Analysis of self-resonant bent antennas

Analyses of Self-Resonant Bent Antennas

Mohammod Ali

B.Sc. (E lectrical & E lectron ic Engineering). B angladesh U niversity o f Engineering & Technology. Dhaka. 1987

M.A.Sc. (E lectrical &: C o m p u te r Engineering). U niversity o f V icto ria. 1994 -A. D isse rta tio n S u b m itted in P a rtial Fulfillm ent of th e

R eq u irem en ts for the Degree of D O C T O R O F PH IL O SO PH Y

in the D e p a rtm e n t of E lectrical C o m p u te r E ngineering

We acc e p t th is dissertatio n as conform ing to the required sta n d a rd

Dr. S.S. ^ ^ c h ly . S u p erv iso r (D ep t, of Elec. &: C om p. Eng.)

________________________________________ Dr. .1. B o m em ann. D e p a rtm e n ta l M ember (D ept, of Elec. & C om p. Eng.)

Dr. M. O koniewski. D e p a rtm e n ta l M ember (D ept, o f Elec. &; C om p. Eng.

Dr. S. D ost. O u tsid e M em b er (D ept, of M echanical E ngineering)

Dr. E .\'. .lull. E x tern al M em ber (D ept, of Elec. Eng.. U niversity o f B ritish C o lu m b ia)

(c)M oham m od .A.H. 1997 U niversity of \'ic to ria

All rights reserved. T h e sis m ay not be reproduced in whole or in p a rt, by photocopy or o th e r m eans, w ithout the perm ission o f th e a u th o r.

S u p e n ’isor: Dr. S. S. Stuchly

A b str a c t

T he prim ary' focus of this d is se rta tio n is on the analyses of self-reso n an t bent an ten n as. T he need for the a c c u ra te c h aracterizatio n of such a n te n n a s d u e to th e ir grow ing im p o rtan c e in present d ay w ireless com m unications is the m o tiv a tio n for this work. To this end. several self-resonant bent an ten n as are analyzed w hich includes an inverted-L a n te n n a (ILA ). a m ean d er-lin e dipole (M LD ) a n te n n a , a m ean d er-lin e bow -tie (M L B T ) a n te n n a , a d u al m e a n d e r anten n a, an d a p rinted m e a n d e r an ten n a.

.A. sim ple a n a ly tic a l m odel, based on the induced E M F m eth o d , is p resen ted to com p u te the in p u t im p ed ance o f th e ILA. F irst, a sinusoidal d is trib u tio n o f current on the a n ten n a , w ith zero current a t th e end is assum ed, and then a n expression for the in p u t im p ed an ce is derived u sin g the near-fields of the a n ten n a . T h e accuracy of th e form ulation is verified by c o m p arin g the results co m p u ted u sin g it w ith th a t from N EC [l] c o m p u ta tio n . Unlike th e an aly tical so lu tio n s available in th e lite ra tu re , o u r proposed so lu tio n is not re s tric te d to anten n as th a t are e lec trica lly sm all. In a d d itio n the new form ulation can be extended to tre a t o th e r a n te n n a s, such as the T -an te n n a . the folded unipole a n te n n a , an d the loop-loaded m onopole a n ten n a .

T he in p u t im p edan ce, ra d ia tio n p a tte rn , and gain of th e MLD a n d M L B T a n ten ­ nas are co m p u ted a n d co rrelated w ith th e ir p aram eters. Input im p ed an ces of b o th a n ten n as are c o m p u te d using N EC . Sim ple analy tical m odels are p re sen te d to com ­ pute the ra d ia tio n p a tte rn s of th e M LD and the M LB T a n ten n as. For each an ten n a, a sinusoidal d is trib u tio n of cu rren t is assum ed and closed-form ex p ressio n s for the ra d ia tio n fields are derived. T he re su lts com puted using the a n a ly tic a l m odels are verified by co m p arin g them w ith th e results from the N EC c o m p u ta tio n . Since in each m odel the ra d ia tio n p a tte rn of an an ten n a is expressed in te rm s o f ready to evaluate algebraic expressions, th e c o m p u ta tio n of such p a tte rn is fast a n d easy.

I l l

are com p u ted using NEC. Sim ilarly as before the in p u t im pedance, ra d ia tio n p a t­ tern , a n d gain of th is an ten n a a re also correlated w ith its p aram eters. T h e in p u t im p edan ce and rad ia tio n p a tte rn o f a p la n a r printed m eander a n te n n a are in v esti­ g a ted using the Finite-D ifference T im e-D o m ain (F D T D ) technique. T he a n te n n a is m odeled on a dielectric s u b stra te b o th in the presence and absence o f a m etallic g round plane. C h aracteristics o f th e a n te n n a are exam ined as function of dielec­ tric co n stan t, an d su b strate thickness. New results of input im pedance, ra d ia tio n p a tte rn , and gain are presented w hich are v ital for the design of such an ten n as.

Several novel applications of self-reso n an t bent an ten n as are described. F irst, a w ide-band dual m eander-sleeve a n te n n a is designed, m anufactured, an d m easu red for ap p licatio n in d u al frequency v eh icu lar personal com m unication. T h e a n te n n a can o p e ra te sim ultaneously in th e 824-894 MHz and 1850-1990 .MHz b an d s o f th e PCS system . Second, an M LB T d ip o le is introduced as a feed for plane sheet reflectors. N um erical results c o m p u te d using NEC show th at the feed when used in front o f a plane sheet reflector, resu lts in superior rad iatio n c h aracteristics th a n a conventional dipole feed, nam ely, it reduces the reflector dim ension by 46% for the sam e front to back ratio, b e am w id th and gain. Finally, a com pact plane sheet reflector an ten n a is described th a t uses an M LBT m onopole feed. Since the a n te n n a uses a m onopole, a balun is not rec^uired. T his a n ten n a has a gain an d half-pow er b eam w id th of 8.4 dB i and 94^. respectively.

Exam iners:

Dr. S.S. Stuchly. S u p erv iso r (D ept, of Elec. & C om p. Eng.)

Dr. .1."B om em ann. D e p artm en ta l M ember (D ept, o f Elec. &: Com p. Eng.)

Dr. M. Okoniew ski. D e p artm en ta l M em ber (D ept, of Elec. & Com p. E n g .)

Dr. S. D ost. O u tsid e M em b er (D ept, of M echanical E ngineering)

Dr. E .\'. .lull. E x tern al M em ber (D ept, of Elec. Eng. U niversity of B ritish C olu m b ia)

C o n te n ts

2 D e fin itio n s o f A n te n n a P a ra m eters a n d L itera tu re R e v ie w 8 2.1 D efinition of P a r a m e t e r s ... 9

2.1.1 R a d ia tio n P a t t e r n ... 9

2.1.2 R a d ia tio n I n t e n s i t y ... 10

2.1.3 D ir e c tiv ity ... 11

2.1.5 E f f i c i e n c y ... 11 2.1.6 G ain an d H alf-Pow er B e a m w i d t h ... 12 2.1.7 B a n d w id th ... 12 2.1.8 Field R e g i o n s ... 13 2.1.9 P o la r i z a tio n ... 14 2.2 R eview o f L i t e r a t u r e ... 15 3 T h e In v e r te d -L A n te n n a 22 3.1 C u rre n t D i s t r i b u t i o n ...24 3.2 T h e Induced EM F M e th o d ...25 3.3 .A n a ly s is ...27 3.3.1 R e s u lts ... 32 3.4 D iscussion ... 38 4 T h e M ea n d e r -L in e D ip o le A n te n n a 42 4.1 In p u t I m p e d a n c e ...43 4.1.1 C o m p u ta tio n T e c h n iq u e ...43 4.1.2 R e s u lts ...44

4.2 R a d ia tio n C h a ra c te ris tic s ... 49

4.2.1 F u n d a m e n ta ls ... 50 4.2.2 C urrent D i s t r i b u t i o n ...52 4.2.3 R ad iatio n P a t t e r n ...53 4.2.4 G a i n ...56 4.2.5 R e s u lts ... 56 4.3 D is c u s s i o n ...62 5 T h e M e a n d e r -L in e B o w -T ie A n te n n a 64 5.1 .A ntenna C o n f ig u r a tio n ... 66 5.2 In p u t I m p e d a n c e ...67

C O N T E X T S vii 5.3.1 C u rren t D i s t r i b u t i o n ...72 5.3.2 R ad iatio n P a t t e r n ...74 5.3.3 R e s u lts ... 78 5.4 D is c u s s io n ...S3 6 T h e D u a l M e a n d er A n te n n a 84 6.1 In p u t I m p e d a n c e ...85 6.2 R ad iatio n P a t t e r n ...88 6.3 D is c u s s io n ... 89 7 T h e P r in te d M ea n d er A n te n n a 92 7.1 .\n te n n a C o n f ig u r a tio n ...94 7.2 F D T D M o d e l i n g ... 94 7.3 R e s u l t s ... 96

7.3.1 .A.ntenna on a G rounded D ielectric S u b s t r a t e ... 97

7.3.2 .A.ntenna on a D ielectric H a lf - S p a c e ... 107 7.4 D is c u s s io n ... I l l 8 A p p lica tio n s 114 8.1 D ual meancier-Sleeve A n t e n n a ...115 8.1.1 I n tr o d u c tio n ... 115 8.1.2 Design C o n s i d e r a t i o n s ... 116 8.1.3 N um erical R esults ... 118 8.1.4 E xp erim en tal P r o c e d u r e ...120 8.1.5 E xp erim en tal R e s u l t s ...121 8.2 P la n e Sheet Reflector .A .n te n n a s ... 124 8.2.1 I n tr o d u c tio n ...124 8.2.2 M LB T D ipole Feed ... 127 8.2.3 M LB T M onopole F e e d ...134

8.3 D is c u s s io n ... 138 9 C o n c lu sio n s an d F u tu r e W ork 140 9.1 C o n c l u s io n s ...140 9.2 F u tu re W o r k ...143 B ib lio g ra p h y 145 A p p e n d ix A 154 A p p e n d ix B 157

IX

L ist o f F ig u r e s

2.1 Spherical c o o rd in a te sy ste m ... 9

2.2 (a) .A. zigzag, a n d (b) a m eander a n te n n a [7]... 17

2.3 Several m e an d e r a n te n n a s (a) N = 2 . (b) N = 4 . (c) N'=6 [S]...18

3.1 .A.n inverted-L m o n o p o le ... 23

3.2 An invert ed-L d i p o l e ...23

3.3 ( a)A tra n s m ittin g a n te n n a fed by a voltage source ( m a g n etic cu rren t ). and (b) an auxiliar." current d is trib u tio n ...25

3.4 T he input re a c ta n c e of an inverted-L a n ten n a as a fu n c tio n of k l = k-(h -I- L) w ith th e ra d iu s of the w ire («) as a p a ra m e te r: //= 40 m m . £ = 4 0 m m . a n d frequency range 100-1550 M Hz...33

3.5 T he input re sista n c e o f an inverted-L a n te n n a as a fu n c tio n of k l w ith the radius of th e w ire (a) as a p a ra m e te r: //=40 m m . £ = 4 0 m m . a n d frequency range 100-1550 M Hz...34

3.6 R eturn-loss verstis frequency c h arac te ristic s of an in v erted -L m onopole w ith the rad iu s o f th e wire, a as a p a ram eter. O th e r p a ra m e te rs of the an ten n a are /< = £ = 40 m m ... 35

3.7 R eturn-loss versus frequency c h arac te ristic s of an inverted-L m onopole. A ntenna 1: h = 20 a n d L = 60.3 m m . a = 0.1 m m . .A.ntenna 2: /? = £ = 40 m m . and a = 0.1 m m ...36 3.8 Input im p ed an ce of an inverted-L a n te n n a as a function of kh w ith

k L as the param eter; w ire rad iu s a = 0.0005A... 37

3.9 The in p u t im pedance o f an inverted-L a n ten n a as a function o f kl: h = £ = 40 m m , and a = 0.1m m . frequency ran g e 100-1875 .MHz. . . 39 3.10 C urrent d istrib u tio n o f a n inverted-L dipole as a function of the w ire

length (21)... 40

4.1 The geo m etry of an M LD a n te n n a : e\ = v ertical segm ent len g th . e> = h o riz o n ta l segm ent len g th , a n d £ = a n te n n a le n g th ...44 4.2 Shortening ra tio . S R a n d reso nan t resistance. Rrcs of an MLD a n ­

tenna p lo tte d as fu n ctio n o f .V w ith ^ as the p a ra m e te r. T he len g th and the ra d iu s of the w ire are c o n sta n t (len g th o f wire. £^.,r, = 32 cm. and ra d iu s of w ire, a = 0.325 m m )... 46 4.3 Input im p ed an ce of a m onopole m ean d er a n te n n a as a function of

an ten n a len gth w ith th e segm ent len g th , e as th e param eter: .V = 2.

a = 0.325 m m ... 47

4.4 Input im p ed an ce of a m onopole m ean d er a n te n n a as a function of an ten n a len g th w ith th e n u m b er of m ean d er sectio n s. .V as the p a­ ram eter: Lu_.,re = 16 cm . a = 0.325 m m . and £ = 8 c m 48 4.5 Input im p ed an ce of a m onopole m eand er a n te n n a as a function of

an ten na leng th w ith th e ra d iu s of the w ire, n as the p a ra m ete r:

Livire = 12.8 cm. -V = 4. an d £ = 6.4 cm ...49

4.6 (a) .A. m eander-line d ip o le a n te n n a : (b) in te g ra tio n p a th ... 50 4.7 R ad iatio n p a tte rn of a n M LD a n te n n a w ith £ as a p a ram eter (.V = 4). 57

L I S T O F F I G U R E S xi

4.8 0-poIarized pow er density p a tte rn of a m ean d er-lin e dipole a n te n n a wdth L = 0.5A (.V = 4): wire rad iu s a = 0.001 A... 58 4.9 ^-p o larized pow er density p a tte rn o f a m ean d er-lin e dipole a n te n n a

w ith L — 0.75A (.V = 4 )... .58 4.10 R elativ e pow er den sity and half-pow er beam w id th (H PB W ) o f the

M LD a n te n n a as a function of a n te n n a length ( N = 4 ) ... 59 4.11 o p o la r iz e d pow er density p a tte rn o f a m ean d er-lin e dipole a n te n n a

w ith a n ten n a len g th L as a p a ra m e te r (.V = 4 )... 61 4.12 o -p o larized pow er density p a tte rn o f a m ean d er-lin e dipole a n te n n a

w ith num ber o f m eanders (.V) as a p a ra m e te r (L = 0.25A)... 61 4.13 G a in of a m ean d er-lin e dipole a n te n n a as a fu n ctio n o f an ten na len g th

L w ith N as a p a ra m e te r... 62

5.1 A m ean d er-line bow -tie (M LB T) a n te n n a ...67 5.2 In p u t im p ed an ce of the m onopole M L B T a n te n n a w ith bow-tie an g le

Cl (degrees) as th e p a ra m ete r... 70 5.3 In p u t reactan ce of the monopole M L B T a n te n n a w ith num ber o f m e­

a n d e r sections (A') as the p a ra m e te r...70 5.4 In p u t resistan ce of the m onopole M LB T a n te n n a w ith num b er of

m e a n d e r section s (A*) as the p a ra m e te r... 71 5.5 (a) .An M LB T a n ten n a , and (b) in te g ra tio n p a th ... 72 5.6 ^-p o larized pow er density p a tte rn of an M LB T d ip o le w ith wire len g th

L^. as a p a ra m e te r (A* = 4 and a = 20°). Solid lines- an aly tica l re su lts. crosses-N EC resu lts... 79 5.7 o p o la r iz e d pow er density p a tte rn o f an M L B T dipole w ith w ire

le n g th as a p a ra m ete r (A' = 4. an d a = 20°). Solid lines- a n ­ a ly tic a l results. crosses-N EC re s u lts ...80

•5.8 R a d ia tio n p a tte rn o f an M LBT dipole a t resonance. Solid lines- a n ­

a ly tic a l results. crosses-N EC re su lts...81 •5.9 G ain o f an M L B T dipole as a function of a n te n n a length; .V = 4. . . 82

6.1 A d u a l m eander a n te n n a on a perfectly c o n d u ctin g infinite g ro u n d

p la n e ... 85 6.2 C o m p u te d input reactan ce of the d u al m ean d er a n te n n a as a fu n ctio n

of a n te n n a length w ith ?•> as a p a ra m e te r... 86 6.3 C o m p u te d input resistan ce of the d u a l m ean d er a n te n n a as a fu n ctio n

of a n te n n a length w ith co as a p a ra m e te r... 87 6.4 C o m p u te d \ 'S \ \ ’R frequency response o f th e d u a l m eander a n te n n a

as a function of frequency w ith eo as a p a ra m e te r... 87 6.5 El). E -plane p a tte rn of a dual m ean d er a n ten n a: e\ = c-> = 0.8 cm .

a = 1.25 mm. L = 6.4 cm . and .V = 4 ... 89

6.6 C o m p arin g the in p u t im pedances of a m ean d er a n d a dual m e an d e r a n te n n a . For b o th antennas L = 6.4 cm . a = 1.25 mm. .V = 4.

c, = e-y = 0.8 cm . an d for the d u al m ean d er alone w = 0.5 c m ... 90 6.7 C o m p u te d \'SV \'R frequency response of a d u al m e an d e r and a m e an d e r. 91

7.1 A p rin te d m eander a n te n n a ...95 7.2 A p rin te d dipole a n te n n a ... 96 7.3 T h e in p u t im pedances of a m ean d er d ipo le in a ir and a m e an d e r

d ip o le p rin ted on a grounded dielectric s u b stra te . T h e p a ra m ete rs of th e a n te n n a in a ir are: .V = 2. e = 12 m m . 2/ — 44 m m . and «’ = 4 m m . w hereas th a t of the printed are: e = 12 m m . 2/ = 44 m m . w = 4 m m . L< = 244 m m . tc, = 244 m m . G = 20 m m . = 2.1...99

L I S T O F F I G U R E S xiii

7.4 T h e in p u t im p ed an ce o f a printed m ean d er a n te n n a as a function of frequency w ith fr as a p aram eter. O th e r p a ra m e te rs are: .V = 2.

e = 12 m m . 21 = 44 m m . a- = 4 m m , = 244 m m . = 244 m m .

ts = 20 m m ...99

7.5 T h e in p u t im p ed an ce o f a printed m ean d er a n te n n a as a function of frequency w ith as a p aram eter. O th e r p a ra m e te rs .V = 2. e = 12 m m . 21 = 44 m m . a- = 4 mm. = 244 mm. iv^ = 244 m m . fr = 2.1. . 100 7.6 R eso n an t resistance. Rres (T^) of a p rin te d m ean d er d ip o le versus su b ­

s tr a te thickness. O th e r p a ra m ete rs of the a n te n n a are .V = 2.

e = 12 m m . 21 = 44 m m . a - 4 m m . £.< = 244 m m . a\, = 244 m m .

fr = 2 .1 ... 101 7.7 R eso n an t resistan ce. Rres (R) of a p rin te d m ean d er d ip o le versus sub­

s tr a te thickness. O th e r p a ra m ete rs of the a n te n n a are .V = 2.

e = 12 m m . 21 = 44 m m . a- = 4 m m . £^ = 244 m m . = 244 m m . Cr = 4 .0 ... 102 7.8 .r(/-plane p a tte rn o f a printed m ean d er an ten n a. P a ra m e te rs of the

a n te n n a are .V = 2. e = 12 mm . 21 — 44 mm. ir = 4 m m . £^ = 244 m m . a\, = 244 m m . 0 = 20 mm. a n d Cp = 1.0...103 7.9 //z-p lan e p a tte rn o f a printed m ean d er an ten n a. P a ra m e te rs of the

a n te n n a are .V = 2. e = 12 m m . 21 = 44 mm . ir = 4 m m . = 244

m m . u's = 244 m m . £, = 20 mm. a n d fp = 1.0...104 7.10 T //-plane p a tte rn o f a p rinted m ean d er an ten n a a t resonance (1.618

G H z). P a ra m e te rs o f th e an ten n a are: .V = 2. e = 12 m m . 21 = 44 m m . «• = 4 m m . £^ = 372 m m . u\, = 372 m m . 0 = 30 m m . and fp = 2 .1 ... 105

7.11 //c-plane p a tte rn of a printed m e an d e r a n te n n a at resonance ( 1.618 GH z). P a ra m e te rs of the a n te n n a are: .V = 2. e = 12 m m . 2/ = 44 m m . IV = 4 m m . = 372 m m . = 372 m m . = 30 m m . and

= 2 .1 106

7.12 .r;/-plane p a tte rn of a printed m e an d e r a n te n n a at resonance (1.73 G H z). P a ra m e ters of the a n te n n a are .V = 2. c = 12 m m . 21 = 44 m m . tc = 4 m m . I., = 372 m m . = 372 m m . ri = 40 m m . and Cr = 2.1... 106 7.13 yc-piane p a tte rn of a printed m e a n d e r a n te n n a an ten n a a t resonance

(1.73 G H z). P a ram eters of the a n te n n a are .V = 2. c = 12 mm .

21 = 44 m m . u- = 4 m m . = 372 m m . = 372 mm. = 40 mm. and = 2.1... 107 7.14 R esonant resistance. Rres (0.) o f a printed m eander dipole on a di­

electric half-space versus s u b s tra te thickness, O th er p aram eters of the a n te n n a are .V = 2. e = 12 m m . 21 = 44 mm. w = 4 mm .

Ls = 244 m m . = 244 mm ... = 2 .1 ... 108 7.15 .ry-plane p a tte rn of a printed m e an d e r dipole on a dielectric half­

space. P a ra m e ters of the a n te n n a are .V = 2. c = 12 m m . 21 = 44 m m . y = 4 m m . = 372 m m . = 372 m m . 0 = 20 m m . and Cr = 2.1...109 7.16 yz-plane p a tte rn of a printed m e an d e r dipole on a dielectric half­

space. P a ra m e ters of the a n te n n a are .V = 2. c = 12 m m . 21 = 44 m m . u- = 4 m m . = 372 m m . y« = 372 m m . t, = 20 m m . and

Cr = 2 . 1 ... 110

7.17 .ry-plane p a tte rn of a printed m e an d e r dipole on a dielectric half­ space. P a ra m e ters of the a n te n n a are .V = 2. c = 12 m m . 21 = 44 m m . y = 4 m m . = 372 m m . = 372 m m . 0 = 4: m m . an d = 2.1.110

L I S T OF FI G UR ES xv

7.18 yr-plane p a tte rn of a p rin ted m eander d ip o le on a dielectric lialf- space. P aram eters o f th e an ten n a are .V = 2. e = 12 m m , 21 = 44 mm, fi- = 4 m m . = 372 m m . ii\ = 372 m m . = 4 m m . an d Cr = 2.1.111 8.1 .A. dual m eander-sleeve a n te n n a ... 117 8.2 C om puted in pu t im ped an ce of the dual m eander-sleeve a n ten n a vs

frequency w ith the sleeve length / as a p aram eter; sleeve spacing

2 S = 3.2 cm ... 118

8.3 C om puted in p u t im p ed an ce of the dual m eander-sleeve a n ten n a vs

frequency for 3rd resonance around 1930 .MHz...119 8.4 M easured \ 'S \ \ ’R frequency characteristics o f the dual m eander-sleeve

antenna w ith sleeve le n g th I (cm) as the p a ra m e te r... 122 8.5 M easured H -plane p a tte rn of the dual m eander-sleeve a n ten n a at 890

MHz. Scale: lin e a r...122 8.6 M easured H -plane p a tte rn of the dual m eander-sleeve a n te n n a at 1890

MHz. Scale: lin e a r...123 8.7 M easured E -plane p a tte rn of the dual m eander-sleeve a n te n n a at 890

MHz. Scale: lin e a r...123 8.8 M easured E -plane p a tte rn of the dual m eander-sleeve a n ten n a at 1890

MHz. Scale: lin e a r...124 8.9 .A. com er reflector a n te n n a ...125 8.10 (a) M LBT dipole (T y p e A ), an d (h) M L B T dipole (T ype B )...128 8.11 C om puted in p u t im p ed an ce of the M LBT dip o le ( Type B) as a func­

tion of frequency (co m p u ted using NEC): w ire length. L^-ire = 2.95A. a = 120°. 21 = 0.28A. h = 0.48A. n = 0.0035A. and .V = 4 ...129 8.12 H orizontal-plane p a tte rn o f the M LBT d ip o le (Type B) a t 835 MHz

8.13 E levation-plane p a tte rn o f th e M LB T d ip o le (Type B) a t 835 M Hz (com puted using N E C )...130 8.14 H orizontal-plane p a tte rn of a plane sh eet reflector (co m p u ted using

N EC). T h e feed elem ents are a stra ig h t-w ire 0.44A dipole an d an M LB T dipole, respectively: S = 0.21A. H = 0.65A. L = 0.21A. a n d

a = 0.05A...1.30

8.15 R eturn loss vs frequency c h a ra c te ristic for a plane sheet reflector. Reflector p aram eters are: L = 0.21 A. H = 0.65A. 5 = 0.21 A. and

G = 0.05A. M LB T feed p a ra m e te rs are - a = 120°. 21 = 0.2SA. h = 0.48A. .V = 4. and a = 0.0036A. D ipole feed p a ra m ete rs are: h = 0.44A. and a = 0.0036A... 131

8.16 H orizontal-plane p a tte rn s o f a plane sh eet reflector (com p u ted using N EC ). T he feed elem ents are a stra ig h t-w ire 0.44A dipole an d an M LBT dipole, respectively. R eflector height [H ) for the dipole feed is 0.98A a n d th a t for the M L B T feed is 0.65A...133 8.17 H orizontal-plane p a tte rn s o f plane sh eet reflectors w ith M L B T and

straig h t-w ire dipole feeds (co m p u ted u sin g N E C ). Reflector p a ra m e ­ ters for th e dipole feed are: L = 0.31A. S = 0.21A. G = 0.05A. an d

H = 0.81 A. Reflector p a ra m e te rs for th e M L B T feed are: L = 0.21 A. S = 0.21 A. G = 0.05A. an d H = 0.65A...133

8.18 E levation-plane p a tte rn o f a plane sh eet reflector (com puted using N EC). T he feed elem ents are a stra ig h t-w ire dipole and an M L B T . respectively. S — 0.20A. G = 0.05A ... 134 8.19 .A. com pact plane sheet reflector fed by a n M L B T m onopole. P a ra m ­

eters of th e an ten n a are: h = 0.5A. a = 114°. I = 0.18A. h = 0.018A. and e = 0.074A. R adius o f w ire is 0.0005A... 135 8.20 Input im pedance of the co m p act plane sh eet reflector a n te n n a (com ­

L I S T O F F I G U R E S xvii

8.21 M easured R etu rn loss versus frequency ch aracteristics o f the co m p act p lan e sheet reflecto r... 137 8.22 H orizontal-plane p a tte rn of th e c o m p a c t plane sh eet reflector: solid

L ist o f T a b les

2.1 P a ra m e te rs a n d characteristics o f th e zigzag a n te n n a in [<]: see Fig.

2.2 16

2.2 C h a ra c te ristic s o f the m eander an ten n as o f [8]: see Fig. 2.3: I = 4.5

cm . a = 0.4 m m . and w = 0.3 mm. /u.,>f = 13.5 c m ... 19

3.1 Expressions for the param eters in eqns. ( 3.24)-( 3.27) ... 31 3.2 Expressions for th e param eters in eqns. (3.28)-(3.31 ) 32

5.1 P a ra m e te rs a n d characteristics of an .MLBT dipole: .V = 2. len g th of \vire= 32 cm . a n d radius of \vire=0.325 m m ... 68 5.2 P a ra m e te rs a n d characteristics of an M L B T dipole: .V = 4. length of

\vire= 32 cm . a n d radius of \vire=0.325 m m ... 69

7.1 R esonant resistan ce. Rres of a printed dipole a n te n n a as a function of s u b s tra te thickness: com parison w ith the resu lts in [34]. P aram eters of th e a n te n n a are: = 2.1. 21 = 44 m m . u’ = 4 m m . ;r, = 244 m m . an d Ls. = 244 m m ...97

XIX

A ck n o w led g em en ts

I wish to express m y deepest g ra titu d e to m y su p e r\iso r. Dr. S.S. S tuchly for his continuous encouragem ent an d guidance show n th ro u g h o u t this research w ork and the process of w riting th is m anuscript. T he valuable discussions th a t we have had for long hours in your office has essentially been the g uid in g light for this work. I can not th a n k you enough for your patience a n d forbearence w ith me. I also express my sincere g ra titu d e to D r. M .A. Stuchly for her valuable suggestions in relatio n to the w ritin g of this thesis. Special thanks are also due to Dr. M ichal O koniew ski for his valuable suggestions as related to my work on the p rin ted m eander an ten n as. Michal, I certain ly learnt a lot from m any of o u r enthusiastic yet realistic discussions in the lab. thanks.

I also wish to th a n k M r. K rzysztof C a p u ta for his day to day help in arran g in g the ex p erim en tal setu p a n d perform ing m easurem ents. Special th an k s go to M ark for m any of our in terestin g an d lively discussions as related to electro m ag n etics and philosophy, in general. T h a n k s to Elise. M ario. Dr. C hris. Bassey. and Mrs. Ewa Okoniewska. .A. h earty th a n k is also extended to all colleagues in the d e p artm en t from w hom I have received valuable suggestions and help. Special th an k s also go to my buddies like M ahm ood. S h a h a d a t. M ahboob. Intekhab. a n d M iah M ahm ood.

Finally. I wish to express my deepest g ra titu d e to my wife. .Ayesha. who has practically relieved me from m any of my fam ily responsibilities and thus has m ade it possible for me to finish w ritin g this thesis. She has been the in sp ira tio n and encouragem ent in this en lig h ten in g p ath of travel. I also th a n k my little ones. Orko and N azia for enduring th e lonely m om ents a n d for providing me w ith the energy and en th usiasm needed to accom plish this work.

To Nnzia. Orko. and A yesh a. the wonderful droplets o f rain in an am a zin y s^l t t i-

Chapter 1

I n tr o d u c tio n

1.1

M o tiv a tio n

W ith the recent advances in telecom m unications, th e need for sm a ll a n d low-profile a n ten n as has g re a tly increased. T h e greatest d em an d for these antennzis is from m obile ap p lic atio n s (vehicles) a n d from portable equipm ent. S m all an ten n as are also in d em an d for ap p licatio n s, such as in base statio n s, in sea m obiles, and in aircrafts.

D epending on ap p licatio n s, th e re are differences in term s of a n te n n a perform ance requirem ents. For exam ple, in a base statio n a n te n n a gain of 9 to 17 dB i m ay be required, w hereas in a personal com m unication serv ices ( PC S) h a n d se t a gain of 5 .1 dB i m ay be a d e q u a te in practice [2]. Similarly, for a base s ta tio n a n ten n a lin ear p o larizatio n is req u ired , while in land-m obile to sa te llite co m m u n icatio n s circular p o larizatio n is u sed [2]. However, am ong all these differences in a n te n n a perform ance requirem ents, a n te n n a s of sm all size are essential for such a p p lic a tio n s, for e ith e r

-A. sm all a n te n n a , as defined in th is d isse rta tio n , is one in w hich its largest dim en­ sion is sm all co m p ared to a sim ila r type of a conventional a n te n n a [3]. For in sta n ce, a m onopole a n te n n a sm aller th a n 0.25A is considered as a sm all a n te n n a [3].

It is well know n th a t, as th e size of the a n te n n a is reduced, th e efficiency tends to degrade a n d the b an d w id th becomes narro w er [4]. This h a p p en s because the input im p ed an ce o f a sm all a n te n n a consists o f a sm all resistan ce an d a relatively large c ap a c itan c e or inductance. Thus, for a size-reduced a n te n n a , m atch in g o f its input im p ed an ce w ith the c h arac te ristic im p ed an ce of the feeding tran sm issio n line is difficult. N onetheless, this m atch in g is im p o rta n t in order to m ake th e a n ten n a useful.

One of th e effective ways to accom plish efficient m atching is to a tta in self­ resonance of th e a n ten n a because such an a n te n n a is purely resistive at the frequency of o p eratio n a n d hence no co n ju g ate m atching circu it is necessary [4]. Perform ance of a self-resonant an ten n a is not degraded by th e losses in the m a tc h in g circu it. T he self-resonance o f a sm all a n ten n a can so m etim es be achieved by th e a n te n n a itself, or by ad d ing passive reactive loadings or activ e devices in the a n te n n a stru c tu re . For instance, a norm al mode helical a n ten n a (.NMH.A) is an a n te n n a th a t can a tta in self-resonance w ith o u t an a d d itio n a l m atch in g circu it.

O th er a n te n n a s th a t are self-resonant include the inverted-L a n te n n a (IL .\) [5]. the m eander a n te n n a [6]-[9]. th e zigzag a n te n n a [7]. the m ean d er zigzag m onopole an ten n a [10]. a n d the sinusoidal an ten n a [Il]-[15]. .All of the above can be m an ­ ufactured by b e n d in g wires or m e ta l ribbons according to the specific geom etrical configurations.

3

th a n straight-vvire half-wave dipoles while o p e ra tin g in dipole c o n fig u ratio n and are sm aller th an straight-w ire quarter-w ave m onopoles while o p e ra tin g in m onopole configuration. To m easure the extent of size re d u c tio n a term called th e shortening

ratio ( S R ) [7] is often used. T he S R is defined in percent ;is

S R = — — X 100 11.1)

O.oA

w here L is the length of a self-resonant bent dipole in w avelengths. T h e S R depends on th e geom etry an d param eters of th e an ten n a.

T h e self-resonant bent antennas have som e in h eren t d isadvantages, such as low reso n an t resistance (th e real p a rt o f the in p u t im p ed an ce a t reso n an ce), narrow b a n d w id th , and undesired cross-polarization. T h ese lim itatio n s m ay becom e severe when the a n ten n a param eters are a d ju sted to increase the slio rten in g ra tio . Thus, a know ledge of the characteristics of the self-resonant bent a n te n n a s is vital for th e ir design to be accurate and efficient. T his know ledge can only re su lt from the analyses of such an tennas. This d isse rta tio n u n d e rta k es the task of a n a ly z in g several ex istin g self-resonant bent antennas from a design point of view. T h e m otiv atio n b eh in d th is work is to fill the gap in th e present s ta te of knowledge p e rta in in g to the analyses and design of such an ten n as. .Antennas th a t are in v e stig ate d include (1) th e inverted-L an ten n a (ILA). (2) the m ean der-lin e dipole (M L D ) a n te n n a . (3) the m eander-line bow -tie (M LBT) a n ten n a . (4) th e d u a l m eander a n te n n a , and (5) the p rin ted m eander antenna.

T h e m ajo r c o n trib u tio n of th is d isse rta tio n in re la tio n to th e a n te n n a analysis, is th e developm ent o f sim p le and a c c u ra te an aly tica l m o d els to stu d y th e c h arac te ristic s o f several e x istin g self-resonant b ent an ten n as. T h e second m a jo r c o n trib u tio n in re la tio n to a n te n n a design, is th e design a n d dev elo pm en t o f a \rid e-b a n d d u a l m eander-sleeve a n te n n a for dual-freq u ency v e h ic u la r a p p lic atio n in th e personal co m m u n icatio n services (P C S ).

Specific c o n trib u tio n s o f th e d isse rta tio n a re as follows:

• D evelopm ent o f an a n a ly tic a l m odel to c o m p u te th e in p u t im p ed an ce o f an inverted-L a n te n n a (ILA ) u sin g the in d u ced E M F m eth o d .

• D evelopm ent o f sim ple a n a ly tic a l m odels for th e c o m p u ta tio n o f the rad iatio n fields of th e M LD and M L B T antennas.

• E stab lish m en t o f the c o rre la tio n betw een th e sh o rte n in g ra tio . S R . the res­ onant re sista n c e. Rr^s. a n d th e c ro ss-p o lariza tio n o f the self-resonant bent an ten n as w ith th eir p a ra m e te rs using N E C a n d an aly tica l techniques.

• C h a ra c te riz a tio n of a p la n a r p rin ted m e a n d e r a n te n n a using the Finite-D ifference T im e-D o m ain technique from a design p o in t o f view.

• Design an d developm ent of a w ide-band d u a l m eander-sleeve a n te n n a for a p ­ p lication as a vehicular a n te n n a in b o th b a n d s (824-894 MHz a n d 1850-1990 MHz) of th e personal co m m u n icatio n s e r \ic e s (P C S ). To desig n th e an ten n a num erical m o d elin g is p erfo rm ed using N E C a n d to confirm its p ro p er o p e ra ­ tion m easu rem en ts are co n d u cte d using a n H P 8720C vector netw ro k analyzer.

• Design o f a novel M L B T dipole as a feed to p lan e sheet reflectors for a p p lic a tio n in base s ta tio n s using N EC.

• Design an d developm ent of a com pact p la n e sheet reflector an ten n a th a t uses an M LB T m onopole as a feed using N EC a n d experim ental techniques.

1.3

O u tlin e

C h a p te r 2 presen ts th e definitions o f various a n te n n a p aram eters, such as ra d ia ­ tion p a tte rn , ra d ia tio n intensity, in p ut im p ed an ce, efficiency, gain and half-pow er b eam w idth. b an d w id th , field regions, and p o la riz a tio n . It also presents a b rie f re­ view on self-resonant bent an ten n as.

C h ap ter 3 describes th e analysis of the in v erted -L an ten n a (ILA ). .After a b rie f in trod u ction an d an overview of th e lite ra tu re th e current d istrib u tio n is given, followed by a d escrip tio n of th e induced EM F m e th o d . .An expression for the in p u t im pedance of th e ILA is derived. T he accu racy o f the newly derived ex p ressio n is verified by co m p arin g the resu lts com p uted using it w ith th a t from N EC [1] co m p u tatio n . Finally, th e adv an tag es and lim ita tio n s of the new form ulation are discussed.

C h ap ter 4 analyzes the m eander-line d ip o le (M LD ) antenna. .A review o f th e present sta te of know ledge is presented first, followed by an analysis of its in p u t im pedance. In p u t im ped an ce is com puted u sin g N EC. T he dependence of th e sho rten in g ratio . S R . th e resonant resistance. Rres- and the cro ss-p o larizatio n on the an ten n a p a ra m e te rs is d e m o n strated . In p u t im pedance graphs as a fun ctio n o f a n te n n a length w ith th ree different p aram eters a re also given.

ch aracteristics o f the M LD an ten n a. The cu rren t d istrib u tio n along the a n te n n a is described, followed by a d e tailed derivation of th e rad iatio n fields which are given in closed-form . T he a n a ly tic a l m odel is verified by com paring the results co m p u te d using it w ith th a t from N E C co m putation. R a d ia tio n ch aracteristics of the M LD an ten n a is discussed as fu n ctio n of various a n ten n a p aram eters. Finally, the c h a p te r is closed by a discussion o f th e analysis and resu lts.

C h ap ter 5 describes an analysis of the m eander-line bow -tie (M LB T) a n te n n a . Sim ilarly to th e MLD a n te n n a the input im pedance of this a n ten n a is also c o m p u te d using N EC. an d a n ten n a c h aracteristics such as. th e S R . Rres- and cro ss-p o larizatio n are correlated w ith the p a ra m e te rs of the a n ten n a. To stud y the rad iatio n c h a ra c ­ teristics a sim ple a n aly tical form ulation like the one for the MLD is presented. T he rad iatio n p a tte rn and gain of the an ten n a are co m p u ted and discussed as fu n ctio n o f its p aram eters.

C h ap ter 6 presents an in v estig atio n of the d u al m eander an ten n a. The a n te n n a is analyzed using NEC. In p u t im pedance, ra d ia tio n p a tte rn , and gain resu lts are presented. T h e advantages an d lim itatio n s of th e a n ten n a are also discussed.

C h ap ter 7 describes th e ch aracterizatio n of p la n ar printed m eander a n te n n a s using the Finite-D ifference T im e-D om ain ( F D T D ) technique. Two cases are c o n sid ­ ered: ( I) a n te n n a p rin ted on a grounded dielctric s u b stra te , and (2) an ten n a p rin te d on a dielectric half-space (n o g rou n d m etallization present). Input im pedances c o m ­ p u ted using a g ap -ex citatio n m odel are presented in graphical forms w ith b o th the dielectric c o n sta n t, a n d th e s u b stra te thickness. as param eters. T he d ep en d en ce o f the resonant resistance on th e su b strate thickness and the dielectric c o n sta n t, is d em o n strated . T he ra d ia tio n p a tte rn and g ain o f the printed m eander a n te n n a

are also p resen ted followed by a b rief discussion.

C h a p te r 8 exam ines th e p o te n tia l a p p lic atio n s of self-resonant bent a n te n n a s . F irst a d ual m eander-sleeve a n te n n a designed using NEC is d escrib ed . E x p e rim e n ta l results for th is a n te n n a are also presented. A pplication o f m eander-line b o w -tie (M LB T) a n te n n a s as feeds to p lan e sheet reflectors is discussed. Novel d esig n s are proposed for ap p lic atio n in base statio n s, followed by a discussion.

D e fin itio n s o f A n te n n a

P a r a m e te r s a n d L ite r a tu r e

R e v ie w

In th is ch apter first som e basic a n te n n a param eters, such as th e ra d ia tio n p a t­ te rn . rad iatio n in ten sity , directivity, in p u t im pedance, efficiency, g a in , b an d w id th , field regions, a n d p o la riz atio n are in tro d u ced . .A.11 definitions a n d m a th e m a tic a l ex­ pressions are ta k e n from [16] unless otherw ise m entioned. T h e d efin itio n s inside q u o ta tio n m arks com e from the IE E E S ta n d a rd D efinitions o f T e rm s for .Antennas (IE E E Std 145-1973) [17].

N ext a lite ra tu re review on self-resonant bent a n ten n a s is p re sen te d . T his in­ clu d es a brief d e sc rip tio n of previous work on the norm al m o d e helical a n ten n a (NMH.A). the invert ed-L a n ten n a (IL.A). the m eander an ten n a, th e zigzag an tenn a.

9 = 0

0=90

0=0

Figure 2.1: Spherical c o o rd in a te system , th e sin u so id al a n ten n a , and th e d u al m eander a n ten n a .

2.1

D e fin itio n o f P a ra m eters

2 .1 .1

R a d ia tio n P a tte r n

T h e radiation pattern of an a n te n n a is defined as the "graphical rep resen tatio n o f the ra d ia tio n p ro p erties of the a n te n n a as a function o f angular co o rd in a tes. In m ost cases, th e ra d ia tio n p a tte rn is d eterm in ed in th e far-fie Id region a n d is represented as a fu n ctio n of th e angular coordinates. R a d ia tio n properties include ra d ia tio n intensity, field stre n g th , phase o r polarization."

R a d ia tio n p a tte rn of an a n te n n a can be e ith e r a power pattern or a field pattern. R eferring to Fig. 2.1, a two dim ensional p a tte rn is o b tain ed by fixing one o f the angle

gives elevation patterns. Sim ilarly, keeping 6 c o n sta n t, and varying o (0 < o < 2 t ) gives azimuthal patterns.

T h e perform ance of an a n te n n a is often d escrib ed by using two principal plane p a tte rn s which are called the E-plane and the H-plane p a tte rn s. T h e E-plane p a t­ te rn for a linearly polarized a n te n n a is defined as "the plane c o n ta in in g the electric field vector an d th e direction of m axim um ra d ia tio n ." Sim ilarly, th e H-plane p a t­ te rn is defined as "th e plane con tain in g the m ag n etic field v ecto r an d th e direction of m axim um rad ia tio n ."

R ad iatio n p a tte rn can be broadly clssified as. isotropic, d ire c tio n a l, an d om nidi­ rectio n al. .An iso tro p ic ra d ia to r is defined as "a h y p o th etical a n te n n a having equal ra d ia tio n in all directions." .An exam ple of such a ra d ia to r is a p o in t source although physically u nrealizable, it can be a useful reference for expressing th e directive prop­ ertie s of practical antennas.

.A directional a n te n n a is one "having the p ro p e rty of ra d ia tin g o r receiving elec­ tro m ag n etic waves m ore effectively in some d ire c tio n s th an in o th e rs". .An omnidi­

rectional pattern is defined as one "having an essentially n o n d irectio n al p a tte rn in

a given plane of th e an ten n a an d a directional p a tte rn in any o rth o g o n a l plane."

2 .1 .2

R a d ia tio n In te n sity

Radiation intensity in a given direction is defined as "the pow er ra d ia te d from an

a n te n n a per un it solid angle. T h e unit solid angle dO. is given by sint9 dO do. R a d ia tio n in ten sity can be expressed as

CiO.o) ~ ^ [ |E o ( g .o ) |- -f- \ E J 6 . o ) \ - ] (2.1)

11

im pedance of the m edium . T h e to ta l power ra d ia te d by an a n te n n a is given by

Prad = [ [ U smO (16 d o (2.2)

70 Vo

2 .1 .3

D ir e c tiv ity

T h e directiv ity of an a n te n n a is defined as "the m a x im u m value o f th e directive gain in the direction of its m axim um value." Thus

D„ = i ^ (2 .3 )

^ rad

w here Do is the directivity. Umax is the m axim um o f th e ra d ia tio n intensity o b ta in e d from (2.1). a n d Prad is given by (2.2).

2 .1 .4

In p u t im p e d a n c e

-■\ntenna input im pedance is defined as "the im p e d a n ce presented by an a n te n n a a t its term in als or the ratio of the a p p ro p riate co m p o n en ts of the electric to m a g n e tic fields at a point." T he input im pedance consists o f a resistance a n d a reactan ce o f which the resistance com prises o f a rad iatio n re sistan ce. Rr a n d a loss re sista n c e.

Rf..

2 .1 .5

EflSciency

.\n te n n a efficiency accounts for th e losses a t the in p u t term in als o f the a n ten n a a n d w ith in the s tru c tu re o f the a n ten n a . Losses in a n a n ten n a m ay occur due to th e m ism atch betw een the feeding transm ission line a n d th e a n ten n a , and also d u e to co n d u cto r and dielectric losses.

In general, the overall efficiency m ay be w ritte n as e, = w here e, is th e to ta l overall efficiency, is the reflection efficiency an d is expressed as (1 — | r | - ) w here F is th e reflection coefficient. e<- is the co n d u ctio n efficiency, an d is th e dielectric efficiency.

Since an d ej can n ot he s e p a ra te d [16]. it is convenient to w rite c, = 1 —|r |~ ) w here e^d is th e a n te n n a ra d ia tio n efficiency. If a n a n te n n a has a loss resistance o f

Rc a n d a ra d ia tio n resistance o f Rr. e^d =

2 .1 .6

G a in a n d H a lf-P o w e r B e a m w id th

.A. usefid m easure to describe th e perform ance o f an a n ten n a is to specify its g ain.

Power gain of an a n ten n a in a specific direction is defined as " d r tim e s the ra tio o f

the ra d ia tio n in ten sity in th a t d ire c tio n to the net pow er accepted by the a n te n n a from a connected tra n sm itte r." T h e m axim um g a in is defined iis

6'o = CfDo- ( 2 . 4 )

"In a plane containing the d ire c tio n of the m axim u m of th e b e am , the angle betw een the d irectio n s in w hich th e rad iatio n in te n sity is o ne-h alf th e m axim um value o f the beam " is defined cis th e half-power beamwidth of an a n te n n a .

2 .1 .7

B a n d w id th

T h e b an d w id th of an a n ten n a c a n be defined as " th e range of frequencies w ith in which the perform ance of th e a n te n n a , w ith respect to som e c h arac te ristic s, conform s to a specified sta n d a rd ."

13

gain, efficiency, p o larizatio n , b eam direction etc. T h e term ran g e of frequencies' may m ean the ratio betw een the u p p e r and the lower frequencies for a b ro a d b a n d an tenna. For narrow band an ten n a s, the bandw idth is usually expressed as a p e r­ cent of the center frequency. T h us for a broadband a n te n n a D \ V = a n d for a narrow band an ten n a D \ V = x 100 where / f . fr.- an d f r are the u p p er, lower, and the center frequencies.

2.1.8

F ield R e g io n s

The space surrounding an a n ten n a is usually subdivided into th ree regions. T hese regions and their o u te r lim it are discussed below.

R e a c tiv e N e a r F ie ld R e g io n T h is region is defined as " th a t region of th e field im m ediately su rro u n d in g the a n te n n a where the reactive field p red o m in ates." T he o uter b o u n d ary of this region for all but sm all a n te n n a s is specified by

R = 0 . 6 2 wher e A is the w avelength and D is the largest dim ension o f the

antenna, and R is the d ista n c e from the surface of th e a n te n n a to th e o u te r boundary.

R a d i a t i n g N e a r F i e l d T his region is defined as " th a t region of the field o f an an ten n a betw een the reactive near-field region an d the far-field region w herein the angular field d istrib u tio n predom inates and w herein th e an g u lar field d is­ trib u tion is dep en d en t upon th e distance from th e a n te n n a . For an a n te n n a focused at infinity, the ra d ia tin g n ear field region is so m etim es referred to as the Fresnel region on the basis of analog}' to o p tical technolog}'. If the a n te n n a has a m axim um dim ension w hich is ver}' sm all co m p ared to th e w avelength, this field region m ay not ex ist." T he outer boundar}' of th is region for m ost

an ten n as is specified by Ro =

F a r-fie ld r e g io n T h is region is defined as "that region of th e field o f an a n ten n a where the a n g u la r field d istrib u tio n is essentially indep en d ent of th e distan ce from th e a n te n n a . If th e antenna has a m axim um overall d im en sio n D. the far-field region is com m only taken to exist at distan ces g re a te r th a n from the a n ten n a . A b ein g th e wavelength. For an a n te n n a focused a t infinity, the far-field region is so m etim es referred to as the Fraunhofer region on th e basis of analog}' to o p tic a l term inolog}."

2.1.9

P o la r iz a tio n

The polarization o f a radiated wave is defined as “th a t p ro p e rty o f a ra d ia te d elec­ trom agnetic wave d e sc rib in g th e tim e-var\'ing direction and relative m a g n itu d e of the electric field vector; specifically, the figure traced as a function o f tim e by the extrem ity of the v e cto r a t a fixed location in space, and th e sense in w hich it is traced, as observed a lo n g the direction of propagation."

P olarization m ay b e classified as linear, circular, and elliptical. Let us consider the in stan tan eo u s e lec tric field o f a plane wave, travelling in the positive z-direction. [18]

S = dj-EJocos(.i,'t — .ic -I- Ox) -f cos(w’t — .iz 4- Oy). (2.5) The m agnetic field is re la te d to the electric field of (2.5) by th e in trin sic im p ed an ce of the m edium .

L in e a r P o l a r i z a t i o n A tim e-harm onic field is linearly polarized a t a given point in space if the elec tric (or m agnetic) field vector at th a t point is alw ays oriented

15

along the sam e straig h t line a t ever}' in stan t o f tim e. T h is can h a p p e n if th e field vector (electric or m a g n etic) possesses (a) o n ly one co m p o n en t or (h) two orthogonal lin early po larized co m p o n en ts th a t a re in tim e p h ase or 180° out o f phase.

C ircu lar P o la r iz a tio n C ircu lar p o la riz atio n can be achieved only w hen th e m a g ­ nitudes of th e two co m p o n en ts in Eqn. (2.5) are th e sam e an d th e tim e -p h a se difference betw een them is o d d m ultiples of ~j'2.

E llip tic a l P o la r iz a tio n E llip tical p o larizatio n can be o b tain ed (a) w hen th e m a g ­ nitudes of th e field co m p o n en ts in (2.5) are n o t equal and th e tim e phase- difference betw een the two co m p o n en ts in (2.5) is an odd m u ltip le of ~j'l or (b) when the tim e-phase difference betw een th e two co m po n en ts is not equ al to m ultiples o f ~ / 2 irresp ectiv e of th e ir m ag n itu d es.

2 .2

R ev ie w o f L itera tu re

A lth o u g h a self-resonant bent a n te n n a can be o f v irtu a lly any im agin ab le g eo m etrical sh a p e , the ones th a t are m entioned an d stu d ie d in th e lite ra tu re include the n o rm al m o d e helical a n ten n a ( XM HA). th e invert ed-L a n te n n a (IL A ), the m e a n d e r a n te n n a , th e zigzag an ten n a, th e sinusoidal a n te n n a , and the d u a l m eander a n te n n a . In the following we provide a brief acco u n t of th e previous w ork as related to th e a n aly sis a n d design of these an tennas.

T h e norm al m ode helical a n te n n a (N M H A ) is an a n te n n a w hich ra d ia te s in the d ire c tio n norm al to th e helical ax is. T h e ra d ia tio n p a tte r n of a sm all N M H A is th e sam e as th a t of a sm all stra ig h t-w ire dipole [19]. T h e s tu d y of th is a n te n n a d a te s

Table 2.1: P a ra m e te rs an d ch arac te ristic s of the zigzag a n te n n a in [7]: see Fig. 2.2. 2Ia-,rc (A) 2Z « r(A ) r (°) Rres (H SR (%) G ain (dB i) H P B W (M

0.50 0.45 129 65 10 2.1 ± 8 0

0.58 0.38 81 46 24 2.0 ± 8 2

0.67 0.33 59 37 34 1.95 ± 8 4

back to th e 1940's w hen K rau s [19] first introduced th e helical an ten n a. However, due to its a ttra c tiv e self-resonance property, and sm all size, th e NMHA has b een found useful for a p p lic a tio n in m obile com m unications and hence has been s tu d ie d quite extensively [19]. [4].

T he inverted-L a n te n n a (ILA ) is a low-profile a n te n n a th a t has found a p p lic a tio n in m issile telem etn.', an d rockets [5]. .-Vs the nam e suggests th e a n ten n a co n sists of a sm all vertical c o n d u c to r on top of which there is a horizontal co nductor. In th e lite ra tu re th e IL.A. h a s been stu d ie d using both a n aly tica l and num erical techniques. Closed-form expressions for the ra d ia tio n p a tte rn of this a n te n n a are available in [4]. K ing and H arrison Jr. [5] have presented an analysis for co m p u tin g th e in p u t im pedance of the ILA . T h e analysis is based on tran sm issio n line theor>' a n d is restricted to the s itu a tio n kh <C 1 w here k is the wave num ber an d h is the le n g th o f the vertical section o f the ILA. Jam e s et al. [4] have presented M ethod of M o m en ts solution for the ILA using piecewise sinusoidal reactio n form ulation. W unsch a n d Hu [20] have derived a closed-form expression for the in p u t im pedance of th e ILA . This expression is re stric te d to an ten n a s th a t are electrically sm all.

N akano et al. [7] describ ed a zigzag and a m eander an ten n a. T h e zigzag a n te n n a described in [7] is show n in Fig. 2.2a. Its geom etrical p a ra m ete rs are e an d r. T h e an ten n a was an aly zed in [7] using the M ethod of M om ents (M oM ) which was verified by ex p erim en tal re su lts. R esu lts from [7] are su m m arized in T able 2.1.

I L

. . . ©

-(b)

■ in ...

F igure 2.2: (a) .A. zigzag, a n d (b) a m ean d er an ten n a [/]

From Table 2.1 it can be seen th a t as r decreases the S R increases and Rres decreases. For a n S R o f as much as 34%. the Rres is ab o u t 37 V.. T h e gain o f the a n ten n a is close to the gain o f a straigh t-w ire half-wave d ip o le o f 2.16 dB i. T he half-pow er b e am w id th . HPBW" is also close to th a t of a stra ig h t-w ire half-wave dipole of 78°. However, th e sam e can n o t be said for the resonant resistance. For instance, the value o f th e resonant resistan ce for a zigzag a n te n n a is a b o u t 37 fl for a sh o rten in g ra tio o f 34%. which is significantly sm aller th a n the reso n an t resistance of a straig h t-w ire half-w ave dipole o f a b o u t 70 fl. T h e m ean d er d ip o le o f Fig. 2.2b resonates at a le n g th of 2Lax = 0.35A (where 2I^.,re = 0.70A. c = 0.0133A) w ith

Rres = 43 n an d S R of 30%. The half-pow er beam w idth (H P B W ) a n d th e gain are

± 8 4 °. and 1.95 d B i.

H ashed and T ai [8] introduced a n o th e r class o f m ean d er a n te n n a s which are shown in Fig. 2.3. T h e shortening fa c to r defined in [9] sta te s th a t if a b ent a n ten n a of len g th I and a con v en tio n al a n ten n a o f length Iq have the sam e reson an t frequency.

I

(a)

(b)

(c)

A .

Figure 2.3: Several m eander an ten n as (a) N = 2 . (h) X = 4 . (c) X=G [8].

the size re d u c tio n (SR ) is.

— I

In X 1 0 0 9 f (2.6)

w hen b o th th e a n te n n a s are m anufactured from th e sam e d ia m e te r wire. T he size red u ctio n for th ese an ten n as [as defined in (2.6)] depends p rim arily on the num ber of sections p er w avelength (X) and the w idth o f th e rectan g id ar loops (fc). Some resu lts from [8] a re sum m arized in T able 2.2.

.\cco rd in g to th e num erical resu lts of T able 2.2 a size red u ctio n o f 36% or m ore m eans th a t th e reso n an t resistance is 20.7 Q o r sm aller w hereas th e ex p erim en tal resu lts show th a t for a size reduction of 29% or m ore. Rres is 22 Q o r sm aller. D espite the differences in the num erical and ex p erim en tal results, it m ay be p red icted from T able 2.2 th a t if som eone intends to m an u factu re th e dipole c o u n te rp a rt of Fig. 2.3.

19

T ab le 2.2: C h arac te ristic s of th e m eander a n te n n a s o f [8|: see Fig. 2.3: I = 4.5 cm .

a = 0.4 m m . a n d w = 0.3 m m . = 13.5 cm .

P a ra m e ters SR(% ) SR(%) R r e s (H) R r e s (H)

(N um erical) (E x p erim en tal) ( N um erical) ( E x p erim en tal)

.\' = 2 41 41 11.5 13

.V = 6 37 33 19.3 21

.V = 10 36 29 20.7 22

an d is in terested to achieve Rres = 50 Q. th e size reduction m ay be less th an 30%. W ong a n d K in g [10] proposed a h eight-reduced m eander zigzag m onopole con­ figuration th a t co n sists of a d riv en elem ent fed from a coaxial line a n d one or m ore closely spaced o p en sleeves. B o th the d riv en elem ents and th e o p en sleeves were m ad e from 2 .0 m m d ia m e ter w ire. T he d u a l zigzag con fig u ratio n was chosen to reduce cro ss-po larizatio n . T h e a n ten n a was designed to o p e ra te in the frequency range of 250-750 .MHz. T he height and w id th o f the an ten n a w ere 13.97 and 11.43 cm . T h ro u g h o u t th e frequency range of 250-750 MHz. the \'S W 'R was less th a n 5.5:1. The ra d ia tio n p a tte rn o f th e h eight-reduced m eander zigzag m onopole on a g ro u n d plane o f d ia m e te r 121.9 cm was s im ila r to the p a tte rn o f a straig h t-w ire q uarter-w ave m onopole u p to 500 MHz. T h e p a tte rn showed sm a ll side lobes for frequencies above 500 MHz.

T h e in p ut (\'S W ’R b a n d w id th ) and the ra d ia tio n (p a tte rn a n d g ain ) ch aracter­ istics of two classes of bent w ire an ten n as e.g. th e sinusoidal a n d th e m eander were m easured e x p erim en tally as fu n ctio n of th e ir sh o rte n in g ra tio s (S R 's) in [13]. T he design variables for these configurations were defined and th e n c o rre la ted w ith the a n te n n a c h arac te ristic s. T he resu lts of the in p u t c h arac te ristic s show th a t for b o th ty p es of a n te n n a s th e b a n d w id th becom es n arro w er as the sh o rte n in g ra tio increases. For a sh o rten in g ra tio larger th a n 30%. V '5 U '/? > 2.0. However, it was found th a t

for the sam e sh o rte n in g ratio the sinusoidal a n te n n a h a d b e tte r \ ’S \\'R frequency ch aracteristics th a n th e m eander.

M easured ra d ia tio n p a tte rn s ( b o th H -plane an d E -p lan e ) of both classes o f amten- nas show th a t these are sim ilar to the p a tte rn of a s tra ig h t quarter-w ave m onopole. T he half-pow er b eam w id th 's (HPBW "s) of these b en t a n te n n a s are som ew hat wider (42° — 44°) th a n th a t of a stra ig h t quarter-w ave m on o p o le (39°). The gain of the bent a n te n n a was found to be decreasing w ith th e increase in SR (4.96-3.84 dBi for a sinusoidal w hen th e SR increased from 18% to 38.82% ). The gain o f a bent a n te n n a is found to be sm aller th a n a stra ig h t cjuarter-w ave m onopole (Ô.1 dB i).

\'u a n d .Tu [21] p roposed two m eander dipole a n te n n a s for possible ap p licatio n in personal co m m u n icatio n netw ork (P C N ) h andsets. B o th th e anten nas were printed on D uroid 6010 (e^ = 10.2: thickness= 0.064 cm ) s u b stra te . T h e ground co n d u cto r of the s u b stra te was etch ed off. For fu rth er size red u ctio n , th e second m eander an ten n a was covered by a n o th e r layer of dielectric. T h e len g th o f th e first an ten n a was 11.2 cm at 880 MHz. T h e size red u ctio n and b a n d w id th o f th is a n te n n a were 34.1% and 7.3% respectively. T h e length of the second m ean d er was 9.2 cm with size reduction and b a n d w id th of 45.9% an d 5.0% respectively. To calc u la te size reduction (1.1) was used.

N akano et al. [22] stu d ie d a printed zigzag dipole using th e M ethod of M om ents (M oM ) [22]. T h e a n te n n a geom etry' w ithout the s u b s tra te is shown in Fig. 2.2a. It was assum ed th a t the a n te n n a consisted of a th in w ire printed on a grounded dielectric s u b stra te o f infinite ex ten t. T he thickness o f th e su b stra te was O.IOI6A0. T h e resonant resistan ce and th e sh o rten in g ra tio for th is a n ten n a were 20 Q and 30%. respectively. T h e cro ss-p o larizatio n was found to be below -45 dB.

21

T h e geom et r}' o f th e a n te n n a w ith o u t th e su b strate is show n in Fig. 2.2b. Sim ilarly to th e analysis given in [2 2] it was assu m ed th a t the a n te n n a consisted o f a th in wire p rin ted on a gro u nd ed dielectric s u b s tra te of infinite ex ten t. The thickness of the s u b stra te was O.IOIGAq. T h e rad iu s o f th e wire was 10“ 'Ao and the elem en t length of the m eander a n te n n a e was taken to be 0.0133Ao [Fig. 2.2b|. The in p u t im pedance of th e printed m ean d er a n ten n a was co m pu ted w ith th e dielectric c o n sta n t of the su b stra te . Cr as a p a ra m ete r. For f.r = 4.0. and 6.05 th e resonant resistan ces were 13 a n d 32 Q. respectively. For f.r = 2.0. and 6.05 th e sh o rten in g ratio s w ere 47 and

C h a p te r 3

T h e In v e r t ed -L A n te n n a

E lectrically sm all m onopoles have draw n th e interests of a n te n n a d esig n ers over the decades due to th eir size an d conform ity w ith geom etries like a irc ra fts, ro ck ets, missiles etc. Sm all m onopoles are also used in low frequencies w hen the size o f a resonant quarter-w ave m on o p o le becomes p ro h ib itiv ely large.

In the lossless case, th e in p u t im pedance of a sm all m onopole c o n sists o f a sm all rad iatio n resistan ce an d a large cap acitiv e reactance. Such an a n te n n a is inefficient an d is difficult to m a tc h to sta n d a rd transm ission lines, w ith c h a ra c te ris tic im pedances of 50 and 75 Q.

The sm all ra d ia tio n resistan ce m ay be increased and the cap acitiv e re a c ta n c e can be reduced o r cancelled en tirely by ad d in g an add itio n al segm ent of c o n d u c to r of length L as shown in Fig. 3.1. The a n te n n a shown in Fig. 3.1 is c a lle d an inverted-L a n ten n a (ILA ) [5]. It consists of a vertical elem ent o f height h a n d a horizontal elem ent of le n g th L.

V 7 7 7 7 7 7 7

F igure 3.1: .A.n in v erted -L m onopole.

/

2h

h-F igure 3.2: .A.n in v e rte d -L dipole

23

on tran sm issio n line theop.'. T h e analysis is re s tric te d to the s itu a tio n where kh <c 1 where k = w ith A being th e o p e ra tin g w avelength. Fujim oto et al. [4] p resen ted a M oment M eth o d solution for the in p u t im p e d a n ce of the a n te n n a using piecew ise sinusoidal re a c tio n form ulation. T h e MoM so lu tio n , however, n eeds m ore c o m p u ta ­ tional power since it deals w ith the c o m p u ta tio n o f the elem ents o f th e generalized im pedance m a trix , m a trix sto rag e, an d m atrix inversion. W unsch a n d Hu [20] p ro ­ posed a closed form expression for th e input im p e d a n c e of the ILA solving Pockling- to n 's integral eq u atio n using a point m atching schem e. The closed form expression presented in [20] is restricted to th e situ a tio n w here kh < 0.5 a n d k L < 0.5.

In this thesis we derive an expression for th e in p u t im pedance o f an ILA u sin g the induced E M F m ethod [24]. To o b ta in this expression, a sinu so id al d is trib u tio n o f current th a t d ro p s to zero a t th e a n te n n a end is assu m e d and closed-form expressions

for the near-fields of the a n ten n a are derived. The closed-form expressions are then used to derive an expression for the input im pedance o f th e an ten n a. Z . T h e expression for Z contains integrals th a t can be easily ev alu ated using a s u ita b le num erical in te g ra tio n routine.

W hile th e transm ission line m odel of King and H arrisson .Ir. [5] is re s tric te d to kh <C 1. a n d the closed-form expression o f W unsh and Hu [20] is ap p licab le to an ten n as w ith k L < 0.5 and kh < 0.5. our form ulation gives acc u ra te re su lts as long as kl = k{h L) < 2 .1 . T h is allows us a m uch w ider range o f an ten n a le n g th s

for which th e input im pedance can be com puted. Thus, o u r form ulation is not lim ited to sm a ll and nonresonant antennas only but it can c o m p u te the im p ed an ces o f resonant a n te n n a s as well.

To verify th e accuracy of the proposed form ulation, the in p u t im pedance co m ­ puted using it is also com pared w ith th at com p u ted using .\'EC [ij.

3.1

C u rren t D istrib u tio n

We consider th e dipole mode of th e inverted-L a n ten n a shown in Fig. 3.2. .Assuming the IL.A [Fig. 3.1] to be rad iatin g on a perfectly conducting infinite ground p lan e, its input im p ed an ce should correspond to half the im pedance of the a n ten n a show n in Fig. 3.2. W h a t follows now is a derivation for the input im p ed an ce of an IL.A b ased on the d ip o le m ode of the inverted-L antenna, which consists o f four wire e lem en ts [Fig. 3.2]. W e call the lower and u p p e r horizontal elem ents a n te n n a elem ents 1 an d 4. and the low er and u pper vertical elem ents a n ten n a elem ents 2 a n d 3 respectively.

T he a n te n n a is fed by a d elta-g ap voltage and is m a n u factu red from a w ire th a t is thin and p erfectly conducting. .Assuming a sinusoidal d istrib u tio n of current alo n g