ANALYSIS OF CIRCULAR MICROSTRIP ANTENNA ON THICK SUBSTRATE

Transcription

1 Jounal of Micowaves and Optoelectonics, Vol., N. o 5, July ANALYSIS OF CIRCULAR MICROSRIP ANENNA ON HICK SUBSRAE A. K. Vema and Nasimuddin Depatment of Electonic Science Univesity of Delhi South Campus, New Delhi-00, INDIA Abstact An impoved cavity model called the modified Wolff model (MWM) is pesented to compute the esonance fequency, input impedance and bandwidth of the cicula micostip antenna on thick substate (substate thickness, 0.003λ g 0.λ g ). he esults of MWM show bette ageement with the expeimental esults as compaed to the esults of thee commecial softwae, including the method of moment (MOM) based Ensemble. he MWM povides deviation in esonance fequency within.69 % and deviation in esonant esistance within 7 % against the expeimental esults. Indexing tems: Micostip antennas, hick substate, Cicula micostip antennas I. INRODUCION An impoved vesion of the cavity model, called the modified Wolff model (MWM) was epoted to compute accuately esonance fequency of the cicula micostip antenna on the lossless substate []. In this wok we extend the MWM fo computation of esonance fequency, bandwidth and input impedance of the pobe fed cicula patch on the thick lossy substate. hese paametes of the cicula patch on thick substate ae computed by the field theoetic methods and the standad cavity model is not consideed accuate []. We have collected the expeimental esults fom the seven published souces [-8] fo the substate thickness between 0.003λ g 0.λ g. he λ g is the guided wavelength in the dielectic medium. We have used these data to compae the computed esults obtained by the pesent MWM and also by thee commecial softwae namely, the MOM based Ensemble [9], the standad cavity model adopted in the PCAAD by Poza [0] and the multipot cavity model (MCM) adopted in the Micopatch by Benalla et al.[ ] against the common expeimental esults. In all cases, the esults of MWM ae much close to the expeimental esults as compaed to the computed esults of these commecial softwae. II. MODIFIED WOLFF MODEL he ectangula and cicula micostip patch antenna fabicated on the same substate ( =.3, h = 0.59 cm) and at the same esonant fequency (f = GHz) povide almost same diectivity (7 db) and efficiency (9%) []. his identical pefomance suggests that the cicula micostip Copyight SBMO ISSN

2 Jounal of Micowaves and Optoelectonics, Vol., N. o 5, July patch antenna can be analyzed by obtaining an equivalent ectangula micostip patch antenna. he cicula patch and its equivalent ectangula patch is shown in Fig.. Y L=π o / Y W = o Equivalent ectangula micostip patch antenna ρ Cicula Patch X o o W = o, tanδ h Pobe-fed Gound plane Fig.. Cicula patch antenna and its equivalent ectangula patch antenna on thick substate. Fo the equivalent ectangula patch of width W = o, the length L = (π/) o is obtained by using the invaiance of electostatic enegy below both the ectangula and cicula patches. he finge capacitance computed along both the length sides of the equivalent ectangula patch is teated same as the finge capacitance of the oiginal cicula patch. he esonance fequency of the cicula micostip antenna on thick lossy substate is computed fom [], f V0α nm = Re[ ] () π eff dyn Fo the fundamental esonating M mode, α nm =.84. V 0 is the velocity of light. he effective adius eff is computed by the expession of Chew and Kong [3], Copyight SBMO ISSN

3 Jounal of Micowaves and Optoelectonics, Vol., N. o 5, July h / h / = + ln + ( ) + ( ) () o eff o / 65 πo h o whee o is adius of the patch, h is height of the substate and / is eal pat of complex elative pemittivity ( ) of the substate. he complex dynamic elative pemittivity of the cicula patch, which takes into account the finge field and modal field vaiation, is obtained fom, C (, h, ) dyn o dyn = (3) Cdyn ( =, h, o ) he total mode-dependent complex dynamic capacitance dyn (, h, ) C of the cicula o patch is computed by the vaiational method in the Fouie domain, whee eal is eplaced by the complex []. he fequency dependent input impedance of the pobe fed cicula micostip patch is detemined by the following equation of a paallel esonant cicuit [4], f f R( ρ) R () ( ρ) f f Z in f = + j X L (4) f f + f f + f f f f he input esistance at the feed point ρ fom the cente of the cicula patch is given by, ( K ρ) ( K ) J R( ρ ) = (5) G J Fo the fundamental M mode, K o equals to.848 and G is the total conductance of the adiating apetue due to the conducto, dielectic, suface wave and adiation losses. At the esonant fequency f, it is elated to the total -facto ( ) by, o G = G R + G D + G C + G SW =.39 4µ oh f (6) and, = (7) C D SW R whee D, C, SW, and R ae the - factos, due to dielectic loss, conducto loss (in patch, gound plane and in the co-axial feed), suface-wave loss and adiation loss espectively. Fo the equivalent ectangula patch of width, W = o the D is detemined fom, Copyight SBMO ISSN

4 Jounal of Micowaves and Optoelectonics, Vol., N. o 5, July D (, h, ) π dyn o = (8) λ α 0 d he dielectic loss, α d is detemined fom the standad expession. he fee-space wavelength (λ 0 ) is obtained fom the esonance fequency of the patch. It is detemined fo the loss-less substate i.e., tan δ eff = 0 by the equation (). he C is also computed fo the equivalent ectangula patch of width, W = o fom, C 0 dyn (, h, o ) ( α + α ) π = (9) λ c feed he α c is the conducto loss of the patch and gound plane taken togethe and is detemined by the Wheele s inductance ule, which has been adopted by Vema et al. [5] in the vaiational method. he α feed is loss in the pobe feed, which is detemined by following the method of Collin [6]. o compute R due to the adiation loss, we have adopted two methods. In the model one, called MWM the R is computed fo the equivalent ectangula apetue of width, W = o. he expessions ae summaized in the efeence [7]. Fo the model- i.e. fo the MWM, the R is computed fo the cicula apetue of the cavity esonating in the M mode. he R fo the cicula apetue used in the MWM is [4], R 3 ( α ) 3 / 4 o = (0) h α F dyn ( α ) dyn he function F(X), whee X α = is given by the following appoximate expession,, dyn F ( X) = X X X X X 6 () Finally, SW due to the suface-wave loss is obtained fom, Psp sw = () P sw he adiated powe i.e. powe in the space wave (P sp ) and powe in the suface waves (P sw ) ae obtained fom the closed-fom expessions due to Poza [8]. Fom the total - facto we find the effective loss tangent, tanδ eff of the substate, Copyight SBMO ISSN

5 Jounal of Micowaves and Optoelectonics, Vol., N. o 5, July tan δ eff = (3) At this stage, the complex elative pemittivity of the substate is taken as = j tan δ. his is used fo computation of the complex dynamic elative pemittivity eff,dyn of the cicula patch and finally loss dependent esonance fequency by the equation (). Howeve, the decease in the esonance fequency due the suface wave and adiation losses is meaningful only when the substate thickness is moe 0.λ g. Fo the substate thickness 0.λg decease in esonance fequency due to the suface wave and adiation losses is about 3% [9]. he inductive eactance of pobe, X L indicating effect of all non-esonating modes is given by [9], whee, f is the opeating fequency. 377f h v0 X L = log (4) v / 0 πf d o eq III. RESULS AND DISCUSSION he able (a) shows the expeimental esults on the esonance fequency and the input esistance (R max ) of seventeen cicula patches in the substate thickness ange fom 0.003λ g - 0.λ g [-8]. he able (b) and the able (c) compae thee commecial softwae and the MWM against the expeimental esonance fequency and the expeimental input esistance espectively. Both the tables clealy demonstate that the pesent MWM is much bette than all thee models of the commecial softwae. he MWM has maximum deviation within.69 % and 7% fo the esonance fequency and the input esistance espectively. Othe thee models povide the deviation above 5% fo the esonance fequency and the deviation between 35% - 55% fo the input esistance. Only patch numbes 3 and 9 show inconsistent esults. Fo input esistance, the MWM shows bette ageement with the expeimental esults as compaed to the MWM. Fo the MWM, R is computed fo the equivalent ectangula apetue of width, W = o, wheeas fo the MWM, the R is computed fo the cicula apetue of the cavity esonating in the M mode. he able futhe compaes the total - facto ( ) and the bandwidth computed by the mode matching method (MM), MWM and MWM against the expeimental esults fo the patch numbes,4, and 6. Fo these patches the bandwidth is defined fo VSWR < : 3 []. he esults fo obtained by the MM closely follow esults of the MWM. Howeve, fo the bandwidth, the MWM shows bette ageement with expeimental esults. It appeas that the deviation in bandwidth and computed by the MWM fom the expeimental esults is due to the fact that the expession of Poza [8] fo the suface wave loss is applicable to the conducto backed infinite dielectic medium not to the finite size case of micostip antenna. his has given appoximate esults on the -facto due to the suface wave loss. Fig. futhe compaes the nomalized eal and imaginay pats of input impedance of the thick cicula patch numbe 6 computed by MWM, MM and MOM based Ensemble against Copyight SBMO ISSN

6 Jounal of Micowaves and Optoelectonics, Vol., N. o 5, July the expeimental esults. he esults of MWM and MM show bette ageement with the expeimental esults as compaed to the esults of Ensemble. Ref. [3] able (a): Expeimental Results of Resonance Fequency ( f ) and Input Resistance (R max ). Patch h (mm) h/λ g o ρ tanδ f R max No. (mm) (mm) (GHz) (Ω) [4] [5] [6] [7] [8] [] able ( b ) : Computed Resonance Fequency (f ) and % Deviation fom Expeimental Results. Patch Ensemble [9] PCAAD [0] MCM [] MWM No. f GHz % Dev. f GHz % Dev. f GHz % Dev. f GHz % Dev Copyight SBMO ISSN

7 Jounal of Micowaves and Optoelectonics, Vol., N. o 5, July Max. % Dev Aveage % Dev RMS % Dev able (c): Computed Maximum Resonant Resistance (R max ) in Ohms and % Deviation fom Expeimental Results: Patch Ensemble [9] PCAAD [0] MCM [] MWM MWM No. R max Dev. R max Dev. R max Dev. R max Dev. R max Dev Aveage % Dev. RMS % Dev Patch No. facto MM [] able : Compaison of otal -Factos and Bandwidth [] % Bandwidth (VSWR < 3:) Expt. [] % Bandwidth (VSWR < 3:) MM [] facto % Bandwidth MWM MWM MWM MWM Copyight SBMO ISSN

8 Jounal of Micowaves and Optoelectonics, Vol., N. o 5, July MWM Expt [] MM[] Ensemble[9] MWM Expt[] MM[] Ensemble[9] Nomalized Input Impedance X i R in Fequency (GHz) Fig.. Nomalized Input Impedance of cicula patch on thick substate fo the patch no. 6. IV. CONCLUSION he MWM based cavity model fo the cicula patch antenna has bette accuacy than accuacy of the thee consideed commecial softwae. Following the pevious investigation on the multilaye ectangula micostip patch antenna [0], the pesent model can be extended to a cicula micostip patch antenna unde the multilaye condition. he pesent MWM is flexible, accuate and computationally faste compaed to the field theoetic methods like MOM and MM. heefoe, the pesent MWM is suitable fo the inteactive CAD. REFERENCES [] A.K. Vema and Z. Rostamy, Modified Wolff Model fo detemination of esonance fequency of dielectic coveed cicula micostip patch antenna, Electonics Lettes, Vol. 7, pp , Nov. 99. [] M. Davidovitz and Y.. Lo, Input Impedance of a Pobe-fed cicula micostip antenna with thick substate, IEEE ans. on Antennas and Popagation, Vol. AP-34, No. 7, pp , July 986. Copyight SBMO ISSN

9 Jounal of Micowaves and Optoelectonics, Vol., N. o 5, July [3] J. S. Dahele and K. F. Lee, Effect of Substate hickness on the pefomance of Cicula- Disk Micostip Antenna, IEEE ans. on Antennas and Popagation, Vol. AP-3, pp , Mach 983. [4] J. S. Dahele and K. F. Lee, heoy and Expeiment on Micostip Antenna with ai gaps, IEE, Poc., Vol.3, Pt. H, pp , Dec.985. [5] K.R. Cave, Pactical analytical techniques fo the micostip antenna, Poc. Wokshop on Pinted Cicuit Antenna echnology, 7-9 Oct.979, New Mexico State Univesity, Las Cuces, New Mexico, pp [6] S. Yano and A. Ishimau, A heoetical Study of the Input Impedance of a Cicula Micostip Disk Antenna, IEEE ans. on Antennas and Popagation, Vol. AP-9, pp , Jan.98. [7] W. C. Chew and J. A. Kong, Analysis of a cicula Micostip Disk Antenna with a thick Dielectic Substate, IEEE ans. on Antennas and Popagation, Vol. AP-9, pp , Jan.98. [8] S. A. Long, L. C. Shen, M. D. Walton and M. R. Alleding, Impedance of a Cicula Disk Pinted Cicuit Antenna, Electonics Lettes, Vol. 4, pp , Oct.978. [9] Ensemble Vesion 6., Ansoft Co., USA, Sept [0] D. M. Poza, PCAAD 3.0, Pesonal Compute Aided Antenna Design, Antenna Design Associates, Inc [] A. Benalla, C. H. hng and K. C. GUPA, Compute-Aided design and analysis of micostip patch antennas, Micopatch Vesion.0, 993. [] R. Gag, P. Bhatia, I. Bahl, A. Ittipiboon, Micostip Antenna Design Handbook, Atech House, Inc., 00, pp [3] W. C. Chew, and J. A. Kong, Effects of finging fileds on the capacitance of cicula micostip disk, IEEE ans., Micowave heoy ech., Vol. 6, no., pp , 980. [4] F. Abboud, J. P. Damiano, and A. Papienik, A new model fo calculating the input impedance of coax-fed cicula micostip antennas with and without ai gaps, IEEE ans. Antennas Popagat., vol. AP-38, pp , Nov [5] A. K. Vema and A. Bhupal, Conducto loss of multilaye micostip line using single laye eduction fomulation, Micowave Opt. echnol. Lett., Vol.9, No., pp. 0-4, 998. [6] R. E. Collin, Antennas and Radiowave popagation, McGaw-Hill, New Yok, 985, pp [7] J. R. James and A. Hendeson, and P. Hall Micostip antenna pefomance is detemined by substate constaints, MSN, pp , August 98. [8] D. M. Poza, Rigoous closed-fom expessions fo the suface wave loss of pinted antennas, Electon. Lett., Vol. 6, No.3, pp , 990. [9] A. K. Vema and Nasimuddin, Resonance fequency of ectangula micostip antenna on thick substate, Electon. Lett, Vol. 37, No. 3, pp , Nov. 00. [0] A. K. Vema and Nasimuddin, Input Impedance of Rectangula Micostip Patch Antenna with Iso/Anisotopic Substate-supestate, IEEE Micowave and Wieless Components Lettes, Vol., No., Nov. 00. Copyight SBMO ISSN