A Flexible Transmission Line Model For Series-line Antennas Array Design M. Abri, N. Boukli-hacene, F. T. Bendimerad and M.

Transcription

1 69 VOL.5 NO. MARCH A Fexibe Transmission Line Mode For Series-ine Antennas Array Design M. Abri, N. Bouki-acene, F. T. Bendimerad and M. Bousaa Laboratoire de teecommunications, departement de teecommunications Facute des Sciences de Ingenieur, Universite Abou-Bekr Bekaïd -Temcen Bp, pôe cetouane, temcen- Ageria E-mai: abrim@yaoo.fr Abstract- In tis paper, a transmission ine mode is used to design series-fed antennas arrays over a band of frequencies for sateite communications. Te transmission ine mode is simpe, precise and aowing taking into account te woe geometrica, eectric and tecnoogica caracteristics of te antennas arrays. To vaidate tis ast, te obtained simuation resuts are compared wit tose obtained by te moment s metod (MoM). Using tis transmission ine approac te resonant frequency, input impedance, return oss can be determined simutaneousy. Agreements between transmission ine mode data and te moment s metods resuts were acieved. Index Terms- Anaysis, microstrip antennas, array, transmission ine mode, Moment s metod. I. INTRODUCTION Microstrip antennas ave been widey used in modern appications and became a significant matter of researc in te teoretica and practica eectromagnetic fied. Tey are we-known for teir good desirabe pysica caracteristics suc as teir igtness, teir ow cost and teir sma overa dimensions, easy of instaation and its aerodynamic profie. For a tese reasons, tey are suitabe for many appication and are used in many communication systems suc as wireess area network (LAN), mobie and sets, radars, etc. Many researcers studied teir basic caracteristics and great efforts were aso devoted to teir determination (resonant frequency, te band-widt, radiation... etc) by using teoretica modes. Tese modes can be cassified into tree groups. Te transmission ine mode is a simpe mode due to its assumptions. Tis eads to a set of inear equations wit ow dimension. In te cavity mode, wic converts te open antenna probem into a cosed one, tis dimension increases. Finay, te integra equation mode soves te Maxwe equations directy. Te equations are ard to compute and te dimension of te set is very arge. Te utiity of any soution, owever, depends on te accuracy of te resuts, as we as on te simpicity of te metod. Microstrip antennas tat operate as a singe eement usuay ave a reativey arge af power beamwidt, ow gain and ow radiation efficiency. In order to improve tese parameters, microstrip antennas are used in Series-fed array configuration to improve te gain and range of te radiating structure. Tis configuration offers a very convenient form of array fabrication because bot te feed network and te radiating eements can be made potoitograpicay, witout any need for sodering to te eements []. In tis paper, a transmission ine mode is presented for te anaysis of antennas array operating in and 4.8 GHz for sateites communications. A rigorous metod wic is te moment s metod was adopted to sow te vaidity of te suggested mode by comparing te resuts of te return osses, input pase as we as te input impedance ocus. A comparison of te resuts sowed te vaidity of te proposed mode. IJMOT ISRAMT

2 VOL.5 NO. MARCH 7 Te numericay efficient procedure presented in tis paper is empoyed to anayze two different geometries and teir resuts are presented. A comparison of te resuts produced by te fina mode wit te moment s metod data sowed te vaidity of te proposed mode. Tis aows te anaysis of very arge arrays even on rater sma computer. II. TRANSMISSION LINE MODEL ANALYSIS In tis section, an equivaent circuit mode for te proposed antenna is deveoped. Tis mode is capabe of predicting te sot radiation conductance and te antenna input impedance near resonance. Tis approac provides very epfu insigt as to ow tis antenna and its feed network operate. As mentioned before, tis mode is aso needed to find a proper matcing network for te antenna. Te antenna as a pysica structure derived from a microstrip transmission ine. In tis mode, te microstrip antenna is modeed as a engt of transmission ine of caracteristic impedance Z and propagation constant γα+jβ. Te fieds vary aong te engt of te patc, witc is usuay a af-wave engt, and remains constant across te widt. Radiation occurs mainy from te fringing fieds at te open ends as sown in Fig. [-]. Radiating sots III. INPUT IMPEDANCE Te effect of radiation is accounted for by te radiation and admittance caed sef admittance Ys attaced to te open ends of te transmission ine. Te transmission ine mode represents te antenna by a ine section wic finises by an admittance Y s on te eve of its two ends. An equivaent eectric representation of tis mode is scematicay sown in Fig. [4]. Fig.. Equivaent circuit of van de capee Y s stands for te equivaent admittance of te main sits, Y m teir mutua admittance, Y c is te caracteristic impedance of te transmission ine and γ p is te compex propagation constant in tis ine. Tis is a tree-port mode wic depends on te tecnique used for te antenna suppy. If we consider tat te antenna is fed at its extremity by a microstrip ine, and if we negect te mutua couping between te two radiating sots, te equivaent mode of te microstrip source can be represented by a transmission ine section wit te same caracteristics, terminated at bot ends by a radiation admittance Y s of conductance G and susceptance B. A genera representation is sown in Fig.. L I L I Dieectric substrate Ground pane L L L 5 Ω V() ~ V R G r jb Y c, γ p R G r jb V Fig.. eement Equivaent network of microstrip radiating Fig.. Rectanguar microstrip antenna Due to te fringing fieds aong te radiating edges of te antenna tere is a ine extension associated wit te patc, wic is given by te formua [5]: IJMOT ISRAMT

3 7 VOL.5 NO. MARCH w ε eff.. 4 εeff. 58 w +. 8 () G λ B λ 4 ( k ) [. 66n( k ) ] (7) Te effective dieectric constant ε eff due to te air dieectric boundary is given by [6]: ε + ε ε r + r eff + () w ere: and λ π k. λ, λ is te free space waveengt Te resonant frequency can be estimated by using te formua [7]: fr ere : µ ε ( L + L) εeff µ : Permeabiity of free space ε o : Permittivity of free space L : Pine extension ε eff : Effective dieectric constant () Te antenna effective widt is given by te foowing formua : v (4) fr µ ε + fr + Te rea engt of te antenna can be given and it is given by te foowing formua: L fr eff µ ε L (5) en te antenna resonates (L~ λg/), te tota admittance becomes rea and is cacuated using te formua [8]: Y G +jb (6) Because te sots are identica, we ave: Y Y ; G G ; B B Te conductance of a singe sot can aso be obtained by using te expression fied derivative from mode cavity. In genera, te conductance is defined by: P G rad (8) V By using te eectric fied one can cacuate te radiated power: V P rad πη K sin cos θ π sin θdθ cos θ (9) Te sef conductance can be cacuated using te foowing expressions: I G () π ere I is te integra defined by: Te expressions of G and B are given by te reations beow: IJMOT ISRAMT

4 7 VOL.5 NO. MARCH k w θ π sin cos I sin θ dθ cos θ () Y in Y +Y G () Z in Yin Rin () G However te above equation for input impedance does not take into consideration te mutua couping between te radiating sots, so we can redefine te input resistance: R in ( G ± G ) (4) ere: - G : Mutua conductance - G : Sef conductance. - (+) : Odd resonant modes - (-) : Even resonant modes Te mutua conductance is defined in term of fied by te foowing expression: G Re s E H ds V (5) Zc π ε reff.. n n + eff 4 Te input resistance is given by: Rin cos g B sin Yc ( G + G ) G ( ) + B β L + sin ( β L) ( β L) g Y c IV. SERIES FED ARRAY g (7) (8) One is interested in te case of a inear array fed in series by a caracteristic ine microruban of impedance Zc as presented by Fig.. (a). To cacuate te input impedance of te printed antennas array, one supposes to expoit te eectric mode are equivaent of eac aeria eement estabised previousy to ead to a compete eectric modeing of te entire array. Te equivaent diagram of tis ast is sown in te foowing Fig.. (b). Te mutua conductance G is cacuated using te foowing expression: L G π k w sin cos θ π J cos θ ( k L sin θ) sin θ dθ (6) 5 Ω V() ~ N- N- N (a) ere: J is te Besse function of te first kind. Te impedance caracteristic is given by. Fig.. (b) (a) Te mask ayout for te antennas array (b) Equivaent circuit of te antennas array IJMOT ISRAMT

5 7 VOL.5 NO. MARCH w ε eff.. 4 εeff. 58 w +. 8 () G λ B λ 4 ( k ) [. 66n( k ) ] (7) Te effective dieectric constant ε eff due to te air dieectric boundary is given by [6]: ε + ε ε r + r eff + () w ere: and λ π k. λ, λ is te free space waveengt Te resonant frequency can be estimated by using te formua [7]: fr ere : µ ε ( L + L) εeff µ : Permeabiity of free space ε o : Permittivity of free space L : Pine extension ε eff : Effective dieectric constant () Te antenna effective widt is given by te foowing formua : v (4) fr µ ε + fr + Te rea engt of te antenna can be given and it is given by te foowing formua: L fr eff µ ε L (5) en te antenna resonates (L~ λg/), te tota admittance becomes rea and is cacuated using te formua [8]: Y G +jb (6) Because te sots are identica, we ave: Y Y ; G G ; B B Te conductance of a singe sot can aso be obtained by using te expression fied derivative from mode cavity. In genera, te conductance is defined by: P G rad (8) V By using te eectric fied one can cacuate te radiated power: V P rad πη K sin cos θ π sin θdθ cos θ (9) Te sef conductance can be cacuated using te foowing expressions: I G () π ere I is te integra defined by: Te expressions of G and B are given by te reations beow: IJMOT ISRAMT

6 74 VOL.5 NO. MARCH According to te figure above, one notices tat te transmission ine mode of te of is cose to te axis 5 Om, wie te moments metod curve is one can far. B. 4.8 GHz antennas array In tis section, oter geometry is anayzed by using te metod proposed in tis paper. Te permittivity and te substrate tickness are.55 and.59 mm respectivey and te operation frequency is 4.8 GHz. A probe of 5 Om is empoy to feed te antennas array. Fig.8 presents te mask ayout for te antennas array presenting resonance at 4.8 GHz. 5 Om Fig m m Antennas array arcitecture 7.5 m m Te input computed return osses S of te antennas array functioning at 4.8 GHz as been reported in Fig.9. According to te figure above, even toug tere is a sift in te resonant frequency, te transmission ine mode tracks te return oss profie predicted by te moment metod very cosey. Te sma sift in te resonant frequency can be attributed to a faiure to consider te discintinuty between te antennas and te feed ines..4 m m According to te figure above, even toug tere is a sift in te resonant frequency, te transmission ine mode tracks te return oss profie predicted by te moment metod very cosey. Te sma sift in te resonant frequency can be attributed to a faiure to consider te discintinuty between te antennas and te feed ines. Te input pase of return oss of te antennas array is sow in figure. Pase [ ] 5 Fig Frequency [GHz] Computed pase of return TLM MoM According to te figure above, one notices tat te modes ave te same pace in spite of te unduations presented by te moment s metod. TLM MoM S db(s(,)) [db] TLM MoM Frequency [GHz] Fig. 9. Computed return osses Fig.. Smit's cart of te input impedance return osses. Frequency points given by start 4. GHz, stop 6. GHz. IJMOT ISRAMT

7 75 VOL.5 NO. MARCH Te input impedance or te antenna as been cacuated over a frequency range of GHz. It can be seen from Figure tat te comparison for te input impedance between transmission ine mode and te moment metod resuts are in good agreement. One notices tat te resonant frequency is very cose to te axis of 5 Om. VI. CONCLUSION A fexibe and computation-efficient transmission ine mode is deveoped to anayse te antennas array. Te resuts so far sow tat te transmission ine mode can be successfuy used to predict te input caracteristic of te antennas array over wide band frequencies. Even toug te mode is conceptuay simpe, it sti produces accurate resuts in a reativey sort period of computing time. Te resuts obtained igigted an exceent agreement between te transmission ine mode and te moment s metod. REFERENCES [] M. Abri,N. Bouki-acene,F. T. Bendimerad and E. Cambiaggio, Design of a Dua Band Ring Printed Antennas Array, Microwave journa, vo. 49, no. 5, pp. 8-, May. 6. [] A. G. Derneryd, Lineary Poarized Microstrip Antennas, IEEE trans, AP. pp , November 976. [] A. G. Derneryd, A Teoretica Investigation of te Rectanguar Microstrip Antenna, IEEE trans, AP., Vo. 6, N 4, pp. 5-55, Juy 978. [4] H. Pues, A. Van de capee, Accurate Transmission Line Mode for te Rectanguar Microstrip Antenna, IEE Microwave, Antennas and propagation proceedings, vo., Pt. H, no 6, pp. 4-4, Dec 984. [5] C.A. Baanis, Antenna Teory Anaysis and Design, Second Edition. United States of America. Jon iey & Sons 997, p74. [6] P. Bartia, K. V. S. Rao, R. S. Tomar, Miimeterwave Microstrip and Printed Antennas. Norwood: Artec House 99, pp.. [7] I. J. Ba, P. Bartia, Microstrip Antennas, Norwood: Artec House Dedam, MA,98. [8] E. O. Hammerstad, Equations of Microstrip Circuit Design, Proc. Fift European Microwave conf., sep. 975, pp IJMOT ISRAMT