A Novel Model for the Input Impedance of Coax- Fed Circular Microstrip Patch Antennas for CAD

Transcription

1 Damascus Univ. Jounal Vol. -No. 5 Abboud A Novel Model o the Input Impedance o Coax- Fed Cicula Micostip Patch Antennas o CAD Abstact Faiz Abboud We pesent a Novel model o the input impedance o a cicula micostip patch antenna. This model is well suited o compute aided design CAD. It is based on classical methods: a the cavity model detemining the equency and the input esistance at esonance, b a new eective dielectic constant, e o a cicula micostip patch antenna to take into account the inluence o the inging ield at the edges o the cicula patch antenna and c the esonant paallel LC cicuit with an inductive eactance. This model is valid o electically thin and thick substate coveing the entie ange o dielectic constants. The theoetical esults ae in good ageement with the expeimental data. Faculty o Mechanical & Electical Eng. Damascus Univesity, Syia. 8

2 A Novel Model o the Input Impedance o Coax-Fed Cicula Micostip Patch Antennas o CAD - Intoduction : igoous methods developed by a numbe o authos [-3] enable computation o the input impedance and the adiation patten o cicula micostip patch antenna with good pecision. Howeve, these methods involve complex analysis o physical phenomena, which oten take consideable computation time and do not easily yield the equivalent cicuit. Sometimes, less accuate esults suice, and can be obtained much aste with the help o simple methods such as the cavity model [-6], which adequately descibe the esonant equency, input impedance, bandwidth and adiation patten by a simple design equation. An analytical expession is given hee o the input impedance o a cicula micostip patch antenna excited by a coaxial pobe Fig. a using the cavity model and the equivalent esonant cicuits. It shows explicitly the dependence o the input impedance on the chaacteistic paametes o a patch antenna, and is valid o electically thin and thick substates. - Analysis : The cavity model is a bidimensional model that can be applied to patches whose geometies ae speciied simply by cuvilinea othogonal coodinate systems cicula, ectangula, etc... It is possible to conside eithe the dominant mode o the complete spectum o modes. The cicula micostip patch antenna can be consideed in the undamental mode, modeled by a simple esonant paallel LC cicuit Fig.b. To take the coax-eed pobe into account, it is necessay to modiy the input impedance by an inductive tem [ 7 ] : 377 H c L Ln c d Whee c o is the velocity o light in vacuum and d o is the diamete o the pobe. All expession pesented heeate ae valid o the dominant mode. The input impedance is then obtained as [] : 8

3 Damascus Univ. Jounal Vol. -No. 5 Abboud 83 J Z T T L T Whee T is the quality acto associated with system losses and is the input esistance at the esonance the esistance o the L - C cicuit. T includes adiation losses, dielectic losses D and conducto losses C [] : D C T 3 - has the ollowing om om the expession by Bahl [8,eq.3-7, eq.3-] : / 3 3 / F H a Whee F is given by the ollowing expession with the help o the development o Bessel unction J [9] : dt t J J F F 6 The dielectic losses have been obtained by [] : /tan D 7 Whee tanc is the dielectic loss tangent. 3 The losses in the conducto can be obtained by [-] : /, / µ H s s c 8 s is the skin depth whee is the conductivity o the conducto and µ is the pemeability o the dielectic. is the esonant esistance o the esonant paallel -L-C cicuit [,eq.] which is given by : a K J K J G 9

4 A Novel Model o the Input Impedance o Coax-Fed Cicula Micostip Patch Antennas o CAD Whee is the eed position eeed to the cente o the disc o adius a. K is the popagation constant. The undamental mode coesponds to Ka equal to as.88 and G T includes the conductances due to ohmic, dielectic and adiation losses : G T G GD GC The conductance due to adiation losses is given by [] :.39 G µ H The conductance due to dielectic losses is given by [,eq.8] :.39 tan GD µ H 3 The conductance due to ohmic losses is given by [,eq.9] : 3 /.39 µ GC 3 H The Bessel unction o ode one, J, is expanded in tems o polynomial [9], o 3 < t < 3 : 6 t t / t / t / 3 J t t / t / 3 An impoved omulation is deived o the esonant equency [3] o the TM modes in a cicula micostip antenna given by : nm c, nm 5 a e, e Whee nm is the mth zeo o the deivative o the Bessel unction o ode n, the dominant mode is the TM n m. Fo this mode,.88. c is the velocity o light in vacuum, ae is the eective adius o cicula patch deined though 6, and, e is deined as :,, e 6, 8

5 Damascus Univ. Jounal Vol. -No. 5 Abboud The tem, e is intoduced to take into account the eect o in combination with the amic dielectic constant [], to impove the model., e is deduced as 6 to yield the esonant equency as an aveage o the equencies esulting om 5 by substituting and, sepaately in place o, e., is a unction o the static main and static inging capacitances and the mode o esonance as given by [] : C, 7 C C can be witten [,eq.6] as: C C, Ce, 8 C, is the amic main capacitance o the dominant mode TM elated to the static main capacitance C, stat o the patch without consideing the inging ield. It is given by [,eq.] : C,.355 C, stat 9 Ce, epesents the amic inging capacitance o the dominant mode given by [,eq.5] : C e, Ce, stat A compaatively ecent omulation o the static capacitance o a cicula micostip disc obtained by Wheele [5] is applied to calculate C, stat and C e, stat since the esult in [5] is much impoved ove the ealie ones [], [6], [7], [8] and is widely applicable to the entie ange o dielectic constants and to all H / a values o the antenna. The expession o the capacitance given by Wheele [,eq.5] can be moe explicitly witten as: a C q H T 85

6 A Novel Model o the Input Impedance o Coax-Fed Cicula Micostip Patch Antennas o CAD Whee: q u v uv u a H ln p v t 3t 8 a g H t a H.3a H P.9 a H g.6 a H. 9 H a 6 7 In,the ist tem is equal to the static main capacitance stat and the tem q aises due to the inging ield at the edge o the disc capacito. The inging capacitance C e, stat thus is deined as: Ce, stat C, stat q 8 Whee: a C, stat 9 H Equation 7 also deines the eective adius o the micostip disc a e a q 3 esults: In this section computations concening the undamental mode m,n ae pesented and compaed with measuements and pevious computations. table I detail the expeimental esults o esonance equency. In table II We pesent computed values o the esonant equency o thin and thick substates. We obseve that ou esults all among those calculated by othe methods, and ae close to measued values in most cases. C, 86

7 Damascus Univ. Jounal Vol. -No. 5 Abboud The ageement between ou theoetical and expeimental values o the esonant equency is typically within.5 % o values o electical thickness H /.. Fig. shows the input impedance o a thinne patch substate opeating at about.9ghz. The esults computed by Babu [] and the measuements o Kumpaset [ 5] ae epoted. Fig.3 pesents the input impedance o a thicke substate opeating about 3.6GHz. Ou computations ae compaed with the computed and measuements o Lo [ 6 ]. The paamete, e intoduced in the pesent theoy thus becomes signiicant o all lage and small values o a H. Conclusion: We have developed a simple model yielding the input impedance o a pobe-ed cicula micostip patch antenna, which gives esults in accodance with expeiment. This model can be used successully in compute An impoved analytical omulation based on a esonato model is pesented aided design CAD o cicula micostip patch antenna aays. 87

8 A Novel Model o the Input Impedance o Coax-Fed Cicula Micostip Patch Antennas o CAD eeences [] Losada. V., Boix..., Hono. M., esonant modes o cicula micostip patches in multilayeed substates, IEEE Tans., Vol.MTT- 7,pp.88-97, 999. [] Mosig. J.., and Gadiol. F.E., Geneal integal equation omulation o micostip antennas and scattes, IEE Poceeding, Vol.3, pp.-3, 985. [3] Poza. D.M., PCAAD 3., Pesonal compute aided antenna design, Antenna design associated, Inc [] Abboud. F., Damiano. J.P., and Papienik. A., New detemination o esonant equency o cicula disc micostip antenna: Application to thick substate,electon.lettes,vol.,no.7,pp.-6, 988. [5] Gag.., Bhatia. P., Bahl. I.J., Ittipiboon., Micostip antenna design handbook, Ed. Atech house, Dedham MA,. [6] Poza. D.M., Micowave Engineeing, John Wiley & Son, NY, USA, nd edn 998. [7] Deshpande. M.D., and Bailey., Input impedance o micostip antenna, IEEE Tans, Vol.AP-3, pp.65-65, 98. [8] Bahl. I.J., and Bhatia. P., Micostip antennas, Dedham, MA, Atech House, 98. [9] Abamowitz. M., and Stegum. I.A., Handbook o mathematical unction, Nat. Bu. Stand. Appl. Math. Se. 55, Washington, Dc, 96. [] Long. S.A., Shen. L.C., and Moel. P.B., Theoy o the ciculadisc pinted-cicuit antenna, Inst.Elec.Eng. Poc., Vol.5, pt.h,n., pp.95-98, 978. [] Deneyd. A.G., Micostip disc antenna coves multiple equencies, Micowave J., pp , May 978. [] Deneyd. A.G., Analysis o micostip-disk antenna element, IEEE Tans., Vol.AP-7, pp.66-66, sept.979. [3] Abboud. F., A new model o calculating esonant equency o cicula micostip antennas with and without ai gaps,damascus Univesity Jounal., to be published. [] WOLFF I., KNOPPIK N.," ectangula and Cicula Micostip Disk Capacitos and esonatos," IEEE Tans., Vol.MTT-, No.,pp ,97 [5] WHEELE H.A.," A Simple Fomula o the Capacitance o a Disc on Dielectic on a Plane," IEEE Tans., Vol.MTT-3,pp.5-5, 98 [6] CHEW W.C., KONG J.A.," Eects o Finging Field on the Capacitance o Cicula Micostip Disk," IEEE Tans.,Vol.MTT- 8,No.,pp.9-,98 88

9 Damascus Univ. Jounal Vol. -No. 5 Abboud [7] Shen. L.S.,Long. S.A., Alleding. M.., and Walton. M. D.," esonant equency o a cicula disc, pinted-cicuit antenna," IEEE Tans.,Vol.AP-5,pp ,977. [8] LEONG M.S., ET AL.," Detemination o Cicula Micostip Disc by Noble's Vaitional Method," IEE Poceeding, Vol.8,pt.H, pp.36-3, 98 [9] Itoh. T., and Mitta.., Analysis o micostip disk esonato, Ach Eleck. Ubetagung, Vol.7, N., pp.56-58, 973 [] Vema A.K., and Nasimuddin.," Analysis o cicula micostip patch antenna as an equivalent ectangula micostip patch antenna on iso/anisotopic thick substate," IEE Poc-micowave. Antenna popag., Vol.5, N..pp.3-9, 3. [] Ensenble, vesion 6., Ansot Co., USA, 999. [] Poza. D.M., Pesonal compute aided antenna design, Antenna design associates, Inc., 996. [3] Benella. A., Thng. C.H., and Gupta. K.C., Compute aided design and analysis o micostip patch antennas, Micopatch vesion., 993. [] Babu. S., and Kuma. G., Paametic study and tempeatue sensitivity o micostip antennas using an impoved linea tansmission line model, IEEE Tan..,Vol.AP-7,No., pp.-6, 999. [5] Kumpaset. N., and Kianon. W., Simple and accuate omula o the esonant equency o cicula micostip disk antenna, IEEE Tans., Vol.AP-3, pp , 995. [6] Davidovitz. M., and LO. Y.T., Input impedance o a pobe-ed cicula micostip antenna with thick substate,ieee Tans., Vol.AP- 3, pp.95-9,

10 A Novel Model o the Input Impedance o Coax-Fed Cicula Micostip Patch Antennas o CAD Table : Expeimental esonance equency o the cicula patches e. Patch H /mm Patch H/: g Measued esonance numbe adius /mm equency /GHz [ ] [9] [ ] [ ]

11 Damascus Univ. Jounal Vol. -No. 5 Abboud Table : Compaison o expeimental esonance equency with cicula patch models Patch numbe Ensemble [ ] Poza [ ] Benella [ 3 ] Vema [ ] Ou model

12 A Novel Model o the Input Impedance o Coax-Fed Cicula Micostip Patch Antennas o CAD 9

13 Damascus Univ. Jounal Vol. -No. 5 Abboud 93

14 A Novel Model o the Input Impedance o Coax-Fed Cicula Micostip Patch Antennas o CAD eceived, Octobe,. 9