IJRRAS 15 (1) April 13 www.arpapress.com/volumes/vol15issue1/ijrras_15_1_15.pdf DESIGN AND NUMERICAL ANALYSIS OF A SINGLE HALF-WAVE DIPOLE ANTENNA TRANSMITTING AT 35MHz USING METHOD OF MOMENT Adewumi Adebayo Segun 1, Alade Michael Olasope, Rotimi Cornelius Okeowo 3 & Akinleye Abiodun Ismail 4 1,,4 Department of Pure and Applied Physics, Ladoke Akintola University of Technology, P.M.B 4, Ogbomoso, Oyo State, Nigeria 3 Department of Physics, College of Education, P.M.B 75, Ikere-Ekiti, Ekiti State, Nigeria ABSTRACT This paper deals with design and numerical analysis of a single Half- wave dipole antenna suitable for transmitting UHF television signals at a frequency of 35MHz using Method of Moment. Two equations, namely the radiating field and the electric field strength equations were used to determine the variations in the electric field strength and free space loss with distance in kilometers. Other parameters such as the power radiated, gain and voltage standing wave ratio of the antenna at this frequency were also evaluated. The radiation patterns obtained shows that the antenna is a good radiator while the variations in electric field strength and free space loss with distance actually show the distance covered and the rate of loss of the signal transmitted at this particular frequency using half wave dipole antenna. Keywords: Design, Numerical Analysis, Half-wave dipole Antenna, Method of moment, far field pattern 1. INTRODUCTION This work was motivated by a desire to improve on the performances of some antennas used for transmitting Television signals in some parts of south west region of Nigeria so as to enhance uniform distribution and higher efficient transmission of Television signals from base stations. The resulting analysis will enhance industry s ability to design antennas that will meet performance specifications and enable Television broadcasting stations to know the importance of design and analysis of antennas before they are employed in transmissions. In today s transmission systems, efficient antennas are required for transmission so as to produce high energy radiating signals that can be transmitted over a long distance for wide coverage before the signal is completely attenuated. An efficient radiating antenna coupled with high power transmitter will reduce the number of repeaters stations and eventually save cost of installations. Gautama A.K observed and reported that in order to ensure higher power radiation an antenna must have the ability to match the transmission line with the load impedance; it must also have the ability to transfer energy from electrostatic to electromagnetic energy or vice versa. In this study, the design and numerical analysis of a single short half-wave dipole Antenna suitable for transmitting at the same frequency as that of Nigeria television station NTA Ogbomosho (35MHz) is presented. Half Wave dipole is chosen because of it wide acceptance in practice and its uses as a reference antenna. The characteristics of a Half-Wave dipole antenna in literature show that it has distributed capacitance and inductance which make it behave like a resonant circuit with voltage and current out of phase. Half Wavelength dipole is one of the most commonly used antennas because its radiation resistance is 73 ohms, which is very near the 75-ohm characteristic impedance of some transmission lines, it matching to the line is simplified especially at resonance compare to other antennas. (Kennedy and Davis, 5; Balanis, 5). The diagram figure1 shows the transmitting antenna used for transmitting signal at a frequency of 35MHz in Nigeria Television Authority (NTA) station Ogbomosho, Oyo State, Nigeria. Ogbomosho is located on the latitude 8 8' 1" N and longitude 4 14' 48" E. This station transmits at frequency of 35MHz with a transmitters power of 5kw but from information gathered from other cities and towns of about 4km away, it has been observed that the signals hardy reach 35km away from the base station before it is completely attenuated. I think this is the main reason why government has to install another Nigerian Television transmitting station in Oyo town which is just 47km away from Ogbomosho which could have been covered by the same base station if efficient antenna properly match with transmission line cable and powered by efficient transmitter is used for transmission. Though the role of free space path loss and other attenuation factors cannot be overlooked yet the importance of a well designed antenna in transmitting systems both at the transmitting and receiving ends cannot be underrated. 17
IJRRAS 15 (1) April 13 Figure.1 Nigeria Television Authority (NTA) Transmitting Antenna Ogbomosho. However, in this paper a single Half -wave dipole antenna suitable for transmitting at the same frequency (35MHz) as that of NTA Ogbomosho is designed and analyzed numerically to observe its performances and effectiveness over the designed frequency using method of moment.. DESIGN ANALYSIS Step1: The initial condition for the design of the half-wave dipole antenna expected to operate at the design frequency of 35MHz is that the half-wave dipole antenna length dl shown in figure is assumed to be.5λ, that is dl is λ/ long such that λ = c/f. Z P θ dl ϕ Y X Figure. Diagram showing the Half- wave dipole antenna located in space. Since the transmitting half-wave dipole antenna is usually located in free space carrying an oscillating current, it will give rise to two fields H (Far field radiation) and E θ (Electric field strength) which can be obtained using the equation (Gautam, 9). H = I odlsinθ 4π and [ ω rc cosω t r c ] 1 E θ = I odlsinθ 4πε c r [cosω(t r c ] where dl is the dipole antenna length (.5λ), r is the distance of the far field region from the dipole element usually 18
IJRRAS 15 (1) April 13 greater than (dl) λ chosen to be 1.5m. λ is the wavelength (1.76595745m). C is the speed of light (3 1 8 m/s). t is the period (1/f) ω = πf, f is the frequency (35MHz). θ is the angle of radiation in degree (-36 ) ε is the permittivity of free space ( 8.85 1 1 F/m ) i o is the peak value of current. dl is the length of the dipole antenna..1 Determination of the peak value of the dipole antenna current using method of moment step: To determine the peak value of the dipole current i o using method of moment (circuit equation) technique, the step is as follow: the Half-wave dipole antenna is divided into 4 segments Δz =.15λ long and each assumed to have a uniform current over each segment given by i 1 i i 3 and i 4 as shown in figure 3. ΔZ 4 ΔZ 3 ΔZ ΔZ 1 a Figure3. Single Half-wave dipole antenna.5λ long divided into 4 segments Δz 1 =Δz =Δz 3 =Δz 4 =.15λ long Where the radius a = r 11 = r = r 33 = r 44 =.1. The Half-wave dipole is assumed to be symmetrical so that r 1 = r 1 = r 3 = r 3 = r 34 = r 43 3 r 13 = r 31 = r 4 = r 4 and r 14 = r 41 4 Also G11=G=G33=G44, 5 19
IJRRAS 15 (1) April 13 G1=G1=G3=G3=G34=G43, 6 G13=G31=G4=G4and G14=G41. 7 The peak value of the current was determined as follow Using equation 8, 9, 1and 11 (Kraus et al., ; John David Jackson, 1998; Balanis, 5). E z (z m ) = Where N n=1 I n G(r mn z n )dz (Vm -1 ) 8 G r mn = z Δz λ 8π r 3 λ jπr λ 1 + jπr λ 3 a r + 4π a λ (Ωm - ) 9 r = r mn m=observation point n=source point Putting G mn = G(r z mn )dz G r mn z n (Ωm -1 ) 1 n Then equation 3 becomes E z z m = I 1 G m1 + I G m + + I n G m3 + + I N G m4 (Vλ -1 or Vm -1 ) 11 Since the short dipole antenna has been divided into 4 segments (m=1,, 3, and 4), equation (11) can now be used to obtain a set equation as follow: I 1 G 11 + I G 1 + I 3 G 13 + I 4 G 14 = E Z (Z 1 ) I 1 G 1 + I G + I 3 G 3 + I 4 G 4 = E Z (Z ) 1 I 1 G 31 + I G 3 + I 3 G 33 + I 4 G 34 = E Z (Z 3 ) I 1 G 41 + I G 4 + I 3 G 43 + I 4 G 44 = E Z (Z 4 ) This can be expressed in matrix form as: G 11 G 1 G 13 G 14 G 1 G G 3 G 4 G 31 G 3 G 33 G 34 G 41 G 4 G 43 G 44 I 1 I = I 3 I 4 And in compact notation by E z (Z 1 ) E z (Z ) E z (Z 3 ) E z (Z 4 ) 13 G mn I n = [E m ] (Vλ -1 orvm -1 ) 14 Where m=1,,..., 4 n=1,,., 4 Multiplying both sides of the equation by the distance z, z G mn I n = z[e m ] (V) 15 This can be written as z mn I n = [V m ] (V) 16 11
IJRRAS 15 (1) April 13 The value of G 11 to G 44 can be obtained using the equation (Kraus et al., ) G r mn = j z Δz λ 8π r 3 λ cosπr λ jsinπr λ 1 + jπr λ 3 a r + 4π a λ Ωm -1 17 Where m = 1,, 3, 4. n = 1,, 3, 4. Z r =.15, r λ =.1 = a To determine G 11 using equation (17) G 11 = j377.15.1 8π.65 3 cosπ.65 jsinπ.65 1 + jπ.65 3.65 + 4π.1 = 187.6148 j6843.5386 Ω λ -1 18 G 1 = j377.15.1 8π.15 3 cosπ.15 jsinπ.15 1 + jπ.15 3.15 + 4π.1 = 471.555 j617.6456351 Ω λ -1 19 G 13 = j377.15.1 8π.5 3 cosπ.5 jsinπ.5 1 + jπ.5 3 + 4π.1.5 = 117.866799 j79.65659311 Ωλ -1 G 14 = j377.15.1 8π.375 3 cosπ.375 jsinπ.375 1 + jπ.375 3 + 4π.1.375 G 14 = 5.3583196 j4.89663 Ω λ -1 1 Introducing equation (18), (19), (), (1) in equation 1 and multiplying by z (=.15), we obtain: I 1 34.7681 j855.465483 + I 58.9446566 j77.57439 + I 3 14.7358499 j9.95774139 + I 4 6.54478995 + j3.11379 = V 1. I 1 58.9446566 j77.57439 + I 34.7681 j855.465483 + I 3 58.9446566 j77.57439 + I 4 14.7358499 j9.95774139 = V. 3 I 1 14.7358499 j9.95774139 + I 58.9446566 j77.57439 + I 3 34.7681 j855.465483 + I 4 58.9446566 j77.57439 = V 3. 4 I 1 6.54478995 + j3.11379 + I 14.7358499 j9.95774139 + I 3 58.9446566 j77.57439 + I 4 34.7681 j855.465483 = V 4. 5 By symmetry I = I 3, I = I 4 also for a centre-fed dipole V = V 3 = and V = V 4 = 1 (Kraus et, al.) Equation (), (3), (4) and (5) was written in matrix form and reduced to x matrix for simplification using Cramer s rule (Riley et al., 1999). 48.88866 j865.36364 65.48885561 j74.145111 117.8881313 j154.411488 48.88866 j865.363634 = 6 1 I 1 = I 3 = 1.9735368 1 3 A. 7 I = I 4 = 1.8341794 1 4 A. 8 Therefore the peak value of current I O = 1.9735368 1 3 A. Determination of the Corresponding Values H with respect to Angle (θ) Step3: Introducing the value of I O and other variables in equation (1) the results is as shown in table 1. 111
IJRRAS 15 (1) April 13 Table 1: Angles and their corresponding far field radiation values θ (deg) 3 6 9 1 H..9144517.1561348759.188953.1561348759 θ (deg) 15 18 1 4 7 H.9144517. -.9144517 -.1561348759 -.188953 θ(deg) 3 33 H -.1561348759 -.9144517. Far Field Radiation Pattern 3. 33.1 -.1 3 6 7 -. 9 4 1 1 18 15 Figure4. Far field radiation pattern of the Half-wave dipole antenna at a frequency of 35MHz..3 Determination of the Corresponding Values (E θ ) with respect to Angle (θ) Step4: Introducing the value of I O and other variables in equation () the results is as shown in table. Table : Angles and their corresponding values of electric field strength θ (deg) 3 6 9 1 E θ..34917185.5939499874.68583437.5939499874 θ (deg) 15 18 1 4 7 E θ.349171851. -.349171851 -.5939499874 -.68583437 θ (deg) 3 33 E θ -.5939499874 -.349171851 11
IJRRAS 15 (1) April 13 Electric Field Strength pattern 33.1.5 3 3 6 -.5 7 -.1 9 4 1 1 15 18 Figure5. Electric field strength pattern of the Half-wave dipole antenna at a frequency of 35MHz STEP5: The power radiated was determined using the equation (Kraus et al., ) P θ = E θ 9 The results is as shown in table3 Table 3: Angles and their corresponding power radiated values θ (deg) 3 6 9 1 P θ..117591958.357765875.473687833.357765875 θ (deg) 15 18 1 4 7 P θ.117591958..117591958.357765875.473687833 θ(deg ) 3 33 P θ.357765875.117591958 Power radiated (Pθ) 3 7.5 33 3.4.3..1 6 9 4 1 18 15 1 Figure6. Power radiated pattern of the Half-wave dipole antenna at a frequency of 35MHz 113
IJRRAS 15 (1) April 13 STEP6: Normalizing this power with respect to its maximum value yields a normalized power as a function of angle obtained as follow in table 4. i.e. pnθ = p(θ)/p θ max 3 Table 4: Angles and their corresponding normalized radiated power θ(deg) 3 6 9 1 15 18 1 4 7 3 33 (Pnθ)..5.75 1..75.5..5.75 1..75.5 Normalized power pattern 7 3 33 1.8.6.4. 3 6 9 4 1 1 15 18 Figure7 Normalized power pattern of the Half- wave dipole at a frequency of 35MHz STEP7: Normalized power in decibel was obtained from the equation (Kraus et al; ) db = 1log 1 pn(θ) 31 The result is as shown in table 5. Table5: Angles and their corresponding normalized radiated power. θ (deg) 3 6 9 1 Pn(θ)(dB). -6.599983-1.49387349. -1.49387349 θ (deg) 15 18 1 4 7 Pn θ (db) -6.599983 -. -6.599983-1.49387349. θ (deg) 3 33 Pn θ (db) -1.49387349-6.599983 114
IJRRAS 15 (1) April 13-1 Normalized power in(db) 5 1 15 5 3 35 - -3-4 Pn(θ)(dB) -5-6 -7 Figure8. Normalized power pattern in decibel of the Half- wave dipole at a frequency of 35MHz STEP 8: To determine the antenna s directivity, the equation is as follow (Kraus et al; ) P θ max D = =.473687833 P(θ)av 4.11576854 1 Where P θ max is the maximum value of P θ and p(θ) av is the average value of the power radiated 3 = 1.14857143 Or.57991947dBi 3 Step9: To determine the gain G of the antenna, the equation is as follow (Kraus et al; ) G=KD Where K is a constant taken to be.61 for half-wave dipole therefore, G =.61 1.14857143 Step1: The power is given by the equation (Gautama, 9) P passive = 3( 1 λ ) I Watts 33 I = I O =.19735368 =.7768597 A R r = 3( 1 λ ) = 3(.6389787 1.76595745 ) = 79.99999Ω 34 Thereforep = I R r = 4.7768383 1 3 Watt 35 When this antenna is now fed with the NTA Ogbomosho station transmitter of 5kw the total power radiated will be: T Pr = P passive + pi = 4.7768383 1 5 + 5 watts 36 Where (Tpr) is transmitting power radiated by the antenna and (Pi) is the input power or power fed to the transmitter. G = P r = 5.985 = 1. 37 P i 5 Step11: The Voltage Standing Wave Ratio (VSWR) is determined using the equation (Kraus et al; ) VSWR= I max +I min = 1.9735368 1 3 +1.8341794 1 4 I max I min 1.9735368 1 3 1.8341794 1 4 = 1.3 38 115
IJRRAS 15 (1) April 13 Step1: The variation in electric field intensity relative to distance is obtained from the equation (Gautama, 9) 9P r E = 39 r Where E is the electric field intensity, r is the distance covered by the signal in kilometers and P r is the power radiated by the half-wave dipole. The corresponding values of E over distance are as shown in table 6. Table 6: Variation of E with distance Distance (km) 1 3 4 5 E (V/Km) 67.8413 33.54166.366844 16.775133 13.416486 Distance (km) 6 7 8 9 1 E (V/Km) 11.1834 9.58314876 8.38555165 7.45356147 6.78413 Distance (km) 11 1 13 14 15 E (V/Km) 6.98367393 5.591711 5.161575 4.79157488 4.4713688 Distance (km) 16 17 18 19 E (V/Km) 4.1967583 3.946431 3.767873 3.53633754 3.354166 Distance (km) 1 3 4 5 E (V/Km) 3.194389 3.49183696.9166149.7958555.68381653 Distance (km) 6 7 8 9 3 E (V/Km).587851.484549.3958719.313173839.366844 Distance (km) 31 3 33 34 35 E (V/Km).163936817.96313791.3789131 1.973115 1.9166975 Distance (km) 36 37 38 39 4 E (V/Km) 1.8633937 1.8138144 1.765316877 1.7534 1.6775133 Distance (km) 41 4 43 44 45 E (V/Km) 1.636147349 1.59719146 1.5647473 1.54591848 1.49719 Distance (km) 46 47 48 49 5 E (V/Km) 1.4583546 1.4777475 1.3975458 1.369151 1.3416486 Distance (km) 51 5 53 54 55 E (V/Km) 1.315334144 1.93956 1.65698893 1.464 1.19673479 Step13: The free space loss of the signal at the design frequency is given by the equation; (Mishra, 7) L = 3.4 + log 1 f + log 1 (d) 4 where f is the frequency in Megahertz and d is the distance in kilometers. The result is shown in table 7. 116
IJRRAS 15 (1) April 13 Table7: variation of Free space loss with distance Distance(km) 1 3 4 5 Free space loss (db) 18.8797491 18.659444 18.868643 19.16536 19.168446 Distance(km) 6 7 8 9 1 Free space loss (db) 19.18996365 19.5947687 19.3188553 19.37477 19.41617545 Distance(km) 11 1 13 14 15 Free space loss (db) 19.4571831 19.49414318 19.579359 19.5589891 19.5877148 Distance(km) 16 17 18 19 Free space loss (db) 19.6143895 19.6393984 19.6667577 19.6846674 19.754196 Distance(km) 1 3 4 5 Free space loss (db) 19.75713 19.7437636 19.76147753 19.7784539 19.7945835 Distance(km) 6 7 8 9 3 Free space loss (db) 19.81649 19.8491186 19.83917153 19.8588651 19.8669548 Distance(km) 31 3 33 34 35 Free space loss (db) 19.87883318 19.8911395 19.93171 19.9145174 19.956557 Distance(km) 36 37 38 39 4 Free space loss (db) 19.936453 19.946976 19.957989 19.9669835 19.976596 Distance(km) 41 4 43 44 45 Free space loss (db) 19.9859518 19.9956113.393841.15941.13863 Distance(km) 46 47 48 49 5 Free space loss (db).98169.373335.451998.58898.641199 Distance(km) 51 5 53 54 55 Free space loss (db).677757.749781.83483.8894849.95746 3. RESULTS AND DISCUSSION Figure 4,5 and 6 show the far field radiation pattern, the electric field strength radiation pattern and the power radiation pattern of the Half-wave dipole antenna at the design frequency of 35MHz using method of moment. The patterns obtained show that the antenna is a good ominidirectional antenna. Figure 7 and 8 show the normalized pattern in degree and decibel which shows that the antenna has maximum beamwidth or maximum directivity at θ = 9 and θ = 7. Also figure7 shows that the electric field is left circularly and right circularly polarized with 9. Figure 9 shows the variation in Electric field strength of the Half-wave dipole antenna with respect to distance at the design frequency of 35MHz. It can be observed from fig.8 that the electric field strength decreases with increase in distance. It can be observed from figure8 and table 6 that the electric field strength decreases rapidly within the shortest distance of to 3 km away from the base station. This account for the reason why the signal cannot travel far distance within the same state or region before it is completely attenuated. Figure1 shows the corresponding free space loss in signal strength as the distance increases. It is obvious from the graph that the loss increases with increase in distance. Also, figure 11 shows the reduction in power density as the distance increases. 117
Free space loss (db) Electric field stregth(v/km) IJRRAS 15 (1) April 13 4 35 3 5 15 1 5 E (V/Km) 4 6 8 Distance (km) Figure 9 Variation of Electric field with distance.. 19.8 19.6 19.4 19. 19 18.8 18.6 18.4 18. 18 1 3 4 5 6 Free space loss (db) Distance (km) Figure 1 Free space loss per distance 118
Power Density (W/Km²) IJRRAS 15 (1) April 13 4.5 4 3.5 3.5 1.5 1.5 1 3 4 5 6 Distance(km) Figure11 Variation of power density with distance. 4. CONCLUSION The result obtained, in this research, shows that half- wave dipole antenna is not too good for long distance transmission of television signal at the design frequency of 35MHz and that there is need for accurate design and analysis of television station transmitting antennas before implementation so as to minimize the cost of installation and maintenance of multiple transmitting stations within short distance that would have possibly be covered by single transmitting and efficient antenna. Arrays of wide bandwidth antennas coupled with high power transmitters can be employed in television signal transmission for efficient and effective transmission over long distance. 5. ACKNOWLEDGEMENTS My gratitude goes to God Almighty, who made it possible for this research work to be completed. Also, I am very grateful to Dr. M. O Alade for his support. 6. REFERENCES Alade, M.O. and Adewumi A.S, 1. Design and Construction of a Folded Dipole Log- periodic Stack Array Antenna at UHF/L Band. Int. J. Mobile Commun., 5(4): 41-45, 11. Balanis, C.A., 5. Antenna Theory. nd Edn., John Wiley and Sons (Asia) printing Ltd., Singapore, ISBN: 9971-51-33-5. Gautam, A.K. 9.Antenna and Wave Propagation.4th Edn., S.K. KATARIA & SONS, Delhi., ISBN 476-61/3. Jackson, J.D 1. Classical Electrodynamics. 3rd Edn., John Wiley & Sons. INC., USA., ISBN: -471-393. Kennedy, G. and B. Davis, 5. Electronics Communication Systems.4th Edn., McGraw-Hill, USA., ISBN: -7-46368-. Kraus, J.D., R.J. Marhefka, B.A. Muuk, A. Letho, P. Vainikainen, E.H.B Newman and C. walker,. Antenna for all Applications. 3rd Edn., McGraw-Hill, USA., ISBN: -7-313- Mishra, R., 7. Advanced Cellular Network Planning and Optimisation. John Wiley & Sons, Ltd., England, ISBN-13 978--47-1471-4(HB). Riley, K.F., M.P. Hobson, S.J. Bence 1999. Low price edn., Cambridge University press., UK., ISBN:515556. 119