ROCKET-SPACE DEVICE ENGINEERING AND INFORMATION SYSTEMS Vol. 4, Iss. 3, 2017, pp. 42 53 RADIO ENGINEERING AND SPACE COMMUNICATION Integrted Antenn for Second Genertion Emergency Rdio Becons of the COSPAS-SARSAT System S.N. Boyko, Cnd. Sci. (Physics nd Mthemtics), osnik2012@yndex.ru A rnch of ORKK - NII KP, Moscow, Russin Federtion A.V. Isev A rnch of ORKK - NII KP, Moscow, Russin Federtion D.S. Kosorukov A rnch of ORKK - NII KP, Moscow, Russin Federtion Yu.S. Yskin, Cnd. Sci. (Engineering) A rnch of ORKK - NII KP, Moscow, Russin Federtion Astrct. A uilt-in ntenn for distress econs of the second genertion for serch nd rescue COSPAS-SARSAT system tht consists of Huygens element in the form of comined hlf-wve frme (loop) nd dipole is proposed. The formtion of the rdition pttern in the crdioid form is chieved y specific excittion of the dipole nd loop. An engineering design methodology of the ntenns is developed nd the comprison of the results of numericl simultion with experimentl dt is presented. The performnce of the ntenn meets the requirements of COSPAS-SARSAT to the second genertion econs on frequency of 406 MHz. An exmple of ppliction of the developed ntenn in the personl distress econ with its plcing on the inner side of the side wll of the frme with the dimensions of 200 75 45 mm is given. The min dvntges of this ntenn re esy mnufcture, protection from externl mechnicl effects, nd low cost. Keywords: dipole-loop ntenns, crdioid pttern, hemisphericl rdition pttern, uilt-in ntenns
INTEGRATED ANTENNA FOR SECOND GENERATION EMERGENCY RADIO BEACONS 43 Introduction The interntionl serch nd rescue system COSPAS- SARSAT ws estlished in 1977 for the purpose of distress lerting nd the loction of personl rdio econs nd rdio econs instlled on wtercrft nd ircrft in the event of n emergency. Up to now, the system ws sed on low-orit stellite constelltion, nd the min type of ntenn for trnsmitting signl to stellite t frequency of 406 MHz ws monopole. The min direction of the development of the COSPAS-SARSAT system is currently the cretion of spce segment sed on the MEOSAR medium-orit stellites to crete uniform coverge of the entire visile hemisphere of the sky in ny prt of the gloe, which will llow continuous sptil nd temporl monitoring of the ctivted econ serch zone. As consequence, the min requirement for the ntenns of second-genertion econs is the formtion of hemisphericl (crdioid) rdition pttern (RP) with liner or circulr polriztion, the mximum of which is directed to the zenith. The design of ntenns with crdioid RP shpe for personl rdio econs proves to e quite chllenge, since the econs themselves must hve smll dimensions nd mss. The Expert Group of the COSPAS-SARSAT Committee considered the known types of ntenns (spirl, microstrip, plnr F-ntenns nd L-ntenns) with hemisphericl shpe of the rdition pttern nd cme to disppointing conclusion out the inpplicility of these ntenns in the personl rdio econs of the second genertion: either the dimensions nd mss exceed the permissile limits, or the efficiency of rdition is insufficient. Thus, there ws no vrint of the ntenn pplicle in the second-genertion personl rdio econs. The serch for solution to this difficult prolem y the employees of the NII KP reserch institute led to constructive version of the integrted ntenn for second-genertion econs, which hs cceptle dimensions, mss nd DN in the form of crdioid. This result is chieved due to the comintion of dipole nd shortened loop ntenn, which is prcticl implementtion of the Huygens element. The lgorithm of clculting the dipole-loop ntenn with the crdioid shpe of the rdition pttern is presented in the rticle, the stges of its design re descried in detil, nd the results of computer simultion re compred with the mesured chrcteristics of the ntenn model t frequency of 406 MHz. Algorithm for clculting n emedded ntenn for second genertion econs The ide of forming sphericl rdition pttern in the form of Huygens element ws descried in mny monogrphs, such s [1]. The Huygens element is n elementry source of unidirectionl rdition formed y orthogonl in-phse electric nd mgnetic dipoles. The field of the Huygens element in the fr zone is sphericl wve, nd the RP does not depend on the ngle φ, nd in ny plne ϕ = const is determined y the expression F( θ) = 1+ cosθ. The sic implementtion of such n ntenn, which hs loop ntenn with perimeter equl to the wvelength λ in free spce, is not pplicle in secondgenertion econs ecuse of the lrge dimensions. The pper [2] sets forth the theoreticl sis for the formtion of crdioid-type rdition pttern with dipole-loop pir provided tht the dimensions of ll the rditors re much smller thn the wvelength. In [3], design vrint of n ntenn for moile communiction with RP in the form of crdioid is proposed, which is comintion of n symmetric dipole nd n electriclly smll loop, energized in qudrture reltively to the dipole (ech rm). However, in [3] the mteril is illuminted riefly, s consequence the method for clculting dipole-loop ntenn with hlf-wve frme is not presented. The uthors of this rticle tried to fill this gp. The design of this ntenn ws tken y us s sis, in which the chnges necessry for this prticulr ppliction were mde. A schemtic digrm of the ntenn design is shown in Fig. 1,. A truncted loop with perimeter of λ /2 contins three continers, one of which is included in the center of the loop, nd two others - t the eginning of its two rms. The inclusion of cpcitnce C 1 in the ntinode of the voltge mkes it possile to shorten the loop with perimeter equl to the wvelength λ to loop with perimeter equl to hlf the wvelength [4], however, the input impednce of such frme t the operting frequency will e inductive. To compenste for the inductive component of the input impednce, the cpcitnces C 2 nd C 3 included t the input of the frme. The frme emitter in this form is prcticlly hlf-wve dipole with cpcitive lod, wound into loop, fed y current.
44 S.N. BOYKO, A.V. ISAEV, D.S. KOSORUKOV, YU.S. YASKIN Fig.1. Schemtic digrm of the ntenn () nd the shpe of the dipole-loop ntenn rdition pttern () In [3] it ws noted tht for the formtion of sphericl rdition pttern of n ntenn, the dimensions of ll rditors of which re much smller thn the wvelength, it is necessry to oserve the following conditions: 1) the centers of emission of the dipole nd the loop must coincide, while the mutul influence etween the emitters should e minimized; 2) the powers emitted y the dipole nd the loop must e equl to ech other; 3) the currents flowing in the dipole nd the loop must hve phse difference of 90. If these conditions re met, the ntenn will hve directionl digrm in the form of crdioid with mximum rdition in the direction of the rnch of the frme, energized with phse of + 90 reltive to the dipole, nd minimum rdition in the reverse direction (Fig. 1). Antenn consists of severl elements, nd its clcultion nd design is complex tsk, which must e divided into severl stges. We used the following lgorithm for designing such n ntenn: Step 1. The clcultion of n symmetric dipole on printed circuit ord is crried out seprtely; Step 2. The clcultion of hlf-wve loop on printed circuit ord is crried out seprtely; Step 3. A microstrip power divider is designed with lods in the output rms equl to the clculted resistnce of the dipole nd loop rdition, provided tht the powers of the signls entering the loop nd the dipole re equl; Step 4. Clcultion of the lncing trnsformer on lumped elements is crried out; Step 5. Clcultion of the ntenn ssemly; Step 6. The line-uilding-out network of the ntenn is clculted. Step 7. Optimiztion of the reltive positioning of the ntenn nd the rdio econ trnsceiver ord is crried out in order to minimize the effect of the ord on the form of the RP.
INTEGRATED ANTENNA FOR SECOND GENERATION EMERGENCY RADIO BEACONS 45 Fig.2. The electric circuit of the dipole-loop ntenn The electricl circuit of the comined ntenn is shown in Fig. 2. The digrm shows tht the dipole is connected directly to the power divider, nd the loop rms re energized with phse shift of +90 reltive to the dipole through lnced-unlnced trnsformer formed y the pirs of lumped elements L 1, C 7 nd C 6, L 2. In this cse, the shoulders of the loop re energized opposite in phse to ech other. The cpcitive L-section mtches the input impednce of the ntenn with 50- ohm pth. At the first stge of ntenn design, it is necessry to clculte the dimensions of n symmetricl dipole consisting of qurter-wve emitter nd coxil ground plne (counterweight), which re locted on one side of the printed circuit ord (Fig. 3). In this cse, the emitter is locted strictly long the longitudinl xis of the ord. On the sme side of the ord is power divider. At the next stge, loop for working frequency of 406 MHz is designed. The loop ntenn is mde in the form of strip on the ck side of the printed circuit ord long its externl contour so tht the dipole rditor is locted inside the frme on its xis (Fig. 3), which is due to the first condition for the formtion of the crdioid type RP ove. The perimeter of the frme is constructive prmeter tht is determined minly y the length of the dipole rditor nd the width of the ord, dictted lso y the first condition for the formtion of crdioid type RP. Vlues of cpcitnces С 1, С 2, С 3 re clculted y the long-line method pplied to the equivlent circuitry of the loop ntenn t the resonnt frequency (Fig. 4, ). The loop ntenn is replced y long line of two conductive strips of width w spced distnce, which is loded t the end y the cpcitnce C 1 nd the rdition resistnce. The power fed to the loop input is clculted using the resistnce trnsformtion formul long the trnsmission line [5]: (1) where Z w is the wve impednce of the trnsmission j line, z í = R p is the lod impednce, l is the ωc1 2π length of the trnsmission line, β = is the wvelength λ constnt of empty spce. The rdition resistnce of the loop R is found y P the formul [6]: 4 R = 197 Π ( p / λ), (2) p
46 S.N. BOYKO, A.V. ISAEV, D.S. KOSORUKOV, YU.S. YASKIN Fig.3. Antenn topology: top nd ottom sides of the ord Fig.4. Equivlent circuit of the loop ntenn (); dependence Zw on w () where P l is the perimeter of the loop. The wve impednce of the trnsmission line cn e determined from the expression for Z w two-wire trnsmission line [5]: z B = 2 276lg( 1 ( ) ) d + + d, (3) where d is the dimeter of the wire, ssuming tht the width of the conductive strip w is equl to twice the vlue of d, i.e. w= 2d (4) Reltion (4) is determined empiriclly, nmely y compring the vlues Z w clculted from formul (3) with the vlues otined with strict electrodynmic clcultions. The dependence of the wve resistnce of two-wire trnsmission line Z w on the mgnitude of w is shown in Fig. 4, the solid line is the grph z ( B ) clculted y formuls (3), (4), the points re w the clcultions of z B in the softwre pckge HFSS15 for the width of the strip w = 1.9 mm nd numer of vlues of the distnce etween the strips = {28 ; 38; 48;
INTEGRATED ANTENNA FOR SECOND GENERATION EMERGENCY RADIO BEACONS 47 58; 68} mm; It cn e seen tht the clcultion ccording to formul (3) ssuming (4) completely grees with the vlues of the wve impednce otined with strict electrodynmic clcultions. After reclcultion z í to the input of the loop y the formul (1), the nominl vlues of the elements C 1, C 2, C 3 re found from the condition tht the imginry prts of the totl resistnce of the loop re equl to zero: 1 1 Im{ z ( )} + 0 jωc + jωc = (5) 2 3 When the elements C re equl, the eqution hs two unknown prmeters: C2 = C3 = C nd C 1. This indictes tht the nominl vlue of one of the elements cn e specified, nd the second one is found from the solution of eqution (5). Figure 5 shows plot of C s function of C 1, which ws otined y numericlly solving eqution (5). This grph cn e used to select pir of mtching cpcitors { C, C }. 1 Clcultion of the power divider is crried out from the condition of equlity of powers rdited y the loop nd the dipole (the second condition for the formtion of crdioid type RP):, Fig.5. The clculted dependence of C on C1 or, (6) where nd I _ p re the effective vlues of the dipole current nd the loop t the connection points. The resistnce of the rdition of the loop R p is given y the previously given formul (2), nd the resistnce of the dipole rdition is [1]: 2 2 R = 80 π ( lä / λ) Ä, (7) where l Ä is the length of the dipole. Tking into ccount (2), (7) nd (6), we otin formul for the rtio of the currents t the points of connection of the dipole nd loop ntenns:. (8) When designing power divider, the reltion for power is used. Since the input power is proportionl to the squre of the current, the expression for the rtio of input powers is: 2 P âõ _ Ä I R _ Ä p m = = =. (9) Ð âõ _ ð I _ p R Ä The lignment of the loop rms with ports 2 nd 3 of the divider is performed using lnced-unlnced trnsformer, its rms re essentilly high-pss filter (HPF) nd low-pss filter (LPF), which in ddition to the phse-shifting circuit function lso ply the role of resistnce trnsformers [5]. The chrcteristic impednce Z P of length of long line equivlent to the stges of the LPF nd HPF, ensuring the trnsformtion of the loding resistnce R to the input resistnce R 0l is [7]: R Z R R R 2 L C = 2 = = (10) Π 0p 0p In ddition, the following condition must e met: f 0 2π 1 =, (11) LC where f 0 is the center frequency of the operting rnge. From the formuls (12) nd (13) we otin formuls for clculting the L nd C elements tht mke up the lnced-unlnced trnsformer: ZΠ L1 = L2 = 2π f, (12) C 1 = C =. 2π fz 6 7 0 0 Π (13) If the L nd C elements re equl in the rms of the lnced-unlnced trnsformer, the HPF specifies phse shift of minus 90 degrees, nd the LPF shifts the
48 S.N. BOYKO, A.V. ISAEV, D.S. KOSORUKOV, YU.S. YASKIN Fig.6. Topology of the microstrip power divider (); the dependence of the moduli of the trnsmission coefficients on the frequency () phse y plus 90 degrees. Thus, the third condition for the formtion of hemisphericl (crdioid) rdition pttern is met utomticlly. Clcultion of the dipole-loop ntenn As the mteril of the ntenn ord ws chosen FR-4 glss fier 1 mm thick with reltive permittivity ε r = 4.4. According to the clcultion performed with the softwre pckge HFSS15, the length of n symmetric virtor with resonnt frequency of 406 MHz for strip width of 5 mm ws 162 mm with counterweight of 100x40 (mm) 2. Tking into ccount the length of the symmetric dipole, the clculted perimeter of the loop ws P l = 366 mm with loop width = 38 mm nd loop length l = 164 mm. As result, the overll dimensions of the ntenn ord, tking into ccount the counterweight, were 260 mm (length) x 40 mm (width). For the selected width, the loop strip w = 1.9 mm t = 38 mm, the clculted vlue of the loop wve impednce clculted from formuls (3), (4) ws z B = 528.73 Ohm. For the dimensions of the symmetricl dipole nd the loop given ove, formuls (2), (7) nd (9) clculte the vlues of the rdition resistnce nd the power division coefficient: R = 37.5 Ohm, R = 12 Ohm, Ä p m = 0.32. As result, the power divider must divide the input power in the following rtios:, where is the power coming into ech shoulder of the loop. The power division is executed using microstrip lines. The topology of the power divider is shown in Fig. 6,. The loop is connected to the power divider through segments of identicl microstrip lines, nd the dipole is connected directly to the rekout of the power divider. Lods of the three outputs of the divider re the rdition resistnces of the loop R p (hlf of ech output of the divider connected to loop rm) nd the dipole R Ä. The criteri for the synthesis of the power divider were conditions (10), (11), nmely, the modulus of the trnsmission coefficient etween the divider input (port 4) nd the dipole connection point (port 1) is equl to s 14 = 6 db; The trnsmission coefficient modules etween the divider input nd the connection points of the loop rms (ports 2 nd 3) re equl to s24 = s34 = 4.3 db. The required power splitting ws chieved y selecting the width L2 nd the length L7 of two identicl microstrip lines in the rms of the power divider. As result of the synthesis, the following widths nd lengths of the intermedite trnsmission lines were otined: L2 = 0.01 mm, L7 = 38 mm. Due to the technicl impossiility to mnufcture divider rms 0.01 mm in width, it ws decided to increse the L2 vlue to physiclly relizle vlue of 0.5 mm. With this topology, the output impednce of port 1 is,
INTEGRATED ANTENNA FOR SECOND GENERATION EMERGENCY RADIO BEACONS 49 Fig.7. Clculted chrcteristics of the ntenn: - the modulus of the reflection coefficient t the ntenn input; - rdition pttern t resonnt frequency Fig.8. Dipole-frme ntenn model (); form of RP during opertionl position of the ntenn () R 0d = 200 Ohm, nd the output impednces of ports 2 nd 3 re R 0l = 72.5 ohms ech. For these vlues of lod resistnces, the necessry power division is provided (the clculted dependences of the trnsmission coefficient moduli on frequency re shown in Fig. 6 ), ut it ecomes necessry to mtch the rdition resistnce of the dipole nd the loop with the ove-mentioned resistnces of outputs (ports) of the power divider. The mtching of the dipole with port 1 of the divider ws chieved y introducing step trnsition with width L8 = 2 mm nd length L3 = 4 mm. The mtching of the loop with ports 2 nd 3 of the power divider is crried out using mtching-lncing trnsformer. The nominl vlues of the lumped elements of the loop trnsformer re clculted y the formuls (10) - (13) for the lod resistnce R=R Σl /2 = 6 Ohm, clculted y formul (1) of the input resistnce of the loop, R 0l =72.5 Ohm, were: L 1 =L 2 = 4.7nH, C 6 =C 7 =32.6 pf. Clcultion of the input impednce of the ntenn ssemly (dipole + loop with lnced-unlnced trnsformer + power divider) ws crried out in the softwre pckge HFSS15. The clculted vlue of the z 8 6 input impednce ws âõ = + j Ohm. Since the input impednce hs low vlue of the ctive component nd non-zero vlue of the inductive component, mtching trnsformer is needed to mtch the ntenn input to the 50-ohm pth. In our cse, it ws implemented in the form of L-shped mtching circuit, consisting of seril nd prllel cpcitnces. The clcultion of these cpcitnces ws crried out ccording to the method descried in [8], [9]. As result, the cpcitnce vlues were: C 4 =15 pf, C 5 = 7.5 pf. The clculted reflection coefficient s 11 t the ntenn input nd its rdition pttern re shown in Fig. 7 () nd 7 (), respectively. The modulus of the reflection coefficient t the resonnt frequency is -26 db, which
50 S.N. BOYKO, A.V. ISAEV, D.S. KOSORUKOV, YU.S. YASKIN Fig.9. Photo of the RFxpertRFX2 scnner () nd the type of PR of the dipole-frme ntenn mesured on the scnner () econ csing, the counterweight of the dipole ws ent t n ngle of 90 degrees to the ord in such wy tht the longitudinl dimension of the ord with the topology of the ntenn does not exceed 180 mm (the fold line is shown in Fig. 3). In the simultion, it ws determined tht with such counterweight configurtion, the chnges in the shpe of the rdition pttern re negligile nd cn e compensted for y smll chnge in the cpcitnces C 6, C 7 in the frme mtching circuits. Fig. 10. The experimentl frequency dependence of the VSWR t the ntenn input corresponds to the input VSWR = 1.1. The K u vlue of the ntenn t the mximum of the RP ws 2.8 db. It cn e seen from Fig. 7 () tht in the lower prt of the digrm there is smll prsitic rdition, which is connected with the presence of counterweight to the ntenn, which is undesirle for the frme emitter. On this the ntenn design process could e considered complete, ut the resulting longitudinl ntenn size (260 mm) is clerly lrge nd does not llow it to fit into the dimensions of the personl rdio econ. Therefore, in order to incorporte the ntenn into the The results of mesurements of the prototype of the ntenn nd comprison with the clculted dt To test the proposed technique for designing dipole-loop ntenn, model ws mde, consisting of n ntenn ord nd counterweight connected to it. The ntenn ord ws mde on mteril of FR-4 (ε r = 4,4) with thickness of 1 mm, the counterweight ws mde of tinned sheet 0.2 mm thick. The topology of the ntenn ord is mde ccording to the clcultions crried out y the lgorithm descried ove. The mtching cpcitors C1, C2, C 3 were selected ccording to the chrt in Fig. 5 nd re equl to: C2 = C3 = 1.8 pf, C 1 = 0.5 pf (dotted mrkers in Figure 5). Other options re lso possile C1, C2, C 3 ccording to the chrt in Fig. 5, for exmple: C 1 = 0.25 pf, C 2 = C 3 = 3 pf or C 1 = 1 pf, C 2 = C 3 = 0.9 pf.- The cpcitors in the lnced-unlnced trnsformer re vrile to fine-tune the phse difference in the loop
INTEGRATED ANTENNA FOR SECOND GENERATION EMERGENCY RADIO BEACONS 51 Fig.11. Mesured in the nechoic chmer (solid lines) nd clculted (dotted lines) ntenn RP: - for φ = 0, - for φ = 90 Fig.12. Dipole-frme ntenn in the econ housing rms. The photogrph of the ntenn lyout is shown in Fig. 8 (), the clculted three-dimensionl RP in the opertionl position of the ntenn is shown in Fig. 8 (). An dditionl (second) ending of the ntenn s counterweight t n ngle of 90 degrees is due to the need to incorporte the ntenn into the projected ody of the second genertion personl rdio econ. The ntenns re locted on three nrrow sides of rectngle with dimensions (180x65x40) mm 3. The finl testing nd tuning of the ntenn ws crried out y the form of RP with the RFxpertRFX2 scnner y EMScn, which llows to determine the shpe of the ntenn rdition pttern in rel time directly t the workplce [10]. This device mesures the ner field of the ntenn nd reclcultes it into fr zone field with RP disply in three-dimensionl form with sufficient ccurcy for tuning the ntenn. The comined ntenn ws plced on the working surfce of the scnner y
52 S.N. BOYKO, A.V. ISAEV, D.S. KOSORUKOV, YU.S. YASKIN the plne of the ord (counterweight up), then smll djustment of the cpcitnces C 6, C 7 ws mde in the lnced-unlnced trnsformer to chieve crdioid shpe of the RP. A photogrph of the scnner nd the rdition pttern of the ntenn mesured with it re shown in Fig. 9, nd 9,, respectively. Then, the VSWR nd PR of the scnner-tuned ntenn were mesured in the fr zone in n nechoic chmer. The mesured dependence of the VSWR t the ntenn input on the frequency is shown in Fig. 10. It follows from the figure tht t the operting frequency of 406 MHz the vlue of the VSWR is 1.1, which fully coincides with the clculted vlue. The RP of the ntenn in the upper hemisphere t φ=0 nd 90, mesured in n nechoic chmer, re shown in Fig. 11 () nd 11 (), respectively. Also in these figures, the dshed line shows the results of clculting the RP in the softwre pckge HFSS15. The mesured vlue of gin t the mximum of the RP is 2.5 db, nd the clculted vlue is 2.8 db. From the ove nlysis it cn e seen tht good rte of coincidence of the clculted nd experimentl dt hs een chieved. It should e noted tht ccording to the requirements of the COSPAS-SARSAT stndrd on the secondgenertion rdio econs in 90% of the rdition pttern, the ntenn gin should e in the rnge from minus 7 to plus 4 db for elevtion ngles from 15 to 90. The otined experimentl vlues of gin (θ) stisfy this requirement: the vlues of gin vry in the rnge from minus 6 db to plus 2.5 db in given rnge of ngles (see Figure 11). When the ntenn is plced inside the rdio econ its ord is locted long one of its long side wlls, nd the counterweight is long the djcent short side wll, with smll overlpping with the opposite long wll (Fig. 12). Since there is trnsmitter-receiver ord perpendiculr to the ntenn ord in the rdio econ, it ws necessry to mesure its effect on the chrcteristics of the ntenn. Therefore, computer simultion nd experiments determined the est position of the trnsmitter-receiver ord with respect to the ntenn ord for the opertion of the ntenn, in which the shpe of the RP is retined (Fig. 8, ). The dipole-loop ntenn hs severl dvntges s uilt-in ntenn. Firstly, ecuse of the lck of rdition in the lower hemisphere, it mkes it possile to reduce the negtive influence of the underlying surfce on the DN shpe. Secondly, it is protected from externl mechnicl influences y the rdio econ housing. Thirdly, it hs simple mnufcturing technology nd low cost. Conclusion In this rticle: A dipole-frme ntenn is proposed for use in the new (second) genertion of the COSPAS-SARSAT personl rescue econ. A detiled description of the design stges of such n ntenn is given nd n engineering procedure for its clcultion is proposed. The input stnding wve rtio of the ntenn (SWR = 1.1) nd the hemisphericl RP of the ntenn t frequency of 406 MHz with gin = 2.5 db were clculted experimentlly. By chnging the configurtion of the counterweight, the ntenn is emedded in the rdio econ with dimensions (200 75 45) mm 3. The influence fctor of the trnsmitter ord on the form of the ntenn RP is tken into ccount. Its est position in the rdio econ csing is chosen. References 1. Frdin A.Z. Antenno-fidernye ustroystv [Antenn feeder devices]. Moscow, Svyz, 1977. (in Russin) 2. Vendik O.G., Pkhomov I.A. Electric- nd mgnetic-field strengths in the Fresnel zone of microrditor formed y n electric nd mgnetic dipole. Technicl Physics, 2005, Vol. 50, No. 11, pp. 1479 1484. 3. Turlchuk P.A., Kholodnyk D.V., Vendik O.G. Novel low-profile ntenn with hemisphericl coverge suitle for wireless nd moile communictions. 2008 Loughorough Antenns & Propgtion Conference. 17-18 Mrch 2008, Loughorough, UK, pp. 337 340. 4. Turkin N. Elektricheski ukorochenny rmochny ntenn [Electriclly shortened frme ntenn]. Rdio [Rdio]. 2002, No. 12, pp. 58 59. (in Russin) 5. Szonov D.М. Antenny i ustroystv SVCh [Microwve ntenns nd devices]. Moscow, Vyssh. shk., 1988, 432 p. (in Russin) 6. Rotkhmmel K. Entsiklopediy ntenn. [Encyclopedi out ntenns]. Moscow, DMK Press, 2011, 814 p. (in Russin)
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