Numerical and Experimental Analysis of Impedance Matched Inverted-L and Stair Inverted-L Antenna for 5 GHz WLAN Operation

Transcription

1 1 JOURNAL OF COMMUNICATIONS, VOL. 5, NO. 8, AUGUST 1 Numerical an Experimental Analysis f Impeance Matche Inverte-L an Stair Inverte-L Antenna fr 5 GHz WLAN Operatin Khale Mahbub Mrshe *, Debabrata Kumar Karmkar #, an Mitun Taluker * * Department f Electrnics & Cmmunicatin Engineering # Department f Electrical an Electrnic Engineering Khulna University f Engineering & Technlgy, Khulna-93, Banglaesh {kmm_ece, ebeee_kuet, mithunk5}@yah.cm Abstract This paper presents impeance matche high gain inverte-l antenna (ILA) an stair ILA fr 5 GHz wireless lcal area netwrk (WLAN) by means f numerical an experimental analysis. Numerical simulatin is carrie ut using meth f mments in Numerical Electrmagnetic Ce (NEC-) an agilent vectr netwrk analyzer, watts antenna trainer, an micrwave engineering trainer are use fr the measurement. The experimental results shw that ILA an stair ILA has 1-B return lss banwith f 5 MHz ( MHz) an 3 MHz (53 58 MHz) respectively cvering the unlicense natinal infrmatin infrastructure (U-NII) mi frequency bans fr 5 GHz WLAN peratin. Omniirectinal raiatin patterns are achieve fr bth antennas in XY plane an the antennas have peak gain f.5 an Bi respectively at center frequency (5.5 GHz) f antenna perating banwith. Mrever, the antennas have raiatin efficiency f greater than 8% an 91% respectively within the return lss banwith. Inex Terms ILA, Matching netwrk, Stair ILA, WLAN. I. INTRODUCTION WLAN links evices like ntebk, vie game cnsle, smart phne, MP3 player, persnal igital assistant etc. transmit/receive infrmatin thrugh air via a wireless istributin meth knwn as rthgnal frequency ivisin multiplexing r sprea spectrum. WLAN stanars incluing IEEE 8.11a/b/g systems were establishe by the IEEE 8.11 grup. IEEE 8.11b/g uses the. GHz inustrial, scientific an meical (ISM) ban an unlicense natinal infrmatin infrastructure (U-NII) ban use in IEEE 8.11a, which ffers mre nn-verlapping channels than the channel ffere in the. GHz ISM frequency ban. This U-NII ban has three separate frequency ranges as , Manuscript receive February 11, 1; revise April, 1; accepte May 11, 1. This paper is base n Numerical Analysis f Impeance Matche Inverte-L Antennas fr Wi-Fi Operatins Khale Mahbub Mrshe, Debabrata Kumar Karmkar, an Abu M. Numan-Al-Mbin, which appeare in the prceeings f 1th Internatinal Cnference n Cmputer an Infrmatin Technlgy (ICCIT), December, 9, Dhaka, Banglaesh. IEEE an GHz. Varius antennas esigne n the printe circuit bar (PCB), FR substrate have been prpse fr 8.11a (5 GHz ban) e.g., printe-spiral-strip [1] an T-shape, uble T- shape, tw step tapere mnple antennas [-]. A simple strip mnple has the avantages f lw prfile but the presence f hrizntal strip t frm T- shape mnple intruces a capacitive cupling with the grun plane causes impeance matching prblem which can be reuce by the use f a shrting line t frm shrte T-shape mnple antenna but the mifie antenna has lw gain thugh the banwith is imprve [-3]. Micrstrip feeing prvies higher efficiency in micrstrip antenna esign, whereas this feeing technique is use in tw step tapere-mnple antenna t imprve the antenna gain but the gain is limite [-]. Lw antenna impeance prblem can be slve by esigning iple an fle iple antennas because they shws higher antenna impeance than mnple antenna but planar iversity fle iple an M-slt fle patch antenna has lwer gain in assciate applicatin [5-8]. Asymmetric annular-ring patch fe by a 5 micrstrip line, ban-ntche planar mnple antenna cmpse f an asymmetric annular-ring patch an a stair-style grun plane, ring mnple antenna with uble meaner lines an tap mnple antenna supprt wie frequency ranges have been prpse fr 5 GHz WLAN peratin [9-1]. In cplanar waveguie (CPW)-fe slt antenna esign impeance matching prblem minimize by varying the angle f tapering an the istance frm the center strip [13]. Thus, ifferent mnple structures, slt antennas, planar antennas fr 5 GHz WLAN peratin suffer frm gain limitatins thugh ther perfrmance parameters f thse antennas are in acceptable level [1,,, 8, 11, 13]. Fr the antenna size reuctin capacitive la can be use withut egraing the antenna perfrmance [1-1]. In esigning antenna is f cmpact size matching is the key t enhance the perfrmance parameters. If the antenna input impeance es nt matche with the impeance f feeing cable/cnnectr, micrstrip line equivalent t resistr, inuctr an capacitr (RLC) netwrk can be use. Fr the RLC matching tw 1 ACADEMY PUBLISHER i:1.3/jcm

2 JOURNAL OF COMMUNICATIONS, VOL. 5, NO. 8, AUGUST 1 13 techniques prpse ne is parallel RLC resnatr cell in series [17] an the ther ne is cupling element base meth [18]. Inverte-L antenna (ILA) is f simple structure an cmpact size but esigning f ILA is a prblem because f its lwer input impeance [19]. The purpse f this wrk is t prpse a new antenna with high gain fr 5 GHz WLAN peratin. In this paper impeance matche, high gain ILA an lae ILA title as stair ILA is prpse an analyze by means f numerical simulatin an their perfrmance teste by means f experimental measurement. Using filter transfrmatin the input impeance matching prblem f the antennas is slve by esigning micrstrip line equivalent t matching RLC netwrk. The antennas numerically analyze using meth f mments (MMs) in numerical electrmagnetic ce (NEC-) []. Fr the simulatin we cnsiere the RT/uri 588 substrate with permittivity f r =. an substrate thickness f 1.58 mm. Fr the measurement f return lss Agilent Vectr Netwrk Analyzer is use an the gain an raiatin pattern measure using Watts Antenna Trainer. Vltage staning wave rati (VSWR) f the antennas measure using Micrwave Engineering Trainer. In the simulatin the central cnuctr f the feeing cable/cnnectr is cnnecte t the antenna feeing pint an the uter cnuctr cnnecte t the grun plane. II. ANTENNAS AND MATCHING NETWORKS DESIGN Starting frm the lw prfile printe T-shape mnple antenna [] we examine the pssibility f increasing the antenna gain by simplifying the structure f the antenna fr 5 GHz WLAN peratin. Inverte-L antenna is f very simple structure than T-shape mnple antenna. Fig. 1 shws the structure f ILA an Fig. shws the mifie ILA incluing impeance matching micrstrip line equivalent t matching RLC netwrk. When a strip perpenicular t the mnple is ae then it is calle ILA. During simulatin the imensin f the grun plane cnsiere as mm. r =. Matching strip line fee h Grun plane l w t=1.58 Figure 1. Inverte-L antenna (ILA). Figure. Stair inverte-l antenna (stair ILA). -3 h= mm -5 h= mm h=8 mm - h=1 mm h=1 mm -75 Figure 3. Effects f height (h) n the return lss f ILA f Fig. 1. r =. fee Grun plane l Matching strip line t= l= mm -5 l=5 mm l=35 mm - l= mm l=5 mm -75 Figure. Effects f length (l) n the return lss f ILA f Fig. 1. Effects f height n the return lss (S11) f the antenna (ILA) as a functin f frequency are shwn in Fig. 3. Frm the simulate results as the h ecreases, the antenna resnance frequency shifte t the lwer frequency. Fig. represents the effect f l n S11 f ILA w 1 ACADEMY PUBLISHER

3 1 JOURNAL OF COMMUNICATIONS, VOL. 5, NO. 8, AUGUST 1 structure f Fig.1, an Fig. 5 represents the effect f strip with (w). Frm the simulate results f Fig. an 5, as l increases the resnance shifte t lwer frequency an similar cases take place fr w. Mre negative value f antenna return lss means mre effectively pwer transmitte by the antenna in electrmagnetic frm int free space. Frm the simulatin results btaine, the ptimum antenna gemetry cnfiguratin f ILA is l = 35 mm, h = 8 mm, an w = 3 mm w= mm - w=3 mm w= mm -75 Figure 5. Effects f with (w) n the S11 f ILA f Fig =3 mm - =5 mm =7 mm -7 Figure. Effects f spacing () n the return lss f stair ILA f Fig l=3 mm - l=35 mm l= mm -7 Figure 7. Effects f length (l) n the return lss f stair ILA f Fig.. If la is applie t the ILA by using f similar structure, then the mifie structure is title as stair ILA. Variatin f return lss f stair ILA with the variatin f separatin () as a functin f frequency is shwn in Fig. an Fig. 7 represents the effects f length l. Small values f an l cause s egraatin f return lss hence pr pwer raiate frm the antenna int free space. But increasing an l shifts the antenna resnance t the lwer frequency with ecreasing return lss. Effects f w n S11 are shwn in Fig. 8. Frm the btaine results w has similar effects as n stair ILA. Frm the simulatin results f stair ILA as shwn in Fig., 7, an 8, the ptimum imensin f the stair ILA is = 5 mm, l = 35 mm, an w = 3 mm w= mm -5 w=3 mm - w= mm -7 Figure 8. Effects f with (w) n the S11 f stair ILA f Fig.. Impeance (hm) 1 8 ILA Stair ILA Figure 9. Impeance variatin f ILA an stair ILA withut matching. Caxial Cnnectr Caxial Cnnectr Xp 1 =.1 pf Xp =. pf Xp =.13 pf Antenna Antenna Figure 1. Matching netwrk with its parameters fr ILA stair ILA. 1 ACADEMY PUBLISHER

4 JOURNAL OF COMMUNICATIONS, VOL. 5, NO. 8, AUGUST 1 15 Frm the simulate results, the impeance f the prpse ILA an stair ILA is 8.39 an 59.8 respectively at its resnant frequency (5.5 GHz) as shwn in Fig. 9. T match the antenna with the feeing cable/cnnectr impeance matching netwrk is require in between them which act as an impeance transfrmer. Fig. 1 shws the RLC matching netwrks use in between them as an impeance transfrmer. This matching netwrk (shwn in Fig. 1) cnverte int equivalent micrstrip line using filter transfrmatin thery [1]. The with (W ) f the equivalent micrstrip line is calculate as W W A 8e A e r 1 B 1 ln(b 1) r Where, fr W / (1).1 ln( B 1).39 fr W / () r Z A 377 B Z r 1 r r 1 r r Here (= 1.58 mm) is the ielectric substrate thickness, r is relative ielectric cnstant, an Z is characteristics impeance f the line. Accring t the thery f transfrmatin, the impeance scale an frequency transfrme element values fr the circuit f Fig. 1 is L 1Z L 1 (3) C1 () L 1Z Z L (5) C C C () Z 1 Here, L1 g1 an C g an the values f g 1 an g taken frm the element values fr maximally flat lw pass filter prttype [1] an is the angular resnant frequency. Frm the values f C1 X p1 an C X p the pruct l is calculate using (7) fr the electrical length f the inuctr sectin an (8) fr the electrical length f the capacitr sectin as LR l (Inuctr) (7) Z h CZl l (Capacitr) (8) R Where R is the filter impeance an L an C are nrmalize element values. Fig. 11 shws the phase angle variatin f ILA an stair ILA. Due t the mismatch, the phase shift is. an 5. fr ILA an stair ILA respectively. The matching filter equivalent micrstrip transmissin line length calculate as l k l (9) e f k (1) c ( /18) l (11) e k r 1 r 1 Where e 1 11 / W Here is the phase shift ue t mismatch, e is the effective ielectric cnstant. Using the values f l calculate frm (7) r (8) accring t the characteristics f the impeance; the length f the impeance transfrmatin line is calculate frm (9), (1) an (11). Accring t the thery f filter transfrmatin (step impeance resnatr) as iscusse abve, Table I shws the length an with f the micrstrip line esigne equivalent t matching netwrk f Fig. 1. Phase angle (Degree) ILA Stair ILA Figure 11. Phase shift f ILA an stair ILA uner mismatch cnitin. TABLE I. IMPEDANCE MATCHING MICROSTRIP LINE PARAMETERS Antenna name Length, l (mm) With, w (mm) ILA Stair ILA ACADEMY PUBLISHER

5 1 JOURNAL OF COMMUNICATIONS, VOL. 5, NO. 8, AUGUST 1 III. SIMULATION AND MEASUREMENT RESULTS The antennas was cnstructe an teste. In experimental esign cpper is use as a grun plate with thickness f.17 mm. Antenna layut esigne n the cpper plate f RT/uri 588 substrate manually using permanent marker pen an FeCl 3 is use t remve the unwante cpper material sectin. In the experimental esign the chice f RT/uri 588 because its cst is lwer than the substrate f higher ielectric cnstant materials. In measurement, central cnuctr f the feeing cable is cnnecte t the antenna feeing pint an the uter cnuctr slere t the grun plane. Fig. 1 shws the implemente prttype f the antennas an Fig. 13 shws the measure an simulate return lss fr the ILA an stair ILA. Fr the bth antennas, the perating ban centere at 5.5 GHz with g impeance matching. ILA has 1-B return lss banwith f 5 MHz ( MHz) an fr stair ILA 3 MHz (53 58 MHz) cvering the U-NII mi frequency bans fr 5 GHz WLAN peratin. ILA has much wier banwith that cvers the U-NII lw, mi an upper bans fr WLAN peratin. The variatin f simulate an measure VSWR fr ILA an stair ILA as a functin f frequency are shwn in Fig. 1. At resnant simulate an measure VSWR very clser t stanar value 1. 5 VSWR 3 simulate measure Figure 1. Cnstructe prttype f the ILA an stair ILA simulate measure VSWR 8 simulate measure simulate measure Figure 13. Measure an simulate return lss f ILA an Stair ILA Figure 1. Simulate an measure VSWR fr ILA an stair ILA. Fig. 15 an 1 shws the raiatin pattern f ILA an stair ILA in vertical plane (XZ, YZ) an in hrizntal plane (XY) at 5.5 GHz. The antenna is teste in nrmal labratry envirnment fr this reflectin f wave s cause s abrupt change in the pattern in bth planes. Simulate an measure raiatin pattern agree each ther quite well. One can bserve frm Fig. 17 that within the antenna banwith ILA has raiatin efficiency greater than 8 % an stair ILA has greater than 91 %. Fig. 18 represents the variatin f peak gain fr bth antennas as a functin f frequency. The gain f ILA varies frm 5.81 t.5 Bi within the return lss banwith an fr stair ILA frm 9. t Bi. 1 ACADEMY PUBLISHER

6 JOURNAL OF COMMUNICATIONS, VOL. 5, NO. 8, AUGUST 1 17 Thugh ILA has mre stable gain than the stair ILA but the gain f stair ILA is much higher than the ILA Bi Bi Z 7 9 Y XY X Figure 15. Simulate an measure raiatin pattern f ILA at 5.5 GHz in vertical plane (XZ, YZ), an hrizntal plane (XY) Bi Bi Z 7 9 Y XY X Figure 1. Simulate an measure raiatin pattern f stair ILA at 5.5 GHz in vertical plane (XZ, YZ) an hrizntal plane (XY). Raiatin efficiency (%) 1 8 Inverte-L Antenna Stair Inverte-L Antenna Figure 17. Simulate raiatin efficiency f ILA an stair ILA as a functin f frequency. Gain (Bi) Gain (Bi) simulate measure simulate measure Figure 18. Simulate an measure maximum antenna gain with respect t the frequency fr ILA an stair ILA. Table II shws a cmparisn between the measure peak gain an peak return lss f the prpse an the existing antennas fr 5 GHz WLAN peratin where the antenna center frequency f 5.5 GHz. Frm the cmparisn table, ILA has higher gain than the antenna exist fr the same applicatin area. Stair ILA has much higher gain cmpare t ther antennas. Mrever, ILA an stair ILA can transmit signal mre effectively than the spiral strip [1], T-shape mnple [], tw step tapere mnple [], planar iversity fle iple [8], 1 ACADEMY PUBLISHER

7 18 JOURNAL OF COMMUNICATIONS, VOL. 5, NO. 8, AUGUST 1 slt [13], an CPW-fee slt [1] antennas because f their mre negative return lss. TABLE II. GAIN AND RETURN LOSS COMPARISON BETWEEN PROPOSED AND REFERENCE ANTENNAS FOR 5GHZ WLAN OPERATION Antenna name Measure peak gain (Bi) Measure peak return lss (B) Printe-Spiral-Strip antenna [1] Printe T-shape mnple antenna [] Tw step tapere mnple antenna [] 5. < -1 Planar iversity fle iple antenna [8] Slt antenna [11] CPW-fe slt antenna [13] ILA.5-8 Stair ILA IV. CONCLUSION An impeance matche ILA an its mifie structure name stair ILA have been analyze an teste in this paper. It shws that bth antennas have impeance mismatch with the feeing cnnectr in nrmal cnitin (withut matching line). Impeance transfrmatin micrstrip line is esigne using the filter transfrmatin thery f micrstrip line t btain matching between the antennas an feeing system. Uner this cnitin bth antennas shw g return lss banwith an measure results agree with the simulate results well. It is bserve frm simulate an measure results that the gain f the ILA is imprve significantly when suitable structure la is applie t the hrizntal strip f the ILA. The analysis f the antennas als shws that it can easily be use at 5.5 GHz an the measure raiatin patterns are well-behave with high gain. Mrever, the prpse antennas are very prmising t perate as a small-size internal antenna fr the case f 5 GHz WLAN peratin. ACKNOWLEDGMENT The authrs f this research paper are very much thankful t the Micrwave Engineering Labratry, Inian Institute f Technlgy, Maras, Inia fr their help in antenna measurement. The authrs als wish t thank Mr. Abu M. Numan-Al-Mbin an Mr. Mnir Hssen fr their review an valuable cmments. REFERENCES [1] C. W. Su, Y. T. Liu, W. S. Chen, Y. T. Cheng, an K. L. Wng Braban Circularly Plarize Printe-Spiral- Strip Antenna fr 5-GHz WLAN Operatin, Micrwave an Optical Technlgy Letters, vl. 1, n. 3, pp ,. [] S. W. Su, K. L. Wng, an H. T. Chen, Braban Lw- Prfile Printe T-Shape Mnple Antenna fr 5-GHz WLAN Operatin, Micrwave an Optical Technlgy Letters, Vl., N. 3,. [3] Y. L. Ku, an K.L. Wng, Printe Duble-T Mnple Antenna fr./5. GHz Dual-Ban WLAN Operatins, IEEE Transactin n Antennas an Prpagatin, Vl. 51 N. 9, pp , 3. [] R. Zaker, Ch. Ghbai, an J. Nurinia, A Mifie Micrstrip-Fe Tw-Step Tapere Mnple Antennas fr UWB an WLAN Applicatins, Prgress in Electrmagnetic research, PIER 77, PP , 7. [5] Cnstantine A. Balanis, Antenna Thery Analysis an Design, Jhn Wiley & Sns, Inc., Secn Eitin, 198. [] Thmas A. Milligan, Mern Antenna Design, Wiley- Interscience, Secn Eitin, 5. [7] F. Jlani, A. M. Dagarpur, an H. R. Hassani, Cmpact M-Slt Fle Patch Antenna fr WLAN, Prgress in Electrmagnetics Research Letters, Vl. 3, pp. 35, 8. [8] G. Y. Lee, W. S. Chen, an K. L. Wng, Planar Diversity Fle Diple Antenna fr 5 GHz WLAN Operatin, Micrwave an Optical Technlgy Letters, Vl. 39, N. 5, 3. [9] W. Ren, J. Y. Deng, an K. S. Chen, Cmpact PCB Mnple Antenna fr UWB Applicatins, Jurnal f Electrmagnetic Waves an Applicatins, Vl. 1, N. 1, 111 1, 7. [1] W. Ren, Z. G. Shi, an K. S. Chen, Nvel Planar Mnple UWB Antenna with 5-GHz Ban-Ntche Characteristic, Jurnal f Electrmagnetic Waves an Applicatins, Vl. 1, N. 1, pp , 7. [11] W. Ren, Cmpact Dual-Ban Slt Antenna fr./5 GHz WLAN Applicatins, Prgress in Electrmagnetics Research B, Vl. 8, , 8. [1] A. A. Elek, Numerical Analysis f a Small Ultra Wieban Micrstrip-Fe Tap Mnple Antenna, Prgress in Electrmagnetics Research, PIER 5, 59 9,. [13] T. Shanmuganantham, K. Balamanikanan, an S. Raghavan, A CPW-fe slt antenna fr wieban applicatins, Internatina jurnal f antennas an prpagatin, Vl. 8. [1] S. Schulteis, C. Walschmit, W. Srgel, an W. Wiesbeck, Design f a Capacitively Lae Inverte-F Antenna fr Wireless LAN Applicatins, Prc. Internatinal ITG Cnference n Antennas, Berlin, pp , 3. [15] S. Schulteis, C. Walschmit, W. Srgel, an W. Wiesbeck, A Small Planar Inverte-F Antenna with Capacitive an Inuctive Laing, Prc. IEEE Antennas an Prpagatin Sciety Internatinal Sympsium, Vl., Issue, pp. 181,. [1] C. R. Rwell, an R. D. Murch, A Capacitively Lae PIFA fr Cmpact Mbile Telephne Hansets, IEEE Transactin n Antennas an Prpagatin, Vl. 5, Issue 5, pp , [17] I. Pele, A. Chusseau, an S. Tutain, Simultaneus Meling f Impeance an Raiatin Pattern Antenna fr UWB Pulse Mulatin, IEEE Antennas an Prpagatin Sciety Internatinal Sympsium, Vl., pp ,. [18] J. Villanen, an P. Vainikainen, The Design f Optimum Impeance Matching Netwrks fr Cupling Element Base Antenna Structures, IEEE Antennas an Prpagatin Sciety Internatinal Sympsium 7, pp , 7. [19] D. A. Wunsch, A Clse-Frm Expressin fr the Driving Pint Impeance f the Small Inverte-L Antenna, IEEE Transactin n Antennas an Prpagatin, Vl., N., 199. [] G. J. Burke, an A. J. Pggi, Numerical Electrmagnetic Ce-, Ver , Arie Vrs, [1] Davi M. Pzar, Micrwave Engineering, Jhn Willey & Sns, Inc., Secn Eitin, ACADEMY PUBLISHER

8 JOURNAL OF COMMUNICATIONS, VOL. 5, NO. 8, AUGUST 1 19 Khale Mahbub Mrshe receive Bachelr f Science in electrnics & cmmunicatin engineering (ECE) with hnrs frm Khulna University f Engineering & Technlgy, Khulna 93, Banglaesh, in 7. He is currently wrking as a Lecturer in the same epartment f this university. He authre an cauthre mre than 15 publicatins in referee jurnals an cnference prceeings in natinal an internatinal level. His current research interests inclue analysis an esign f micrstrip/patch antennas, antennas fr bimeical an RFID applicatins, antenna miniaturizatin, high gain micrstrip antennas fr satellite cmmunicatins, eletrmagnetics. Mr. Mrshe is an Assciate Member f Institute f Engineers Banglaesh (IEB), Life Member f Banglaesh Electrnic Sciety (BES). Debabrata Kumar Karmkar was brn in Satkhira, Khulna, Banglaesh. He receive the Bachelr f Science in electrical an electrnic engineering (EEE) frm Khulna University f Engineering & Technlgy (KUET), Khulna-93, Banglaesh, in 7. He is currently wrking as a Lecturer in the same epartment f this university. He authre an cauthre mre than 1 publicatins in referee jurnals an cnference prceeings in natinal an internatinal level. His main interests inclue analysis an esign f micrstrip antennas, antennas fr bimeical an RFID applicatins, antenna miniaturizatin, high gain micrstrip antennas fr satellite cmmunicatins, eletrmagnetics, wireless cmmunicatin & signal prcessing, an ptical cmmunicatin & netwrks, an pwer system & renewable energy. Mr. Karmkar is a member f Cnsultancy Research an Testing Services (CRTS), KUET an is an Assciate Member f Institute f Engineers (IEB), Banglaesh, Life Member f Banglaesh Electrnic Sciety (BES). Mitun Taluker was brn in Chittagng, Banglaesh, in He cmplete Secnary Schl Certificate in Science frm Cllegiate Schl, Chittagng, Banglaesh, in 3 an Higher Secnary Schl Certificate in Science frm Chittagng Cllege, Chittagng, Banglaesh, in 5. Nw he is a final year stuent f Bachelr f Science in electrnics & cmmunicatin engineering (ECE), Khulna University f Engineering & Technlgy (KUET), Khulna-93, Banglaesh. His current research interests inclue electrmagnetic, antennas an prpagatin, wireless cmmunicatin an igital signal prcessing. 1 ACADEMY PUBLISHER