185

APPENDICES

A- FABRICATED PROPOSED ANTENNAS

Figure (a) Fabricated rectangular patch antenna

Figure (b) Fabricated square patch antenna

186

Figure (c) Fabricated hexagonal patch antenna

Figure (d) Fabricated pentagonal patch antenna

187

Figure (e) Fabricated fractal shaped pentagonal patch antenna

Figure (f) Measurement of pentagonal patch antenna using Vector Network Analyzer

(VNA)

188

Figure (g) Measurement of dielectric loaded pentagonal patch antenna using Vector

Network Analyzer (VNA)

189

B- IEEE FREQUENCY BAND DESIGNATIONS

RADIO BAND DESIGNATIONS

Frequency Wavelength Radio Band designation

30 - 300 Hz 10 - 1Mm ELF (extremely low frequency)

300 - 3000 Hz 1000 - 100 km ULF (ultra low frequency)

3 - 30 kHz 100 - 10 km VLF (very low frequency)

30 - 300 kHz 10 - 1 km LF (low frequency)

300 - 3000 kHz 1000 - 100 m MF (medium frequency)

3 - 30 MHz 100 - 10 m HF (high frequency)

30 - 300 MHz 10 - 1 m VHF (very high frequency)

300 - 3000 MHz 100 - 10 cm UHF (ultra high frequency)

3 - 30 GHz 10 - 1 cm SHF (super high frequency)

30 - 300 GHz 10 - 1 mm EHF (extremely high frequency)

IEEE RADAR BAND DESIGNATIONS

Frequency Wavelength

IEEE Radar Band

designation

1 - 2 GHz 30 - 15 cm L Band

2 - 4 GHz 15 - 7.5 cm S Band

4 - 8 GHz 7.5 - 3.75 cm C Band

8 - 12 GHz 3.75 - 2.50 cm X Band

12 - 18 GHz 2.5 - 1.67 cm Ku Band

18 - 27 GHz 1.67 - 1.11 cm K Band

27 - 40 GHz 11.1 - 7.5 mm Ka Band

40 - 75 GHz -- V Band

75 - 110 GHz --- W Band

110 - 300 GHz --- mm Band

300 - 3000 GHz --- u mm Band

190

SATELLITE TVRO BAND DESIGNATIONS

Frequency Satellite TVRO Band

1700 - 3000 MHz S-Band

3700 - 4200 MHz C-Band

10.9 - 11.75 GHz Ku1-Band

11.75 - 12.5 GHz Ku2-Band (DBS)

12.5 - 12.75 GHz Ku3-Band

18.0 - 20.0 GHz Ka-Band

MILITARY ELECTRONIC COUNTERMEASURES BAND DESIGNATIONS

Frequency

IEEE Radar Band

designation

30 - 250 MHz A Band

250 - 500 MHz B Band

500 - 1,000 MHz C Band

1 - 2 GHz D Band

2 - 3 GHz E Band

3 - 4 GHz F Band

4 - 6 GHz G Band

6 - 8 GHz H Band

8 - 10 GHz I Band

10 - 20 GHz J Band

20 - 40 GHz K Band

40 - 60 GHz L Band

60 - 100 GHz M Band

191

TRAFFIC RADAR FREQUENCIES

Traffic Radar Frequency Bands

Band Frequency Wavelength Notes

S 2.455 GHz 4.8 in

12 cm obsolete

X 10.525 GHz ±25 MHz 1.1 in

2.8 cm one 50 MHz channel

Ku 13.450 GHz 0.88 in

2.2 cm no known systems

K 24.125 GHz ±100

MHz

0.49 in

1.2 cm

one 200 MHz channel

Europe and some US

systems

K 24.150 GHz ±100

MHz

0.49 in

1.2 cm one 200 MHz channel

Ka 33.4 - 36.0 GHz 0.35 - 0.33 in

9 - 8.3 mm 13 channels; 200 MHz/ch

IR --

Infrared 332 THz 904 nm Laser Radar

192

C- TABLES OF RELATIVE PERMITTIVITY AND LOSS TANGENT

Solids

Material Remarks t/°C f r´ 104 × tan δ

Cellulose (see also

paper)

Cellophane . . . . . . unplasticized 20 50 Hz/1 MHz 7.6/6.7 100/650

−30/70 50 Hz 7.2/8.0 100/150

Paper fibres . . . . . calculated 20 50 Hz 6.5 50

Ceramics

Alumina . . . . . . . pure 20/100 50 Hz/1 MHz 8.5 20/5

pure, porosity

1% 20 1 MHz 10.8

Calcium titanate . . a = −200 20 1 MHz 150 3

Lead zirconate . . . a = +140 20 1 MHz 110 30

Magnesium titanate .

20/150 50 Hz/1 MHz 14 1/4

Porcelain . . . . . . h.v. electrical 20/100 50 Hz/1 MHz 5.5 300/80

Rutile . . . . . . . a = −80 20 1 MHz/1 GHz 80 3/8

a = −40 20 1 MHz/1 GHz 40 15/30

a = −2 20

1 MHz/100

MHz 12 30

a = +6 20

1 MHz/100

MHz 15 1

Steatite . . . . . . . a = +13 20 1 MHz/1 GHz 6 20

(low loss) . . . . . a = +13 20 1 MHz/1 GHz 6 2

Strontium titanate . . a = −300 20 1 MHz 200 5

Strontium zirconate . a = +12 20 1 MHz 38 3

Crystals (single,

inorganic)

Alkali halides

LiF . . . . . . .

20/25 1 kHz/10

GHz 8.9/9.1 2

LiCl . . . . . . .

20 1 kHz/1 MHz 11.8/11.0

LiBr . . . . . . .

20 1 kHz/1 MHz 13.2/12.1

LiI . . . . . . .

20 1 kHz/1 MHz 16.8/11.0

NaF . . . . . . .

20 1 kHz/1 MHz 5.1/6.0

NaCl . . . . . . .

20/25 1 kHz/10

GHz 6.1/5.9 5/1

NaBr . . . . . . .

20 1 kHz/1 MHz 6.5/6.0

NaI . . . . . . .

20 1 kHz/1 MHz 7.3/6.6

KF . . . . . . .

20 1 kHz/1 MHz 5.3/6.0

193

KCl . . . . . . .

20 1 kHz/10

GHz 4.9/4.8

KBr . . . . . . .

20/25 1 kHz/10

GHz 5.0/4.9 2/7

KI . . . . . . .

20 1 kHz/1 MHz 5.1/5.0

RbF . . . . . . .

20 1 kHz 6.5

RbCl . . . . . . . .

20 1 kHz 4.9

RbBr . . . . . . . .

20 1 kHz 4.9

RbI . . . . . . . .

20 1 kHz 4.9

Calcite . . . . . . . . CaCO3 20 1 kHz/10 kHz 8.5

|| 20 1 kHz/10 kHz 8.0

Diamond . . . . . . C 20 500 Hz/100

MHz 5.7/5.5

Fluorite . . . . . . . CaF2 20 10 kHz/2

MHz 7.4/6.8

Gallium Arsenide . . .

20 1 kHz 12

Germanium . . . . .

20 1 kHz 16.3

Iodine . . . . . . .

17/22 100 MHz 4.0

Mica, muscovite (best)

20/100 50 Hz/100

MHz 7.0 10/2

Periclase . . . . . . MgO 25 100 Hz/100

MHz 9.7 3

Quartz . . . . . . . SiO2 20/25 1 kHz/35

MHz 4.43/4.43 −/0.4

|| 20/25

1 kHz/35

MHz 4.63/4.63 −/0.3

Ruby . . . . . . . . Al2O3 17/22 10 kHz 13.3

17/22 10 kHz 11.3

Rutile . . . . . . . . TiO2 20 50 Hz/100

MHz 86 100/2

|| 17/22 100 MHz 170

Sapphire . . . . . . Al2O3 20 50 Hz/1 GHz 9.4 2

|| 20 50 Hz/1 GHz 11.6 2

Selenium . . . . . .

17/22 100 MHz 6.6

Silicon . . . . . . .

20 1 kHz 11.7

Sulphur . . . . . . . rhombic

(100) 25 1 kHz 3.8 5

(010) 25 1 kHz 4.0 5

(001) 25 1 kHz 4.4 5

Urea . . . . . . . CO(NH2)2 17/22 400 MHz 3.5

194

Zircon . . . . . . . ZrSiO4 , || 17/22 100 MHz 12

Glasses

Borosilicate . . . . . normal 20 1 kHz/1 MHz 5.3 50/40

low alkali 20 1 MHz 5 30

very low

alkali 20

50 Hz/100

MHz 4 15/5

Fused quartz . . . .

20/150 50 Hz/100

MHz 3.8 10/1

Lead . . . . . . .

20 1 kHz/1 MHz 6.9 17/13

Soda . . . . . . . average 20 1 MHz/100

MHz 7.5 100/80

Minerals

Amber . . . . . . .

20 1 MHz/3 GHz 2.8/2.6 2/90

Asbestos (chrysotile) purified, 50%

R.H. 25 50 Hz/1 MHz 5.8/3.1 1800/250

board 20 1 MHz 3 2200

Bitumen . . . . . . . Gilsonite 25 50 Hz/100

MHz 2.7/2.55 60/10

20 1 kHz 3.5 300

Granite . . . . . . .

20 1 MHz 8

Gypsum . . . . . . .

20 10 kHz 5.7

Marble . . . . . . . pure dry 20 1 MHz 8 400

Sand . . . . . . . . dry 20 1 MHz 2.5

15% water 20 1 MHz 9

Sandstone . . . . . .

20 1 MHz 10

Soil . . . . . . . . . dry 20 1 MHz 3

moist 20 1 MHz 10

Sulphur . . . . . . . cast 20 3 GHz/10

GHz 3.4 7/14

Paper and Pressboard

(see also cellulose)

Unimpregnated, dry

Kraft (tissue) . . . d = 0.8 20/90 1 kHz 1.8 10/15

d = 1.2 20/90 1 kHz 3.0 25/35

Rag (cotton) . . . d = 0.6 20/90 50 Hz/50 kHz 1.7 8/65

Impregnated, mineral oil

(εr´ = 2.2)

Kraft (tissue) . . . d = 0.9 20 50 Hz 3.6 22

d = 1.1 20 50 Hz 4.3 27

Rag (cotton) . . . d = 0.9 20 50 Hz 3.5 13

195

d = 1.1 20 50 Hz 4.2 18

Impregnated

(Pentachlordiphenyl) .

Kraft (tissue) d = 0.9 20 50 Hz 5.7 33

d = 1.1 20 50 Hz 6.0 39

Fibre . . . . . . . .

20 1 MHz 4.5 500

Pressboard . . . . . dry d = 0.8 20 50 Hz 3.2 80

Plastics (non-polar,

synthetic)

Poly-

ethylene . . . .

20 50 Hz/1 GHz 2.3 2/3

isobutylene . . .

20 50 Hz/3 GHz 2.2 2/5

4-methylpentene

(TPX) . . . .

20 100 Hz/10

kHz 2.1 2/1

(dimethyl)

phenyloxide (PPO)

25 100 Hz/1

MHz 2.6 4/7

propylene . . . .

20 50 Hz/1 MHz 2.2 5

styrene . . . . .

20 50 Hz/1 GHz 2.6 2/5

tetrafluoroethylene

(PTFE) . . . . teflon 20 50 Hz/3 GHz 2.1 2

Plastics (polar,

synthetic)

Poly-

amides . . . . . typical Nylon 20 50 Hz/100

MHz 4/3 200

carbonates . . . typical 20 50 Hz/1 MHz 3.2/3.0 10/100

ethyleneterephthalate

20 50 Hz/100

MHz 3.2/2.9 20/150

imides . . . . . typical 20 1 MHz 3.4

methylmethacrylate

20 50 Hz/100

MHz 3.4/2.6 600/60

vinylcarbazole . .

20 50 Hz/100

MHz 2.8 5/10

vinylchloride . . . unplasticized 20 50 Hz/100

MHz 3.2/2.8 200/100

Plastics (miscellaneous)

Aniline resin unfilled 20 3 GHz 3.5 500

paper filled 20 1 MHz/1 GHz 5/4 600/300

196

100 1 MHz 6 800

Cellulose acetate

20 1 MHz/1 GHz 3.5 300/400

Cellulose triacetate

20 50 Hz/100

MHz 3.8/3.2 100/300

Ebonite unfilled 20 1 kHz/1 GHz 3/2.7 90/30

filled

(MgCO3) 20

50 kHz/1

GHz 4.1/3.8 100/180

Epoxy resin

25 1 kHz/100

MHz 3.6/3.5 200

Melamine resin

20 3 GHz 4.7 400

Phenolic resin fabric filled 20 1 MHz 5.5 500

paper filled 20 1 MHz/1 GHz 5 300/800

140

1 MHz/10

MHz 6 800/400

wood filled 20 1 MHz 5 400

Urea resin paper filled 20 1 MHz 6 300

Vinyl acetate (poly-) plasticized 20 1 MHz/10

MHz 4 500

Vinyl chloride (poly-) plasticized 20 1 MHz/10

MHz 4 600

(PVC)

Rubbers

Natural crepe 20/80 1 MHz/10

MHz 2.4 15/100

vulcan, soft 20

1 MHz/10

MHz 3.2 280/200

Butadiene/styrene unfilled 20/80 50 Hz/100

MHz 2.5 5/70

(GR-S) compounded 20/80 50 Hz/100

MHz 2.5 10/200

Butyl unfilled 20 50 Hz/100

MHz 2.4 35/10

Chloroprene Neoprene 20 1 kHz/1 MHz 6.5/5.7 300/900

Silicone filled 67%

TiO2 20

50 Hz/100

MHz 8.6/8.5 50/10

Silicone unfilled 25 1 kHz/100

MHz 3.2/3.1

Waxes, etc.

Chlornaphthalene

(tri and tetrachlor-)

20 50 Hz/100

MHz 5.4/4.2 7/2700

Ozokerite

20 50 Hz/100 2.3 5/10

197

MHz

Paraffin wax

20 1 MHz/1 GHz 2.2 2

Petroleum jelly

20/60 50 Hz 2.1/1.9 1/5

Rosin colophony 20 3 GHz 2.4 6

Wood (% water)

Balsa 0%

20 50 Hz/3 GHz 1.4/1.2 40/140

Beech 16% d = 0.62 20 1 MHz/100

MHz 9.4/8.5 580/830

Birch 10% d = 0.63 20 1 MHz/100

MHz 3.1 400/800

Douglas fir 11% d = 0.45 15 1 MHz/10

MHz 3.2 520/810

compressed d = 0.64 15 1 MHz/10

MHz 4.3 570/950

Scots pine 15% d = 0.61 20 1 MHz/100

MHz 8.2/7.3 590/940

Walnut 0%

20 10 MHz 2 350

Walnut 17%

20 10 MHz 5 1400

Whitewood 10% American 20 1 MHz/100

MHz 3 400/750

Liquids

Material Remarks t/°C f r´ 10

4 × tan

δ

Castor oil

. . . . . . . . 20 1 kHz 4.5

Chlordiphenyl

(tri) . . . . −10/100 50 Hz/20 kHz 7/5 2000/2

(penta-) . .

0/100 50 Hz 5.2/4.3 700/3

Parafin oil

. . . . . . . . medicinal 20 1 kHz 2.2 1

Silicone fluid

. . . . . . 0.65 cS 20 50 Hz/3 GHz 2.2 2/19

1000 cS 20 50 Hz/3 GHz 2.78/2.74 1/100

Transformer

oil . . . . . BS 138 20

50 MHz/100

GHz 2.2 1/42

20

100 MHz/10

GHz 2.2 42/8

198

Material t/°C r´ a

Alcohols (primary)

Methanol 25 32.65 P − 588

Ethanol 25 24.51 P − 612

Propanol 25 20.51 P − 683

Butanol 25 17.59 P − 733

Pentanol 25 15.09 P − 775

Hexanol 25 13.3 P − 806

Hydrocarbons

n-Pentane 20 1.84 − 87

n-Hexane 20 1.89 − 82

n-Heptane 20 1.92 − 73

n-Octane 20 1.95 − 67

n-Nonane 20 1.97 − 68

n-Decane 20 1.99 − 65

n-Undecane 20 2.00 − 62

n-Dodecane 20 2.01 − 60

Benzene 20 2.284 − 88

Cyclopentane 20 1.96

Cyclohexane 20 2.025 − 79

Toulene 20 2.39 − 102

(Chloro/Fluoro)-

hydrocarbons

CCl4 20 2.24 − 89

CCl3F 29 2.28

CCl2F2 29 2.13

CClF3 −30 2.3

CHCl3 20 4.80 P − 368

CHCl2F 28 5.34 P

CHClF2 24 6.11 P

(—CCl2F)2 25 2.52

(—CClF2)2 25 2.26

(—CH2Cl)2 20 10.66 P − 550

( CCl2)2 25 2.30 − 85

CCl2 CHCl 20 3.4 P

F-pentane 20 4.24 P

F-benzene 25 5.42 P

Cl-benzene 20 5.70 P − 229

Miscellaneous

199

Aniline 20 6.89 −341

Acetone 25 20.7 P −472

Diethylketone 20 17.0 P −520

Diethylether 20 4.34 P − 500

Cyclohexanone 20 18.3 P

Nitrobenzene 25 34.8 P − 518

CS2 20 2.64 − 101

Liquid gases T/K

Argon 82 1.53 − 220

Helium 4.19 1.048

,, 2.06 1.055

Hydrogen 20.4 1.22 − 280

Nitrogen 70 1.45 − 200

Oxygen 80 1.50 − 160

Note- Many of these liquids are hazardous, flammable or toxic. Chemical safety

manuals should be consulted before using them.

D- RELATIVE PERMITTIVITY OF GASES AND VAPOURS

Material t/°C 104

( r − 1) Material t/°C 10

4 ( r −

1)

Air dry . . . . . . . 20 5.361 Nitrous oxide . . . . . . 25 10.3

Nitrogen . . . . . . 20 5.474 Ethylene . . . . . . . . 25 13.2

Oxygen . . . . . . . 20 4.943 Carbon

disulphide . . . . 29 29.0

Argon . . . . . . . . 20 5.177 Benzene . . . . . . . . 100 32.7

Hydrogen . . . . . . 0 2.72 Methanol . . . . . . . . 100 57

Deuterium . . . . . . 0 2.696 Ethanol . . . . . . . . . 100 78

Helium . . . . . . . 0 0.7 Ammonia . . . . . . . . 1 71

Neon . . . . . . . . 0 1.3 Sulphur

dioxide . . . . . 22 82

Carbon dioxide . . . 20 9.216 Water . . . . . . . . . 100 60

Carbon monoxide . . 25 6.4 Water (10

mmHg) . . . 20 1.24

Sources;

C. J. F. Bötcher (1973) Dielectrics and Static Fields, Vol. 1, 2nd edn, Elsevier

Scientific Publishing Company, Amsterdam.

C. J. F. Bötcher and P. Bordewijk (1978) Dielectrics in Time Dependent Fields,

Vol. 2, 2nd edn, Elsevier Scientific Publishing Company, Amsterdam.

200

V. V. Daniel (1967) Dielectric Relaxation, Academic Press, London. H. Fröhlich

(1958) Theory of Dielectrics, 2nd edn, Clarendon Press, Oxford.

Nora E. Hill, Worth E. Vaughan, A. H. Price, Mansel Davies (1969) Dielectric

Properties and Molecular Behaviour, van Nostrand Reinhold Company Ltd.,

London. A. R. von Hippel (1954) Dielectrics and Waves, Chapman & Hall, London.

K. F. Young and H. P. R. Frederikse (1973) Compilation of the Static Dielectric

Constant of Inorganic Solids, J. Phys. Chem. Ref. Data, 2(2), 313–410.

R. G. Jones (1976) J. Phys. D: Appl. Phys., 9, 819–27.

S. Jenkins, R. N. Clarke, Measured values and uncertainties for the complex

permittivity of selected organic reference liquids at 20 to 30°C and frequencies up

to 3 GHz, (NPL Report DES 109).

E- TRANSMISSION LINE PARAMETERS

The Tx line model is the simplest of all, representing the rectangular patch as a

parallel-plate transmission line connecting two radiating slots (apertures), each of

width W, height h and z is direction of propagation of the transmission line (Fig h).

Fig h A rectangular patch antenna and fringing fields

The slots represent very high-impedance terminations from both sides of the

transmission line (almost an open circuit). Thus, this structure is suppose to have

highly resonant characteristics depending crucially on its length L along z. The

201

resonant length of the patch is not exactly equal to the physical length due to the

fringing effect. The fringing effect makes the effective electrical length of the patch

longer than its physical length (Leff >L).

The dominant TM001 mode has a uniform field distribution along the y-axis at the slots

formed at the front and end edges of the patch. The equivalent conductance G is

obtained from the theory of uniform apertures while B is related to the fringing

capacitance.

The limitation is necessary since a uniform field distribution along the

x-axis is assumed and the equivalent circuit of a slot is constructed as a parallel R-C

circuit, using the values of G and B.

The equivalent circuit representing the whole patch in the TM001 mode includes the two

radiating slots as parallel R-C circuits and the patch connecting them as a transmission

line whose characteristics are computed in the same way as those of a microstrip

transmission line (Fig i).

Fig i The line parameters of a microstrip antenna

202

Here, Zc is the characteristic impedance of the line, and βg is its phase constant. For

each slot, G represents the radiation loss and B = j C represents the capacitance

associated with the fringing effect. The thickness of the substrate is very small. The

waves generated and propagating beneath the patch undergo considerable reflection at

the edges of the patch. Only a very small fraction of them is being radiated.

At the feed point, the impedance of each slot is transformed by the respective

transmission line representing a portion of the patch.

Fig j Feed line impedances of microstrip antenna

The admittance transformation is given by

provided line is loss-less.

***