Design Study of the Crossed Field Antenna

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1 Jounal of Engineeing and Development, Vol. 10, No. 4, Decembe (006) ISSN Design Study of the Cossed Field Antenna Pof. D. Jamal W. Salman Electical Eng. Dept., College of Engineeing Al-Mustansiiya Univesity, Baghdad, Iaq Asst. Lect. Taiq M. K. Tashan Electical Eng. Dept., College of Engineeing Al-Mustansiiya Univesity, Baghdad, Iaq Abstact Besides the fast development in technology of electonics wold, thee is anthe development in the concepts and pinciples of antennas wok. This pape pesents mathematical expessions fo the main featues of the coss field antenna CFA, like electic field E, magnetic field H, and the poynting vecto S. These expessions ae basically deived by consideing the pinciple of two point chages in the space thow measuing the potential at fa point, leading to the electic field and magnetic field foms of CFA. الخالصة بجانب التطور السريع في تكنولوجيا عالم االلكترونيات هناك تطور أخر في مبادئ عمل الهوائيات. يقدددم هددلا البعددي ترددابير ريااددية لامرددالم ايساسددية لهددوائي تقدداطع المجددال م ددل المجددال الكهربددائي E المجددال المغناطيسي H و متجه القدرة S. تم اشتقاق هله الترابير باعتبار مبدأ شعنتين نقطيتين في الفااء من خالل قياس الجهد عند نقطة بريده مؤديدا للد التربير الريااي لامجال الكهربائي و المغناطيسي لهوائي تقاطع المجال. 197

2 Jounal of Engineeing and Development, Vol. 10, No. 4, Decembe (006) ISSN Intoduction The fist CFA was descibed by F. M. Kabbay et. al. [1]. It intended to synthesize diectly the pointing vecto S fom sepaately stimulated electic field intensity E and magnetic field intensity H, accoding to the fomula S= E H and one impotant esult of development which is useful in engineeing design of antennas in an extemely small size and compact design which is independent of the adiated wavelength. Afte the fist desciption which appeaed in 1989, as any new design thee have been citicisms of design, some coespondents saying that it can not possibly be pacticable, but Byan Well has made models which appea to wok well. He descibed some initial expeiments in the Novembe 1989 issue [1].. Theoy of the CFA All electical and communications enginees ae in some way acquainted with Heaviside s diffeential fom of the Maxwell equations, which ae [] :. D... (1). B 0... () B E.. () t D H J... (4) t whee: E: Electic field stength. H: Magnetic field stength. J: Cuent density. B=µ H: Magnetic flux density. D=ε E: Electic Displacement. It s impotant to ealize that the above equations contain the following extemely valuable infomation: a. A time-vaying magnetic field ceates an electic field (o back e.m.f.). b. A cuent o a time-vaying electic field o both will ceate a magnetic field. The essence of Maxwell s equations conveyed though (a) and (b), is that fundamentally they ae eaction o field poduction equations. The physical, mathematical, and engineeing impotance of the field poduction natue may be moe eadily elayed and undestood if the foms of eqs.() & (4) ae evesed: B E. (5) 198

3 Jounal of Engineeing and Development, Vol. 10, No. 4, Decembe (006) ISSN J D H... (6) eq.() intepeted as An electic field can be elated to the ate of change of a magnetic field. But eq.(5) is intepeted as a time vaying magnetic flux B, ceating an electic field E such that the negative of the cul of the induced E field distibution is equal to the souce B. eq.() is fully deployed in tansfome theoy. Conside now eq.(4) in magnetostatics, it has always been accepted that cuent poduces a magnetic field though the phenomenon called Ampee s Law. But eq.(6) is intepeted as J ceates a magnetic field H, such that the cul of H is equal to the souce J ( J H ) o a time-vaying D field ceates a magnetic field, such that the cul of the H field distibution is equal to the souce D ( D H ). We see now the impotance of evesing eq.(4) to eq.(6) which should now be intepeted as J o Do both can ceate a magnetic field H such that the cul of the H field distibution is equal to the souce ( J + D). The plus sign can, and should be intepeted as analogous to the digital-logic O symbol. Finally we must know that an H field may at any time be the combination of two sepaately induced fields fom independent types of souce i.e. chages motion and displacement cuent. -1 The Magnetic Field Associated with Simple Capacito A capacito essentially consists of two conducting sufaces sepaated by a laye of an insulating medium called dielectic as shown in Fig.(1). To illustate the impotance of the evesed fom eq.(4), and in paticula the featue of D ceating an independent magnetic field fom J. Conside cicula capacito plates with an applied sinusoidal voltage V, fee chage flowing into and out of the capacito and also within the capacito plates themselves, ae a souce of J. Also, due to the build up of fee chage in the capacito E-lines and theefoe D lines exist between the capacito plates [1]. J D-Lines H D ~ f Souce Figue (1) Magnetic field in simple capacito The wavefoms of V, J and D ae shown J below, note that D follows V because D = ε E = ε V/I theefoe D and V in phase as shown in Fig.(). 199

4 Jounal of Engineeing and Development, Vol. 10, No. 4, Decembe (006) ISSN While J is 90 o phase advanced fom V because dv I c c, if V = V m sin(wt), then dt d(v sin(wt )) I m c dt, I c = cw V m cos(wt) = cw V m sin(90 o -α). Amplitude V, D J t Figue () Wavefoms of V, D, and J As the D lines vay in stength due to sinusoidal chage vaiation on the plates, D will ceate a sinusoidal magnetic field. D H D... (7) Since H D is in time phase with D because D H, then H D is 90 o phase advanced fom D as shown in Fig.(). D Amplitude H j, H D t H p Figue () Wavefoms Hj, HD, and Hp Also, since J flowing into and out of the plates is sinusoidal then J H J, poduced a sinusoidal magnetic field H J (in phase with J). In the vicinity suounding the capacito gap, the magnetic field lines fom J into and out of the plates and the magnetic field lines fom D will be concentic cicles suounding the gap and in phase. 00

5 Jounal of Engineeing and Development, Vol. 10, No. 4, Decembe (006) ISSN Now J flowing within the plates themselves will ceate a magnetic field H p. Many components of magnetic field poduced fom individual J contibutions within the plates will cancel, esulting in educed stength cicula field lines suounding the plates [1]. We should expect the ceated field H p to be in phase with H J, but taking into account the geomety and the cuent motion within the plates. Then H p is diected in the opposite diection to H J, this is equivalent to 180 o phase change between H p and H J. - Bael Shaped CFA Fom the expeimental veification of D within lage cicula capacito plates, poducing a suounding magnetic field distibution, a evolutionay engineeing design of antennas has now been developed in which the poynting vecto S E H is diectly synthesized by sepaated E & H field stimulus within a vey small volume, these antennas ae called Cossed-Field Antennas (CFAs) which wee descibed by F. M. Kabbay, M. C. Hately and B. G. Stewat, one paticula CFA design is the bael-shaped CFA as shown in Fig.(4) [1]. Uppe E-plate Uppe D-plate Lowe D-plate Lowe E-plate Figue (4) Bael shaped CFA D-plates Lage cicula capacito plates when supplied with high voltage will poduce stong cicula magnetic field aound the plates though D H. E-plates Two lage cylindical plates of shot length but the same adius as the capacito plates ae positioned one above and one below the D-plates. When the cylindical plates ae diven by an F powe souce they poduce a high-fequency, E lines due to voltage diffeence between the plates. The powe fom the tansmitte is split oughly in half between the E-plates though suitable design consideation and delay aangements between the E and D plate voltage. adiation is then poduced though S E H and powe flows out to space as vetically polaized adio waves of intense powe density. - The Fist Model Dimension of CFA D 01

Jounal of Engineeing and Development, Vol. 10, No. 4, Decembe (006) ISSN 181-78 The fist model dimension of CFA as appea in the Novembe, 1989, issue is as shown in Fig.(5).

6 Jounal of Engineeing and Development, Vol. 10, No. 4, Decembe (006) ISSN The fist model dimension of CFA as appea in the Novembe, 1989, issue is as shown in Fig.(5). The E-plates has a cylindical shape of 100mm. in adius and 0mm. high. 40mm. sepaated between the uppe and lowe plates. The D-plates ae two discs of 100mm. adius sepaated by 80mm; each D-plate has a cente hole of 60mm. diamete. These holes ae only used fo incoming the feed wies. The distance between the uppe E-plate and the uppe D-plate is 80mm. same as lowes E-plate and lowe D-plate [1]. Figue (5) Fist model dimension of CFA -4 Wiing Polaity of the CFA The feedes of the E-plates is connected to the lowe end of the uppe E-plate and the uppe end of the lowe E-plate to be the cuent diection flow in the suface of the two cylindes as shown in Fig.(6). Feedes Figue (6) Wiing polaity fo E-plates 0

Jounal of Engineeing and Development, Vol. 10, No. 4, Decembe (006) ISSN 181-78 Similaly fo the two D-plates the feeding will be fom the intenal hole, as shown in Fig.(7).

7 Jounal of Engineeing and Development, Vol. 10, No. 4, Decembe (006) ISSN Similaly fo the two D-plates the feeding will be fom the intenal hole, as shown in Fig.(7). Feedes Figue (7) Wiing polaity fo D-plates -5 Matching Feed System Fo efficient powe tansmission the antenna chaacteistic should matched with the souce and the space also between space and the eceive, this is achieved by matching feed system [,4]. A matched feed system fo the CFA is impotant because: 1. A matched system with moe o less flat lines might avoid the citicism adiation fom the feed lines.. To obtain coect phasing; Hately confimed that the equied phasing between the plates and cylindes of the CFA is the 90 o, CQ magazine, August 1989, suggested a such phasing unit to give 90 o as shown in Fig.(8). Figue (8) Phasing unit F voltmete fo checking 50:50 powes split The complete matched feed system is shown in Fig.(9). 0

8 Jounal of Engineeing and Development, Vol. 10, No. 4, Decembe (006) ISSN To D-plates To E-plates Matching unit Matching unit Phasing unit 100 watt HF Tansceive Figue (9) Matched feed system. CFA Analysis To analyze the electic and magnetic field distibution we efe to the pinciple of dipole assumption which states that we have two point chages of equal magnitude and opposite sign, sepaated by a distance d in fee space as shown in Fig.(10) [5,6,7]. 1 P + Q θ d - Q θ 1 - = d cos(θ) Figue (10) CFA fields analysis The above figue will be consideed fo each E-plates and D-plates, fist we must find the electic field distibution poduced by these two chages by obtaining the potential field which equal fo this system: 04

9 Jounal of Engineeing and Development, Vol. 10, No. 4, Decembe (006) ISSN Q V Q and - 1 = d cos(θ), but d is vey small with espect to 1 and Qdcos( ) V. (8) 4 o Fo spheical coodinates system we obtain: Qd cos( ) a o Qd sin( ) 4 E o Qd 4 o E cos( ) a sin( ) a o a. (9) -1 The Magnetic Field Expession As in section () the D-plates will ceate the magnetic field (H), the expession fo the magnetic field (H) coming fom the two D-plates measued at a fa point. To find H, we can use eq.(9) and integate ove the whole chage distibution in the D-plates, eq.(9) becomes fo incemental element. The chage distibution ove the D-plates when supply it by sinusoidal cuent (I=I o sin(wt)), each of the suface elements will poduce a field towad an extenal point (P) as shown in Fig.(11). P P x θ Z ρ 0 ρ ρ 1 A Figue (11) Magnetic field analysis 05

10 Jounal of Engineeing and Development, Vol. 10, No. 4, Decembe (006) ISSN x dq de 4 (A ) a o cos( ) a Z a Z sin( ) a dq S ds S d d hee, we can neglect ρ because A>> ρ. Fom the cuent continuity law: dq = - I dt, when I = I o sin(wt) 1 I dt, S S 1 I I sin(wt ) dt o S o cos(wt ).. (10) S ws whee: S: is the total suface aea of the disc S = π (ρ 1 - ρ 0 ) But to calculate H only the z component is needed, and by tansfoming to cylindical coodinates we get: x dq de 4 o cos ( ) 1 a Z By integating fo ρ fom ρ o to ρ 1, and fo φ fom (φ = 0 o ) to (φ = π) then multiplying by ε o we get: x Io cos(wt ) D w D cos ( ) 1 a Z D x Io sin(wt ) cos ( ) 1 a Z... (11) t Let x I K o sin(wt ). Eq.(11) in spheical coodinates becomes: D K D t cos ( ) 1 [cos( ) a sin( ) a ] In CFA, H is obtained fom Maxwell equation eq.(4) component of D. D H and fom a θ cos ( ) 1 sin( ) 5x Io sin(wt ) H... (1) 06

11 Jounal of Engineeing and Development, Vol. 10, No. 4, Decembe (006) ISSN This is the mathematical expession in pola fom of the magnetic field in spheical coodinate it is depends on some paametes which can be modified to get optimum value of H φ. Figue (1) shows the pola diagam of the magnetic field intensity. Figue (1) Patten of the magnetic field of CFA - The Electic Field Expession The electic field is geneated fom the E-plates, to deive the mathematical expession of the electic field coming fom the two cylindes eq.(9) must be used as an incemental field coming fom only two chages then integate it ove the whole suface of the two cylindes. Figues (1-a) and (1-b) show the assumption to calculate the electic field at point (P). ( 1) a (A Z) a Z ( 1 ) (A Z) ( 1) (A Z) But hee ρ >> ρ 1 and A>> Z A 07

12 Jounal of Engineeing and Development, Vol. 10, No. 4, Decembe (006) ISSN P x Figue (1-a) Electical field analysis ρ P A Z 1 ρ ds dz Z o ρ 1 Figue (1-b) Electical field analysis x dq de 4 0 ( cos( ) a sin( ) a ) To poduce pointing vecto in making suface integal and consideing x as (Z 1 +Z o ): 1 (Z1 Z S E 0 0 ) sin( ) a diection, theefoe E will be mainly in a diection, by (Z1 Z0) I0 cos(wt )sin( )... (1) 4 w E 0 08

Jounal of Engineeing and Development, Vol. 10, No. 4, Decembe (006) ISSN 181-78 Figue (14) shows the pola diagam of electic field intensity.

13 Jounal of Engineeing and Development, Vol. 10, No. 4, Decembe (006) ISSN Figue (14) shows the pola diagam of electic field intensity. Figue (14) Patten of the electic field of CFA - Pointing Vecto Equation of CFA The pointing vecto can be obtained diectly by cossing E and H, which epesents the powe adiated fom the CFA pe unit aea as follow: S E H (Z1 Z ) I 5x I 0 0 o sin( ). cos ( ) 1sin( ) a 4 w S 0 5x(Z S 4 Z0) I0 1 sin ( ) cos ( ) 1 a 4 w0 Figue (15) shows the patten of the pointing vecto S. Figue (15) Patten of the Pointing vecto of CFA 09

14 Jounal of Engineeing and Development, Vol. 10, No. 4, Decembe (006) ISSN Conclusions and ecommendation 1. The CFA has special popeties among the fequency independent antennas due to the geneation of electomagnetic wave by sepaated electic field and magnetic field fom two independent souces, which is not appea in Log-peiodic antenna, Spial antenna, and othe types of fequency independent antennas.. Thee ae no dimension limitations in design fo the CFA compaing with the othe fequency independent antennas.. It is ecommended that the deivations in this pape can be veified with simulation o pactical model of CFA. 5. efeences 1. F. M., Kabbay, M. C., Hately, and B. G., Stewat, Maxwell s Equations and the Coss-Field-Antennas, Electonics and Wieless Wold, Vol. 95, Mach 1989, pp Edwad C. Jodan, Electomagnetic Wave and adiation Systems, Second Edition 1974, Pentice-Hall, INC., Englewood Cliffs, N.J.. C., Byan Wells, Electonic Wold & Wieless Wold, Novembe C., Byan Wells, Electonic Wold & Wieless Wold, Mach Matthew N. O. Sadiku, Elements of Electomagnetics, A Division of Halt inehat and Winston, Inc., William H. Hayt, Engineeing Electomagnetics, Fouth Edition, McGaw-Hill, Inc., Paul Loion, and Dale Cason, Electomagnetic Fields and Waves, Second Edition, W. H. Feeman and Company, New Yok,

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