2007 6th International Conference on

ANTENNA THEORY AND

TECHNIQUES

September 17 – 21, 2007

Sevastopol, Ukraine

2 International Conference on Antenna Theory and Techniques, 17-21 September, 2007, Sevastopol, Ukraine

ORGANIZERS Ukrainian National Antenna Association,

IEEE AP/C/EMC/SP Kharkov Joint Chapter of Ukraine Section, V.N. Karazin Kharkiv National University, Sevastopol National Technical University,

Ukraine Ministry of Education and Science, Kharkiv National University of Radio Electronics,

National Technical University "Kyiv Polytechnical Institute", Institute of Radio Engineering and Electronics RAS

Ukrainian URSI Committee, Radio Astronomy Institute of NASU,

Institute of Radiophysics and Electronics of NASU, A.S. Popov Scientific and Technical Society,

IEEE Russian Section

We wish to thank the following for their contribution to the success of this conference: European Office of Aerospace Research and Development, Air Force Office of Scientific Research, United

States Air Force Research Laboratory <http://www.london.af.mil>

AP-S IEEE Radio Astronomy Institute of NASU

Institute of Radiophysics and Electronics of NASU Ukrainian Science Academy SMF “Institute of Automatic System”

Scientific-Production Company “TERA” Proceedings of the 2007 Sixth International Conference on Antenna Theory and Techniques (ICATT’07) IEEE Catalog Number: CFP07540-PRT ISBN: 978-1-4244-1584-7 Library of Congress: 2007905458 Copyright and Reprint Permission: Abstracting is permitted with credit to the source. Libraries are permitted to photocopy beyond the limit of U.S. copyright law for private use of patrons those articles in this volume that carry a code at the bottom of the first page, provided the per-copy fee indicated in the code is paid through Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923. For other copying, reprint or republication permission, write to IEEE Copyrights Manager, IEEE Operations Center, 445 Hoes Lane, P.O. Box 1331, Piscataway, NJ 08855-1331. All rights reserved. Copyright ©2007 by the Institute of Electrical and Electronics Engineers

This material is based upon work supported by the European Office of Aerospace Research and Development, Air Force Research Laboratory under Award No FA8655-07-1-5087

International Conference on Antenna Theory and Techniques, 17-21 September, 2007, Sevastopol, Ukraine 3

ICATT’07 HONORARY CHAIRMAN: Prof. Yakov S. Shifrin, IEEE Fellow Member, Kharkiv National University of Radio Electronics, President of Ukrainian National Antenna Association, Kharkiv, Ukraine

ICATT’07 CHAIRMAN: Prof. Nikolay N. Kolchigin, IEEE Senior Member, Theoretical Radiophysics Dept. V.N. Karazin Kharkiv National University, Kharkiv, Ukraine

ICATT’07 Co-CHAIRMEN: Prof. Viktor A. Katrich, V.N. Karazin Kharkiv National University, Kharkiv, Ukraine Prof. Viktor F. Kravchenko, Institute of Radio Engineering and Electronics RAS, Moscow, Russia Prof. Alexander G. Luk’yanchuk, Sevastopol National Technical University, Sevastopol, Ukraine Prof. Fedor F. Dubrovka, National Technical University "Kyiv Polytechnical Institute", Kyiv, Ukraine

ICATT’07 Organizing Committee

Secretaries: Dr. Khardikov Vyacheslav V. (Kharkiv, Ukraine) Dr. Shishkova Anna V. (Kharkiv, Ukraine)

Members: Antufeyeva Mariya S. (Kharkiv, Ukraine) Belogurov Evgeniy Y. (Kharkiv, Ukraine) Dr. Blinova Nataliya K. (Kharkiv, Ukraine) Dr. Butrym Aleksander Y. (Kharkiv, Ukraine) Dr. Dumin Aleksander N. (Kharkiv, Ukraine) Prof. Ermolov Pavel P. (Sevastopol, Ukraine) Prof. Gimpilevich Yuriy B. (Sevastopol, Ukraine) Dr. Ivanchenko Dmitry D. (Kharkiv, Ukraine) Dr. Katenev Sergey K. (Kharkiv, Ukraine) Kazanskiy Oleg V. (Kharkiv, Ukraine) Kochetov Bogdan (Kharkiv, Ukraine) Litvinov Dmitry D. (Kharkiv, Ukraine) Dr. Maksimova Nona G. (Kharkiv, Ukraine) Dr. Pivnenko Sergey N. (Lyngby, Denmark) Dr. Pochanin Genadiy (Kharkiv, Ukraine) Dr. Shirokov Igor B. (Sevastopol, Ukraine) Prof. Shulga Sergey N. (Kharkiv, Ukraine) Dr. Vetrov Igor L. (Sevastopol, Ukraine) Prof. Yarovoy Alexander G. (the Netherlands) Dr. Zheng Yu (Kharkiv, Ukraine) Rzhevtzeva Natalya L. (Sevastopol, Ukraine) Svetlana V. Pshenichnaja (Kharkiv, Ukraine)

Table of Contents

International Conference on Antenna Theory and Techniques, 17-21 September, 2007, Sevastopol, Ukraine 7

GENERAL ANTENNA THEORY

01. ELECTRIC CHARACTERISTICS OF A SKIN LAYER OF A PLASMA JET GENERATED AS A RESULT OF THE BLANK CARTRIDGE EXPLOSION IN A FREE SPACE Puzanov O. O. ...........................................................................................................................................

104

02. FORMING AND RADIATION OF HIGH-POWER SHORT RADIO PULSES Sirenko Yu. K., Pazynin V. L. and Shafalyuk O. S...................................................................................

107

03. SCATTERING OF AN E-POLARIZED PLANE WAVE BY ELONGATED CYLINDER OF ARBITRARY CROSS-SECTION Vinogradov S. and Wilson C.....................................................................................................................

110

04. A DISCUSSION ON THE PROPERTIES OF ELECTRICALLY SMALL FRACTAL ANTENNAS Volodymir M. Onufriyenko.......................................................................................................................

113

05. 60 YEARS OF ELECTRICALLY SMALL ANTENNAS THEORY Slyusar V. I................................................................................................................................................

116

06. RESONANCE DEGENERATE PLANE LATTICE OF MAGNETODIELECTRIC SPHERES WITH A HOLE Kozar A. I. .................................................................................................................................................

119

07. ELECTROMAGNETIC FIELD OF DIPOLE ANTENNA IN MULTILAYERED MEDIUM WITH LOSSES Kleshchenkov A. B., Lerer A. M. and Labunko O. S................................................................................

122

08. RADIATION OF ELECTROMAGNETIC FIELD PULSES BY PLANAR DIPOLE ANTENNAS AT DIFFERENT MODES OF EXCITATION Orlenko А. А., Kholod P. V., Ruban V. P.................................................................................................

125

09. DIFFRACTION FIELD OF THE VERTICAL DIPOLE FROM SPHERE WITH APERTURE, SCREENING BY THE DIELECTRIC LAYER Rezunenko V. A., Roshchupkin S. V., Radchenko E. I. ............................................................................

128

10 ELECTRODYNAMIC CHARACTERISTICS OF THE TRANSVERSAL SLOT RADIATOR IN A RECTANGULAR WAVEGUIDE WITH A LAYERED DIELECTRIC FILLING Blinova N. K., Lyakhovsky A. A. and Yatsuk L. P...................................................................................

131

11. NEAR-FIELD RADIATION FROM SECTORAL HORNS Anna V. Shishkova, Nikolay N. Gorobets, Elena E. Ovsyannikova .........................................................

134

MICROWAVE COMPONENTS AND CIRCUITS, FIBER-OPTICS LINKS

01. DESIGN OF SPMT SWITCHES MATCHED BY MEANS OF TRANSFORMING FOUR-POLES Oborzhytskyy V. I. ....................................................................................................................................

137

02. HELIX ANTENNAS FOR GENERATORS OF SHORT HIGH-VOLTAGE PULSES Boyko M. I. ...............................................................................................................................................

140

03. SOLID STATE NONSTATIONARY SPECTROMETERS SUBTHZ AND THZ FREQUENCY RANGES FOR ANALYTICAL APPLICATIONS Vaks V. L., Pripolzin S. I., Panin A. N., Nikiforov S. D., Vinogradov A. A. ...........................................

143

International Conference on Antenna Theory and Techniques, 17-21 September, 2007, Sevastopol, Ukraine pp. 116-118

978-1-4244-1584-7/07/$25.00©2007 IEEE

60 YEARS OF ELECTRICALLY SMALL ANTENNAS THEORY

Slyusar V. I.

Central Research and Development Institute of Arms and Military Engineering of the Armed Forces of Ukraine, Kiev, Ukraine

E-mail: swadim@inbox.ru

Abstract In 2007 60 years from the moment of the publication of the first theoretical work

which have proved fundamental limits of achievable parameters so-called Electrically Small Antennas (ESA) are executed. On the eve of a anniversary of the given event - it is high time to sum up the 60-years way gone by theorists and developers of aerials in understanding of limiting restrictions in realization effective of ESA-solutions. The given report also is devoted to this review.

Keywords: Electrically small antennas (ESA), quality factor, fundamental limit.

In 2007 60 years from the moment of the publication of the first theoretical work which have proved fun-damental limits of achievable parameters so-called Electrically Small Antennas (ESA) are executed. It was article of Harold A. Wheeler [1]. On the eve of a anniversary of the given event - it is high time to sum up the 60-years way gone by theorists and developers of aerials in understanding of limiting restrictions in realization effective of ESA-solutions. The given re-port also is devoted to this review.

The author it is offered to distinguish in a history of development of the passives ESA’s theory four stages. First of them covers the period from the moment of the publication of Harold A. Wheeler’s article, and development, becoming since 1948 of the fundamen-tal limit’s theory of Quality Factor of Chu within of the concept of equivalent electric circuits, a concrete definition of its positions from Harrington in 1960.

The Wheeler’s definition of a Electrically Small Antenna is antenna with geometrical dimension which fits inside a sphere of radius 1/a k= where

2 /k π λ= is the wave number associated with the electromagnetic field (Fig. 1).

The radiative properties of such electrically small antennas were first investigated by Wheeler [1] who coined the term "radiation power factor" as the in-verse of the radiation Q (Quality Factor). Using circuit concepts for a capacitor and inductor acting as an an-tenna, he showed that the radiation power factor for either kind of antenna is somewhat greater than

2

13

4Vol

3Q

πλ

− > ,

where Vol is the volume of the cylinder containing the antenna and λ is the wavelength.

A year later, Chu [2] derived an approximate lower limit for the radiation Q (Quality Factor) of an elec-trically small antenna:

2, ,

2, .

ee m

mm e

WW W

PQW

W WP

ω

ω

⎧⎪⎪ >⎪⎪⎪= ⎨⎪⎪ >⎪⎪⎪⎩

If lower the Q factor for the antenna, then wider the useable frequency band of the antenna.

Chu was the first to derive analytic results using Maxwell's equations for omnidirectional, linearly polar-ized radiation. He obtained expressions for the minimum radiation Q that can be obtained for an antenna that fit within a sphere of a given radius. This result assumed no energy remained within the sphere. The fields outside the sphere were expanded in spherical wave functions. The stored energy and radiated power were calculated for each mode using the complex Poynting Theorem and a ladder circuit derived for each mode.

Chu obtained results for transverse-magnetic (TM) and transverse-electric (TE) linearly polarized and circularly polarized modes.

In 1960, Harrington [3] related the effects of an-tenna size, gain and minimum Q for the near and far

Fig. 1. Electrically Small Antenna.

60 Years of Electrically Small Antennas Theory

International Conference on Antenna Theory and Techniques, 17-21 September, 2007, Sevastopol, Ukraine 117

field diffraction zones for linearly and circularly po-larized waves, and also treated the case where the antenna efficiency h is less than 100%. Harrington also extended this theoretical result to include the maximum possible gain. The Chu-Harrington’s limit of Q for linearly polarized waves can be written:

( )

2 2

3 3 2 2

1 3

1

k aQ

k a k a

+=

+ (1)

or approximated for 1ka <<

3 3

1Q

k a≈ . (2)

The beginning of the second stage is connected with offered in 1964. Robert E. Collin and S. Roths-child a method of calculation of limiting Quality Fac-tor ESA on the basis of analytical Equations for the full reserved energy of an electromagnetic field close ESA [4]:

3 3

1 1Q

k a ka≈ + . (3)

This result conflicted with the Chu-Harrington’s limit. The same period was marked by split of theo-rists on two camps-supporters of the theory of Chu and adherents of its revision.

The third stage was marked by detection in 1996 McLean [5] a long-term mistake in treatment of re-sults of Chu admitted Harrington, and the further specification on this basis of Equations for limiting Quality Factor ESA. MacLean [5] re-examined the fundamental limit in order to achieve the highest pos-sible accuracy because it makes little sense to speak of approximate fundamental limits. McLean then pre-sented an exact expression for the minimum radiation Q . Like Chu, he assumed that the antenna radiates only one mode, in this case the 1n = spherical mode. The fields of this mode are equivalent to the fields radiated by a short dipole antenna. He computed the stored energy due to the total fields and then sub-tracts the stored energy due to the radiated fields, leaving only the non-propagating stored energy from which the radiation Q is determined. The resulting expression for Q and linearly polarized waves is

( ) ( )

2 2

3 33 3 2 2 2 2

1 2 1 1

1 1

k aQ

k ak a k a ka k a

+= = +

+ +. (4)

For 1ka << this can be approximated

3 3

1 1Q

k a ka≈ + .

This result confirmed Collin-Rothschild’s limit. Figure 2 shows the minimum Q of (1) – (4) for 100 % efficiency.

The McLean’s limit of Q for circularly polarized waves can be written:

3 3

1 12

Qk a ka

≈ + . (5)

Caswell, Davis and Stutzman [6] re-formulated the theory using the time-domain approach. The classical derivation of the fundamental limits assumed that the electric and magnetic stored energies are completely orthogonal. However, this is not the case for an antenna.

For the time-domain derivation, the Caswell’s definition of Q for circularly polarized waves is modified as follows

[ ]max e mW W

QP

ω ⋅ += .

Computing the peak stored energy in the time do-main assuming that the antenna radiates only one mode, 1n = , gives the final result for radiation Q

3 3 6 6 2 2

1 1 1 12 4

Qk a ka k a k a

= + + + . (6)

The same result give in 1998 Dale M. Grimes and Craig A. Grimes [7].

Figure 3 shows the minimum radiation Q of (3) as derived by Robert E. Collin, S. Rothschild and Mac-Lean compared to the Q in (5) for 100% efficiency. For smallka , both curves converge to the same value. However, as ka increases, the curves diverge. The commonly accepted size limit for small antennas is

Q

ka Fig. 2. The Family of limits: 1 – (3), 2 – (1), 3 – (4),

4 – (2).

Fig. 3. The Family of limits (5) and (6).

Slyusar V. I.

118 International Conference on Antenna Theory and Techniques, 17-21 September, 2007, Sevastopol, Ukraine

1ka = . At the size, the ratio of the two curves is 1.31. The present, fourth stage, originates in 2003 from

publication Thiele, Detweiler and Penno [8] of a limit of Quality Factor ESA for sine wave distribution of a current in a conductor (Fig. 4). Since this moment the basic direction of development of theory ESA is search of the limits sold in practice which are as much as possible taking into account all physical effects in ESA solutions.

For more information about problems of ESA's Theory please look in [9].

REFERENCES 1. Wheeler, H. A. ‘Fundamental limitations of small

antennas,’ Proc. of the IRE, December 1947, 1479-1488.

2. Chu, L. J. ‘Physical limitations of omnidirectional antennas,’ Journal of Applied Physics, Vol. 19, December 1948, 1163-1175.

3. R.F. Harrington, ‘Effect of Antenna Size on Gain, Bandwidth, and Efficiency,’ J. Res. Nat. Bur. Stand., Vol. 64-D, Jan/Feb 1960, 1-12.

4. R.E. Collin and S. Rothschild, ‘Evaluation of An-tenna Q,’ IEEE Trans. Ant. Prop., Vol. AP-12, Jan. 1964, 23-27.

5. McLean, J. S. ‘A re-examination of the fundamen-tal limits on the radiation Q of electrically small antennas,’ IEEE Trans. Ant. Prop., Vol. 44, no. 5, 672-676, May 1996.

6. E.D. Caswell, W.A. Davis, and W.L. Stutzman, ‘Fundamental Limits on Antenna Size,’ Submitted to IEEE Trans. Ant. Prop., April 2000.

7. Dale M. Grimes, Craig A. Grimes, ‘Radiation Q of dipole-generated fields,’ Radio Science, Vol. 34, Number 2, March-April 1999, 281-296. http://www.ee.psu.edu/grimes/publications/radiation_fields.pdf.

8. Thiele, G.A.; Detweiler, P.L.; Penno, R.P. ‘On the lower bound of the radiation Q for electrically small antennas,’ IEEE Transactions on Antennas and Propagation, Vol. 51, Issue 6, June 2003, 1263-1269.

9. Slusar, V. I. ‘60 Years of Electrically Small An-tennas Theory. Some Conclusions,’ Electronics: Science, Technology, Business, 2006, № 7, 10-19. - http://www.electronics.ru/pdf/7_2006/02.pdf.

Fig. 4. The Thiele's limit and Q of the some anten-

nas [8].

Authors List

International Conference on Antenna Theory and Techniques, 17-21 September, 2007, Sevastopol, Ukraine 491

Ruban V. P. 125 Ruchenkov V. A. 312 Rudakov V. I. 320 Rutkas A. G. 158 Ryndyk A. G. 415

S Sadowski M. 335 Samoylyk S. S. 152 Saprykin I. I. 418 Savenko P. O. 193 Savochkin A. A. 446 Sazonov A. Z. 390 Sazontov A. G. 32 Schekaturin A. A. 446 Scherbinin V. V. 357 Sekretarov S. S. 468 Sestroretskii B. V. 312 Shafalyuk O. S. 107 Shakina L. 289 Sharafiev R.S. 295 Sharypin V. N. 438 Shashkin V. I. 351 Shatov D. S. 357 Shckorbatov Yu. 289 Shifrin Y. S. 344 Shirokov I. B. 332 Shishkova A. V. 134, 181 Shitov S. V. 379 Shu Lin 256 Shulga S. N. 317 Sinyavskiy G. P. 449 Sirenko Yu. K. 107 Sitsko N. Yu. 202 Skobelev S. P. 409 Slyusar V. I. 116,441 Smailov Yu. Y. 474 Soldatenkov V. P. 223 Solonskaya S. V. 341 Stadler M. 326 Sukharevsky I. O 390 Suo Ying 65 Syvozalizov N. A. 155

T Tatarchuk O.M. 315 Teimur Heydari 286,298 Thevenot M. 37 Titov A. N. 458 Tkach М. D. 193 Tokarsky P. L. 87, 452 Troitskiy А. V. 284, 400,403 Tuz V. R. 173,177 Tyschuk U. N. 284

U Ulanovskij А. V. 438 Ulyanov Y. N. 344 Uvarov A. V. 379

V Vainikainen P. 281 Vainikainen P. 348 Vaks V. L. 143 Vasylenko D. O. 247 Vasylyshyn V. I. 455 Vavriv D. M. 468 Vdovicheva N. K. 32 Verbitskii I. L. 237 Vesnik M. V. 214 Vinogradov A. A. 143 Vinogradov S.S. 15, 110 Vishnivetsky O. V. 262 Vlasenko L. A. 158 Volkov S. V. 292 Volkov V. A. 468 Voloschuk R. P. 309 Voloshko S. V. 441 Volosyuk V. K. 20 Vovk S. M. 480 Vozianova A. 188 Vyplavin P. 360 Vystavkin A. N. 379

W Wang Miao 196 Wang Nannan 196,199 Wei Li 253 Wilson C. 110 Woestenburg E. E. M. 82

X Xiaohang Xing 323 Xiaoming Zhou 354 Xuemai Gu 256

Y Yang Caitian 199 Yanovsky F. J. 26 Yaparova A. A. 409 Yatskevich V. A. 292 Yatsuk L. P. 131 Yeliseyeva N. P. 376 Yevdokymov A. P. 59 Ying Suo 253 Yurchenko V. B. 93 Yurtsev O. A. 226,229,432,435

Z Zabolotny V. F. 379 Zakamov V. R. 351 Zamorska O. F. 443 Zelenchuk D. E. 232 Zemlyakov V. V. 449 Zheng Yu 181,246 Zhirnov V. V. 341 Zabolotny V. F. 379 Zakamov V. R. 351 Zamorska O. F. 443 Zelenchuk D. E. 232 Zemlyakov V. V. 449

НАУКОВЕ ВИДАННЯ ЗБІРНИК НАУКОВИХ ПРАЦЬ

2007 6th International Conference on Antenna Theory and Techniques, 17-21 September, 2007, Sevastopol, Ukraine

Відповідальні секретари: Хардіков В.В., Шишкова Г.В. Комп’ютерна верстка: Хардіков В.В. Макет обкладинки: Антюфєєва М.С.

Підписано до друку 31.08.2007 Формат60х84 1/8 Папір офсетний. Друк ризографічний. Ум. друк. арк. 52,3. Обл.-вид. арк 60,9

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