Modeling of Tesla's Transmitter using the Wire Antenna Theory with Ground Effects Included

Transcription

1 Modeling of Tesla's Transmitter using te Wire Antenna Teory wit Ground ffects Included Dragan Poljak, Damir Čavka, Zoran Blažević Department of electronics, University of Split HR- Split, Croatia -mail: Abstract According Tesla s idea is magnifying transmitter as been designed not only to efficiently emit Hertian waves, but also to transmit power at large distances. Analysis of Tesla's transmitter by using te wire antenna teory and reflection coefficient approximation is carried out in tis work. Te radiating part of te Tesla's transmitter is represented by an equivalent monopole antenna driven by an ideal current source tus replacing te Tesla's transformer. Te frequency domain formulation is based on a omogeneous Pocklington integrodifferential equation. Te ground effects are taken into account via te corresponding reflection coefficient appearing witin te integral equation kernel. Solving te Pocklington equation via te Galerkin Bubnov variant of te Indirect Boundary lement Metod (GB-IBM) te current distribution along te monopole antenna is assessed. Knowing te current distribution along te vertical monopole te radiated electric field is obtained by integrating te induced current. Numerical results for te monopole current and te related irradiated field are presented in te paper. Te case studies of free space, perfect ground and imperfectly conducting alf-space ave been considered. Tis paper sould be regarded as an extension of te previous work on te subject. Keywords Tesla s transmitter, Monopole antenna model, Integral equation approac, Reflection coefficient approximation, Boundary element metod. INTRODUCTION It is well known in te istory of electricity tat Nikola Tesla unfortunately never finised is ong Island project and never put is famous transmitter in a full operation. Te scientific man does not aim at an immediate result. He does not expect tat is advanced ideas will be readily taken up. His work is like tat of a planner-for te future. His duty is to lay foundation of tose wo are to come and point te way. Nikola Tesla Te invention of radio definitely belongs to Nikola Tesla. Neverteless, te majority of scientific community as still not fully recognised is important role in te subject. One of te main reasons was te notorious fact tat Tesla never accepted Hert s teory and ad considered te radio waves produced by a Hertian dipole as longitudinal sock waves in space, rater tan transversal []. Anyway, Tesla extraordinary ideas and various acievements still live on teir own life, in pysicists and engineers wo got in touc wit is work. Unfortunately, Tesla was never able to fully understand te gap between great ideas and te completely different and rater difficult process to make tem real and getting tem to commercialiation []. Tesla ad a dream, a rater remarkable idea, to develop a particular radio transmitter for a wireless transmission of not only communication signals, but also electrical energy at large distances. He ad designed is magnifying transmitter [3], [4] by wic e ad been able to efficiently emit eiter Hertian waves or, in is own words, currents troug te eart wic ad been subjected to te device design [5], [6]. However, according to is strong belief Tesla considered wireless transmission by te Hertian waves as rater less efficient metod compared to is own concept. Once, e compared Hertian waves to is eart waves like cutting te butter wit blunt instead wit sarp edge of a knife. A tradeoff between te Hertian wave and te current wave can be found elsewere, e.g. in [7]. However, Tesla ad never completed is ong Island transmitter station and ad never got a cance to confirm is assumptions. In spite of a number of proofs tat e ad played an important essential role in te development of radio, particularly in its infancy Tesla s name was unfortunately not listed among six radio pioneers selected by te uropean Broadcasting Union in 996 [8]. Regardless of te fact tat contemporary science considers Tesla s teory more or less fallacious [9], tere are still some attempts not only to explain Tesla s work carried out in Colorado Springs [] and ong Island [], but also to follow on is work. One of te most acceptable teories witin te present state of te art, is te one relaying on coupling to te Scumann cavity []. It is wort empasiing tat te measurements results of cavity parameters (e.g. resonant frequencies, coerence time, etc.) obtained by Tesla are very close to te experimental results obtained muc later. Te experiments Tesla intended to perform were not carried out until te 96s [3], wen it was found tat te art resonances at 8, 4 and H [4]. Tesla s predictions expected te resonances to occur at 6, 8 and 3H. Unfortunately, Nikola Tesla never presented full details ow is World System would function [5]. Wat e provided were just some general concepts and ideas on propagation mecanism. Frankly, tere are only a fair number of reasons confirming a real necessity to continue te researc on te subject. An interesting work on Tesla s transmitter as been carried out by K. Corum and J. Corum [6], [7]. Using te model of Autoried licensed use limited to: Princeton University. Downloaded on June 6, at ::4 UTC from I Xplore. Restrictions apply.

2 slow-wave elical resonator transmission line [6] te magnifying effect is acieved by te standing waves in te secondary. In te same work te transmission line (T) mode T is presented and standing wave formation explained. It is wort noting tat te very similar explanations can be also found in many Tesla s papers. Te drawback of te T models wit lumped source voltage is tat troug tese models is not possible to predict standing wave pattern presented in []. Terefore, T model proposed in [7], instead of a lumped voltage source at te bottom of te secondary, features a distributed voltage along te line and better describes of te Tesla secondary. Discussion on some T aspects of Tesla s propagationtroug-art teory is available in [7]. Tis paper is an extension of our previous study of Tesla s transmitter by using te wire antenna teory [8], [9]. Contrary to te implementation of transmission line models, te approac presented in [8] and [9] treats te radiating part of Tesla s transmitter (secondary) via monopole antenna model. Wile models presented in [8] and [9] are restricted to free-space antenna representations and formulations based on Hert and magnetic vector potentials tis work accounts for te ground effects. Te formulation is based on te omogeneous Pocklington integro-differential equation. Te Pocklington equation is numerically solved by means of te Galerkin Bubnov variant of te Indirect Boundary lement Metod (GB-IBM) and te current distribution along te equivalent monopole antenna is obtained, providing te field assessment.. VRTICA MONOPO ABOV A OSSY GROUND: INTGRA QUATION FORMUATION Figures a and b sow Tesla's transmitter represented by an equivalent perfectly conducting (PC) vertical monopole antenna of lengt and radius a, located vertically at a eigt 5m above a finitely conducting ground is considered. Te wire dimensions (65m, acm) are in accordance to tin wire approximation [] and te current along te wire can be assumed to be -directed only. Te vertical monopole is driven by an ideal current source I g, representing te current induced in te secondary input due to te oscillations in te primary of te transformer being part of te Tesla s transmitter a) Tesla's transmitter: electric b) quivalent monopole sceme antenna above ground Figure - Representation of Tesla's Transmitter via vertical monopole above a lossy ground. Integral quation for Current along te Vertical Monopole Te key point in te matematical model is to assess te current distribution induced along te vertical monopole due to a time-armonic excitation. Tis current distribution is governed by te omogeneous Pocklington integro-differential equation wic can be derived by expressing te electric field in terms of te magnetic vector potential and by satisfying te continuity conditions for te tangential field components at te antenna surface. Starting from Maxwell equations te total electric field can be expressed, as follows: ( A) jωa Due to rotational symmetry te radiated electric field is independent of aimut variable Φ and te resulting field components are: ρ A ρ () () A jωa (3) Te -component of te magnetic vector component can be expressed by te following particular integral []: Autoried licensed use limited to: Princeton University. Downloaded on June 6, at ::4 UTC from I Xplore. Restrictions apply.

3 + μ A g( x,, ' ) I( ') d' 4π (4) were I(') is te unknown current distribution along te vertical monopole, wile g(x,,') is te total Green function given by: (,, ') (,, ') (,, ') g x g x + R g x (5) were free space Green function is of te form: TM ( x ) (6) g,, ' e R jkr te Green function arising from te image teory is given by: g i e R * jkr* ( x,, ' ) (7) were R is te distance from te source point on te vertical monopole in te air to te arbitrary observation point in air, wile R* is te distance from te source point on te image wire to te arbitrary observation point in free space. R TM is te reflection coefficient for transfer magnetic (TM) polariation. and n is given by: R TM n n (8) n + n ε eff ε n (9) Te total tangential electric field on te PC wire surface vanises and te interface condition can be written, as follows: were exc exc sct ( a, ) + ( a, ) () denotes te excitation function and i sct is te related scattered field. Combining equations (3) to () yields te Pocklington integrodifferential equation for te single wire above a lossy ground: + exc + k g(, ' ) I( ') d' () Finally, in te analysis of Tesla's transmitter, te excitation function cannot be expressed in te form of electric field, as te equivalent antenna is neiter illuminated by te plane wave, nor driven by te voltage generator. Consequently, te left-and side of te equation () vanises and te integro-differential equation () becomes omogeneous: + + k g(, ' ) I( ') d' () Te vertical monopole antenna is excited by an ideal current generator wit one terminal connected to te antenna and te oter one grounded in te remote point. Tis type of excitation can be included into te integral equation sceme troug te forced boundary condition applied at te down end of te wire: I ( ) I g (3) were I g denotes te actual current generator. Integral equation () contains te quasi-singular kernel due to te presence of differential operator []. Tis problem can be overcome by implementing te weak formulation of te problem and Galerkin-Bubnov indirect Boundary lement Metod (GB-IBM) []. Solving te omogeneous Pocklington equation te current distribution along te vertical monopole is obtained.. lectric Field Formulas Te complete electromagnetic field irradiated by te equivalent monopole antenna can be assessed knowing te current distribution along te wire. Inserting te vector potential particular integral (4) into () yields te radial field component: (, ', ρ ) + g ρ I( ' ) d' j4πω (4) ε ρ wic can be rearranged performing te integration by parts: ρ j + I( ') g(, ', ρ) d ' ' ρ 4 πωε + I( ') gi (, ', ρ) RTM ' ρ d ' (5) Te axial -component of te electric field is defined by equation (3) and (4), i.e. by te following expression: + + k g(, ', ρ ) I( ') d' (6) Performing te integration by parts (6) becomes: Autoried licensed use limited to: Princeton University. Downloaded on June 6, at ::4 UTC from I Xplore. Restrictions apply.

4 + I( ') g (, ', ρ) d ' ' + I( ') gi (, ', ρ) RTM d' + j4 πωε ' + + k I( ') g(, ', ρ) d' (7) Te integrals in equations (5) and (7) contain quasisingular kernel due to te presence of differential operator []. Tis quasi-singularity can be efficiently treated by te boundary element/finite differences approac []. It is wort noting tat te model presented so far can be farter upgraded by taking into account te influence of te eart via te rigorous Sommerfeld integral approac instead of te simplified Fresnel reflection coefficient. (V/m) a) Monopole in free space COMPUTATIONA XAMP Te electromagnetic radiation from te vertical monopole antenna representing te Telsa s transmitter is studied for te operating frequency f5kh. Te antenna is energied by te unit current excitation, i.e.: I j g e (8) Figure sows te spatial current distribution along te vertical monopole antenna, wile te related tangential electric field component radiated by te monopole for tree different scenarios; wire in free space, wire above a PC ground and wire above a imperfectly conducting alf-space is sown in Fig 3. Te current induced along te vertical monopole sows linear beavior and falls to ero at te free end of monopole satisfying te edge condition proposed by te tin wire approximation []. I (A) abs(i) real(i) imag(i) (m) Figure - Current distribution induced along te vertical monopole (V/m) (V/m) b) Monopole above perfect ground c) Monopole above imperfect ground Figure 3 - lectric field at different eigts for tree different scenarios Autoried licensed use limited to: Princeton University. Downloaded on June 6, at ::4 UTC from I Xplore. Restrictions apply.

5 Analying all tree scenarios from Fig 3 a rapid die-off for te -component of te electric field, important for te antenna radiation, wit distance is clearly visible. Tese results furter confirm te conclusion from te previous papers [8] and [9] tat no significant (Hertian) radiation occurs in te Tesla s transmitting system, i.e. no significant amount of electromagnetic energy is irradiated from te structure into te free space. A very similar conclusion as been drawn in [7] in using te T model as been used. To a certain extent it is plausible to assume tat Nikola Tesla, aving designed is transmitter ad obviously considered a propagation mecanism different from te one well-establised by Heinric Rudolp Hert. 4. CONCUSION It was te very beginning of t century wen great inventor Nikola Tesla, te scientist out of time, deeply believed e was eading to te development and design of communication and power wireless transmission using is World System. He never succeeded to get te sufficient financial support to work tat out, and in spite of a number of proofs tat e ad made a significant contribution to te development of radio in its early pase te name of Nikola Tesla did not appear among six radio pioneers selected by te uropean Broadcasting Union in year 996. However, te spirit of is ideas continues to live on even troug te work of researcers of today. In tis work a vertical monopole antenna model of te Tesla s transmitter as been developed. Te radiating part of te Tesla's transmitter as been represented by an equivalent vertical monopole antenna above a real ground, excited by te ideal current source replacing te Tesla's transformer. Te matematical model is based on te frequency domain omogeneous Pocklington integro-differential equation. Solving te Pocklington equation numerically via te Galerkin Bubnov variant of te Indirect Boundary lement Metod (GB-IBM) current distribution along te vertical monopole is determined. Knowing te current distribution along te vertical monopole te radiated electric field is computed by integrating te induced current along te wire. Analying te obtained numerical results for te antenna current and related field it can be concluded tat no significant radiation in Hertian sense occurs in te Tesla s transmitting system. In oter words, no significant amount of electromagnetic energy is irradiated from te transmitter into te free space. Tis fact in some sense maybe fosters te assumption tat Tesla considered some different propagation mecanism wile aving considered is transmitter. Tis work is a direct extension of te previous work on te subject tat dealt wit te simplified version of te monopole in free space by wic te Tesla's transmitter was represented. RFRNCS [] N. Tesla, Te True Wireless, lectrical xperimenter, May 99, pp. 8-3, 6-63, 87. [] H.K. Forsen, Nikola Tesla:Scientist, ngineer, Inventor, Proc. International Scien. And Prof. Meeting: Te ife and Work of Nikola Tesla, June 8-9, 6, pp [3] N. Tesla, My Inventions. V. Te Magnifying Transmitter, l. xperimenter, June, 99, pp. -3, 48, 73, [4] N. Tesla, Apparatus for Transmitting lectrical nergy, Patent No.,9,73, United States Patent Office, December, 94. [5] Nikola Tesla on His Work wit Alternating Currents and Teir Application to Wireless Telegrapy, Telepony and Transmission of Power: An xtended Interview, ISBN: , 96. [6] N. Tesla, Art of Transmitting lectrical nergy Troug te Natural Mediums, Specification forming part of Patent No. 787,4, United States Patent Office, April 8, 95. [7] Z.Blaevic, D.Poljak, M.Cvetkovic, Simple Transmission ine Representation of Tesla Coil and Tesla s Wave Propagation Concept, TSIKS, Beograd, October 6. [8] Six Great Pioneers of Wireless, BU Tecnical Review, Spring 995., pp [9] P. Nicolson, Te Real Science of Non-Hertian Waves, August. [] N. Tesla, Colorado Springs Notes 899-9, A. Marinčić, ed, Nolit, Beograd, Yugoslavia, 978. [] A. Marinčić, Researc of Nikola Tesla in ong Island aboratory, nergy and Development at te International Scientific Conference in Honor of te 3 t Anniversary of te Birt of Nikola Tesla, 986. [] T. Grot: Te True Meaning of Wireless Transmission of Power, A Journal of Modern Science, 997. [3] A. Marinčić, Some recent Recognition of Pioneering Role of Nikola Tesla in te Development of Radio, Proc. International Scien. And Prof. Meeting: Te ife and Work of Nikola Tesla, June 8-9, 6, pp [4] J.Galeys, Terrestrial Propagation of ong lectromagnetic Waves, New York, Pergamon Press, 97. [5] N. Tesla, World System of Wireless Transmission of nergy, Telegrap and Telepone Age, October 6, 97, pp [6] K.. Corum, J. F. Corum, RF coils, Helical Resonators and Voltage Magnification by Coerent Spatial Modes, Microwave Review, Vol. 7, No.,. [7] K.. Corum, J. F. Corum, Tesla Coils: Years of Cavity Resonator Development, Tesla Sym, Colorado 99. [8] D.Poljak, Z. Blaevic, V.Doric, Modeling of Tesla s Transmitter using te Antenna Teory Approac, Proc. International Scientific and Professional Meeting Te ife and Work of Nikola Tesla, June 6, Zagreb, Croatia, pp 9-5. [9] D.Poljak, Z. Blaevic, V.Doric, M. Cvetkovic, Analyis of Tesla s Transmitter using Wire Antenna Teory, Proc. Int. Symposium: Nikola Tesla/Te Scientist out of Time, Sept. 6. [] D. Poljak, Advanced Modeling in Computational MC, Jon Wiley and Sons, New York, 7. Autoried licensed use limited to: Princeton University. Downloaded on June 6, at ::4 UTC from I Xplore. Restrictions apply.