Dipole Antennas Prof. Girish Kumar Electrical Engineering Department, IIT Bombay gkumar@ee.iitb.ac.in (022) 2576 7436
Infinitesimal Dipole An infinitesimally small current element is called the Hertz Dipole (Length L< λ/50) Assume an infinitesimal current element of length dl carrying an alternating current I o. The instantaneous current is i(t) = I o e jwt i z A = A z z = μ 4π I odl e jkr e jwt z r where, k = 2π λ Dipole and its field components in spherical polar co-ordinate
Uniform Current Magnetic Vector Potential
E and H Fields from Magnetic Vector Potential
Uniform Current E and H Fields
Uniform Current Near and Far Fields Near Field Region Near Reactive Field Region Far Field Region Near Radiative Field Region r > where d is the maximum dimension of the antenna
Uniform Current - Radiation Pattern Far Field Region (kr>>1) E θ = jη ki ol 4πr sinθ H φ = j ki ol 4πr sinθ E θ H φ = η = 120π R r = 80π 2 l λ 2 Impedance of free-space Directivity D 0 U 4 P max rad 3 2 E-plane radiation pattern E r E φ = H r = H θ = 0 3-D radiation pattern Note : Infinitesimal antenna is not an efficient radiator H-plane radiation pattern
Small Dipole Antenna A current element whose length is /50 < l /10 is called small dipole antenna A small dipole Antenna Approximate Triangular Current distribution
Small Dipole Radiation Resistance Small dipole current distribution I e x, y, z = a z I 0 1 2 l z, 0 z Small dipole vector potential A x, y, z = μ 4π a z l 2 a z I 0 1 + 2 l z, l 2 z 0 + a z 0 l 2 l 2 0 I 0 1 + 2 l z e jkr R I 0 1 2 l z e jkr R dz dz Far Field Region (kr>>1) E θ jη ki 0le jkr sinθ 8πr E r E φ = H r = H θ = 0 H φ j ki 0le jkr 8πr sinθ R r = 2P rad I 0 2 = 20π2 l λ For l = λ / 10, R r = 2 Ω l = λ / 4, R r = 12.3 Ω Dipoles also have reactive impedance 2
Input Impedance of Transmission Line l Case 1: Z L = 0, Z in = jz 0 tanβl Case 2: Z L =, Z in = Z 0 jtanβl Z 0 Z L Case 3: Z L = Z 0, Z in = Z 0 Where, β = 2π λ if l < λ tanβl = +ve 4 λ 4 < l < λ tanβl = ve 2 Z in For Short-circuit, Z L = 0, Z in is inductive, so T-Line represents inductance Open-circuit, Z L =, Z in is capacitive, so T-Line represents capacitance
Half wavelength Dipole Electric and magnetic fields of a half-wavelength dipole Directivity of half-wavelength dipole E θ jη I 0e jkr 2πr H φ j I 0e jkr 2πr cos π 2 cosθ sinθ cos π 2 cosθ sinθ D 0 = 4π U max P rad 1.643 D = 2.1 db λ/2 Dipole Radiation Resistance R r = 2P rad I 0 2 73 Design of Dipole Antenna l + d = 0.48λ, where, d is the diameter of wire and d<λ/10 Note: Input impedance for λ/2 dipole is 73+j42.5Ω. To make imaginary part equal to zero, the antenna length is reduced until the input impedance becomes real. Real Input impedance is < 68Ω.
Current Distribution of Dipole Antenna for Different Lengths
Radiation Pattern of Dipole Antenna for Different Lengths
Dipole Antenna Radiation Pattern for l = 1.25λ Two Dimensional Three Dimensional Directivity is maximum for a thin dipole of length l = 1.25λ
Dipole Antenna Resistance and Directivity D 0 = 3.25 R r
Flat Dipole Antenna BW for S 11 < 10 db is from 1.39 to 1.54 GHz (150 MHz, 10.2%) Length of each segment = 50 mm Width = 4mm, Gap = 2mm
Flat Dipole Antenna Pattern and Directivity Radiation Pattern at 1.5, 3.75 and 4.5 GHz Directivity of 4.8 db is maximum at 3.75 GHz where length of dipole is approx. 1.25 λ
Printed Dipole Antenna Length of each segment = 50 mm Width = 4mm, Gap = 2mm FR4 substrate: ε r = 4.4, tanδ = 0.02, h = 1.6mm BW = 1.14 to 1.28 GHz (140 MHz, 11.6%)
Broadband Dipole Antenna Bandwidth of dipole antenna is directly proportional to its diameter Cylindrical dipole antenna (can use hollow pipe also) Biconical dipole antenna (can use wire grid also)
Balun Design Devices that can be used to balance inherently unbalanced systems by cancelling or choking the outside current, are known as baluns (balance to unbalance). l l Coaxial line λ 4 Metal λ 4 Shorted together Inner conductor of coax Outer conductor of coax λ 4 Coaxial Balun (1:1)- Narrow Bandwidth
Balun Design (Contd.) Ferrite core maintains high impedance levels over a wide frequency range. A good design can provide bandwidths of 10 to 1 whereas coil coaxial baluns can provide bandwidths of 2 or 3 to 1. Ferrite core Metal sleeve Z 1 (unbalanced) Z 1 (balanced) Shorted to coax s outer conductor Coaxial line Sleeve or bazooka balun Narrow BW Ferrite core balun Wide BW
Microstrip Balun Dipole Antenna for GSM900 Microstrip Balun Dipole Antenna L = 127 mm, w = 4 mm FR4 substrate: ε r = 4.4, tanδ = 0.02, h = 1.6mm BW for S 11 < 10 db is from 881 to 967 MHz (covers GSM900 band of 890 to 960 MHz)
Folded Dipole Antenna The impedance of the N fold folded dipole is N 2 times greater than that of an isolated dipole of the same length as one of its side. Impedance for 2-fold dipole antenna is Z in = 2 2 Z r Z in = 4Z r 2-fold dipole antennas are used in Yagi-Uda Antennas for TV reception using balanced line of Z 0 = 300 Ω
Dipole Antenna Applications Chip Compact Dipole Antenna for RFID Folded Broadband Dipole Antenna for RF Harvesting (Triangular shape for broadband and multi-fold gave Z in = 750 Ω)