused by the placement of the auxiliary radiator. The calculations were carried out using the formula K= P= P1

(6)

Here, P, and P, represent the irradiation powers for the cases of using both antennas and using only basic radiator (antenna 1), respectively, if the fields in either case in the far zone in a maximum-radiation direction are identical:

I1E, +E212adv,

=,

Figure 6a. The field strength of the radiators as a function of the distance between the monopole and loop antennas: R, =O0m, R 2 =O0.0 15m, R, =O0.06 m, E2 = 1.455 lEjefl92 .

(7) Ij-

J~Ei12 adv, (0)

where or is the conductivity of the head tissues, and V is the volume of the head. In the first approximation, a sphere with a radius of Rhk was used to model the head, and the antenna was drawn parallel to this sphere's tangent at a distance h from it (see Figure 8a). It is possible to show (see the Appendix) that in the calculation of the integrals P, and P1 , the sphere can be replaced by a hemisphere (see Figure 8b), and its interior and exterior radiuses are equal accordingly to R,= h and R?2 =1. 1 5 Rhh . The factor sin .9 was omitted in the expression for the field. Then, considering a to be a constant, we find

0.009 0.000 0.007 0,008 0.000 0 004

-tE

(E

0.003k

0.001

fJIEl (R)12 R2dR,

P1 =

0.002

head 0-02

-------------------------004

008

0.00

0.1

0,12

0.4

0.16

.8

(8) 0.

P,

'

Figure 6b. The field strength of the radiators as a function of the distance between the monopole and loop antennas: R, = Om, R2 = 0.01lm, R, =O0.03m, E2 = 0.881E~e'3 7 7

E=

E1 I(-) +E 2(~

2

flIE1 (R) +E 2 (R)j RdR R,

The calculations of the fields in the near zone were performed using the formulas of Equation (4) in view of the dielectric

a)

V-TUNE

Figure 7. The circuit of the amplifier used for an experimental check of the calculated results. 70

Figure 8a. Changing of the sphere to the hemisphere: the dipole near the sphere. 70 IEEE Antennas and Propagation Magazine, Vol. 49, No. 4, August 2007

permittivity of the tissue, and the calculations of the irradiation powers were performed using the formulas of Equation (8). In this case, the accuracy of this method was similar to the accuracy of simulation software (such as an FDTD package). The calculations results were verified by a measurement of the total near-field dependence on the distance R, including the field in the compensation zone (see the last paragraph of Section 4). In Figure 9, the combined plot for the irradiation decrease factor is given for two monopoles. Along the axis of the abscissa, the distance to a compensation point is shown. The different curves correspond to various distances, h, from the center of the main antenna to the human head (the auxiliary radiator was placed along the tangent to the head). It is seen that each curve had a minimum, which was the optimal compensation point. The value of the magnitude of K at this point varied between the limits of 0.27 to 0.35. Hence, the calculations showed that for the arrangement of an auxiliary antenna in a gap between the head and a basic antenna, it was possible to reduce the irradiation by approximately three-fourths its original size by the right choice of the signal amplitude and phase of the auxiliary antenna. For this purpose, the compensation point should be selected near the surface of the human head. At that point, the overall feeding power increased slightly (about 20%). When examining the results, it is necessary to keep in mind that field attenuation due to the application of an additional radiator takes place not only at the distance R, from the basic antenna, but also in a zone about 1 cm deep. It follows from Figure 9 that in practice, it is best to use the case with h = 2.5 cm, R, = 3cm. F or this case, the main and the auxiliary radiators (with heights of about 8.3 cm and 3.0 cm, respectively) were installed on the top of the metal housing of a cellular telephone at a distance of 2.5 cm from each other (Figure 10). The precise sizes of the radiators were established experimentally for the generator used and for the given phone housing. It is possible to use a version with h = 3 cm and R, = 4 cm, and also intermediate versions. The version with h = 4cm and R, = 5 cm is the less-practical version. This is true for the version with h = 2 cm. However, in the last case, application of an additional radiator ensuring the compensation of the fields at R, = 2cm to R, = 2.5 cm enabled a significant reduction in the thermal losses in a surface layer of the head about 0.5 cm deep, which resulted in a decrease of the dissipation power by almost a factor of three.

K

Figure 10. The installation of the main (1) and the auxiliary (2) radiators (with heights of about 8.3 cm and 3.0 cm, respectively) on the metal housing of a cellular telephone.

This method also permits the cancellation of an unfavorable field in the region most sensitive to irradiation, even in the case of minor irradiation.

6. Conclusion The proposed method, and the theoretical analysis with simulations, showed that there exists a way to solve the problem of irradiation of human tissue. The method described enables a reduction in the irradiation by a factor of three to four. At the same time, the quality of communication with the correspondents (base stations) in any direction is preserved. This near-field cancellation technique can be used in a variety of cases, for example for decreasing the mutual effect (interference) of two closely located antennas.

7. References 1. M. A. Jensen and Y. Rahmat-Samii, "EM Interaction of Handset Antennas and a Human in Personal Communications," Proceed7 17 ings of the IEEE, 83, 1, 1995, pp, - .

Figure 9. The irradiation decrease factor (K) due to the application of two monopoles. IEEE Antennas and Propagation Magazine, Vol. 49, No. 4, August 2007

2. Q. Balzano, 0. Garay, and T. J. Manning, "Electromagnetic Energy Exposure of Simulated Users of Portable Cellular Telephones," IEEE Transactions on Vehicular Technology, 44. 3. 1995, pp. 390-403. 71

3. A. D. Tinniswood, C. M. Furse, and 0. P. Gandhi, "Computations of SAR Distributions for Two Anatomically Based Models of the Human Head Using CAD Files of Commercial Telephones and the Parallelized FDTD Code," IEEE Transactionson Antennas and Propagation,A-P-46, 6, 1998, pp. 829-833.

17. M. A. Mangoud, R. A. Abd-Alhameed, N. J. McEwan, P. S. Excell, and E. A. Abduhriula, "SAR Reduction for Handset with Two-Element Phased Array Antenna Computed Using Hybrid MoM/FDTD Technique," Electronics Letters, 35, 20, 1999, pp. 1693-1694.

4. J. 0. Nielsen, G. F. Pedersen, K. Olesen, and J. Z. Kovacs, "Statistics of Measured Body Loss for Mobile Phones," IEEE Transactions on Antennas and Propagation,AP-49, 9, 2001, pp. 1351-1353.

18. R. Y.-S. Tay, Q. Balzano, and N. Kuster, "Dipole Configurations with Strongly Improved Radiation Efficiency for Hand-Held Transceivers," IEEE Transactions on Antennas and Propagation, AP-46, 1998, pp. 798-806.

5. C. R. Rowell and A. D. Murch, "A Capacitively Loaded PIFA for Compact Mobile Telephone Handsets", IEEE Transactions on Antennas and Propagation,A-P-45, 5, 1997, pp. 837-842.

19. B. M. Levin, "The Field of Linear Vibrators and Loops in Near Zone," Proceedings of the 16th International Wroclaw Symposium on Electromagnetic Compatibility, Wroclaw, 2002, pp. 23-28.

6. S.-G. Pan, T. Becks, A. Bahrwas, and J. Wolff, "N Antennas and Their Applications in Portable Handsets," IEEE Transactions on Antennas and Propagation,AP-45, 10, 1997, pp. 1475-1483.

20. M. Bank, "On Some Misunderstandings Using a Dipole or a Monopole," IEEE Antennas and Propagation Magazine, 45, 1, February 2003, pp. 143-147.

7. Z. D. Liu, P. S. Hall, and D. Wake, "Dual-Frequency Planar Inverted-F Antenna," IEEE Transactions on Antennas and Propagation,AP-45, 10, 1997, pp. 1451-1458.

21. N. Kuster and Q. Balzano, "Energy Absorption Mechanism by Biological Bodies in the Near Field of Dipole Antennas above 300 MHz," IEEE Transactions on Vehicular Technology, 41, 1992, pp. 17-23.

8. K. D. Katsibas, C. A. Balanis, P. A. Tircas, and C. R. Birtcher, "Folded Loop Antenna for Mobile Hand-Held Units," IEEE Transactions on Antennas and Propagation, AP-46, 2, 1998, pp. 260-266. 9. G. Lazzi and 0. P. Gandhi, "On Modeling and Personal Dosimetry of Cellular Telephone Helical Antennas with the FDTD Code," IEEE Transactions on Antennas and Propagation,AP-46, 4, 1998, pp. 525-530. 10. J. F. Rowley and R. B. Waterhouse, "Performance of Shorted Microstrip Patch Antennas for Mobile Communications Handsets at 1800 MHz," IEEE Transactions on Antennas and Propagation, AP-47, 5, 1999, pp. 8 15-822. 11. B. M. Green and M. A. Jensen, "Diversity Performance of Dual-Antenna Handsets Near Operator Tissue," IEEE Transactions on Antennas and Propagation,AP-48, 7, 2000, pp. 10 17-1024.

8. Appendix: Integration Over a Sphere by Passing to Integration Over a Hemisphere An antenna represents a dipole located at the original of coordinates along the z axis. The dipole field is E (R, 9, p) = E(R) sin S. Let us calculate the quantity of energy dissipated inside a sphere of radius PD, centered on the x axis, with its surface passing through the origin of coordinates (see Figure I11a). It is easy to prove that the coordinate, R, , of any point on a sphere's surface is equal to R, = 2ROsin S cosqp.

12. M. Yang and Y. Chen, "A Novel U-shaped Planar Microstrip Antenna for Dual-Frequency Mobile Telephone Communications," IEEE Transactions on Antennas and Propagation,AP-49, 6, 200 1, pp. 1002-1004.

To demonstrate this, one can deduce from the figure that

13. J. F. Rowley, R. B. Waterhouse, and K. H. Joyner, "Modeling of Normal-Mode Helical Antennas at 900 MHz and 1,8 GHz for Mobile Communications Handsets Using FDTD Technique," IEEE Transactions on Antennas and Propagation,AP-50, 6, 2002, pp. 812-820.

where

2

2

2

(9)

2

R6 = R1 +13 +)74,

R3 = R, sin,9 sin (p,

14. C. A. Balanis, Antenna Theory: Analysis and Design, New York, Harper and Row, 1982. 15. H. 0. Ruoss and F. M. Landstorfer, "Slot Antenna for Handheld Mobile Telephones Showing Significantly Reduced Interaction with the Human Body," Electronics Letters, 32, 6, 1996, pp. 513-5 14. 16. H. 0. Ruoss and F. M. Landstorfer, "New Conformal Antenna Concepts for Hand-Held Telephones with Significantly Reduced Interaction with the User," Proceedings of the Colloquium, London, January 1997. 72

Figure 11. Integration over a sphere and over a hemisphere: (a) the sphere, (b) the circular cone. IEEE Antennas and Propagation Magazine, Vol. 49, No. 4, August 2007

Introducing the Feature Article Authors

A4 = R, sin d Cos ip- R0 , whence the expression in Equation (9) immediately follows. The power dissipated inside the sphere is calculated as an integral over a volume, V : (10)

P=, f Po(R,9,rp)R'sin9dV, (V)

where P0 (A, J9, (p) = E2 (A, S, (p) G is the power dissipated in a volume unit, E(R,0, (p) = E (R) sin S is the electrical field strength at a point (R, ,9,v), and G is the specific medium conductivity inside the sphere. From Equations (10) and (9), we get

~Rosin,9cosp P =4GfJdqJsin' 9dS 0

f.

E2 (R) R 2 dR.

0

0

Michael Bank received the BA and MSc degrees in Communications Engineering from the Leningrad Institute of Communications in 1960. He received the PhD degree in 1969 in the field of FM signal detection. He received the Doctor of Science degree (Russian equivalent of professor) in 1990. Since 1992, he has been a consultant to the Israeli communications company Bezeq, and a lecturer in the Holon Academic Institute of Technology. His research interests include digital modulation, digital signal processing, and RF receiving theory.

if in the first approximation (11)

'0

E()=

where E, = const (R), then (12)

P = 37 E0 GA0 . 2

Let us replace the sphere by a circular cone with an angle 2a at the top (Figure 1lb). The power dissipated inside the cone with a generator of length 1 is equal to 2

P, = 4f dipfsin 9d8JP,(R,,9,.)ARdA. 0

0

0

If Equation (11) is true, P,, = 4aj~ Cosa + Cos a1) EO:ta is, ata=I 2 P1= 4 1r E2Gl. 3

(13)

As can be seen from Equations (12) and (13), the magnitudes P and P,, are identical if 1= 9 A 0 . Thus, in the first approximation, 8 a the integration over the volume of a sphere can be replaced by an integration over the volume of a cone with a generator length of 9 1

8

IEEE Antennas and Propagation Magazine, Vol. 49, No. 4, August 2007

Boris Levin was bom in Saratov, Russia, in January 1937. He graduated from Leningrad Polytechnic Institute in 1960, received his PhD in Radio Physics in 1969, and the Doctor of Sciences degree in Physics and Mathematics from St. Petersburg Polytechnic University in 1993. From 1963 to 1998, he worked for the design office "Svyazmorproyekt" of the Russia Shipbuilding Department. From 2000 to 2002, he worked for the company "MARS," in Holon, Israel. Boris Levin has authored three books, 70 original papers in technical journals, and 26 papers in the proceedings of international scientific conferences. His main research interests are in the fields of electromagnetic theory, the theory of linear antennas, and antenna optimization. l

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