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Home , Dipole antenna, Radiation resistance

Antennas

Prof. Girish Kumar Electrical Engineering Department, IIT Bombay

[email protected] (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 Io. The instantaneous current is

푗푤푡 푖(푡) = 퐼표푒 푖푧

−푗푘푟 2π 휇 푒 푗푤푡 where, k = 퐴 = 퐴 푧 = 퐼 푑푙 푒 푧 λ 푧 4휋 표 푟 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

Near Radiative Field Region

Far Field Region

where d is the maximum dimension r > of the Uniform Current - Pattern

Far Field Region (kr>>1)

Umax 3 푘퐼표푙 D0 4 퐸 = 푗휂 sin휃 Prad 2 휃 4휋푟 푘퐼 푙 퐻 = 푗 표 sin휃 휙 4휋푟 퐸 E-plane 휃 = 휂 = 120휋 Impedance of 퐻휙 free-space 2 푙 푅 = 80휋2 푟 휆

퐸푟 ≃ 퐸휙 = 퐻푟 = 퐻휃 = 0 3-D radiation pattern Note : Infinitesimal antenna is not an efficient radiator H-plane radiation pattern Small

A current element whose length is /50 < l  /10 is called small dipole antenna

A small dipole Antenna Approximate Triangular Current distribution Small Dipole –

Small dipole current distribution Far Field Region (kr>>1)

−푗푘푟 2 푘퐼0푙푒 퐼 푥′, 푦′, 푧′ = 푎 퐼 1 − 푧′ , 0 ≤ 푧′ ≤ 푙 2 퐸휃 ≃ 푗휂 sin휃 푒 푧 0 푙 8휋푟 퐸푟 ≃ 퐸휙 = 퐻푟 = 퐻휃 = 0 2 푎 퐼 1 + 푧′ , − 푙 2 ≤ 푧′ ≤ 0 푘퐼 푙푒−푗푘푟 푧 0 푙 퐻 ≃ 푗 0 sin휃 휙 8휋푟 2 2푃푟푎푑 2 푙 푅푟 = 2 = 20휋 Small dipole vector potential |퐼0| 휆

0 휇 2 푒−푗푘푅 퐴 푥, 푦, 푧 = 푎 퐼 1 + 푧′ 푑푧′ 4휋 푧 0 푙 푅 For l = λ / 10, R = 2 Ω −푙 2 r 푙 2 l = λ / 4, R = 12.3 Ω 2 푒−푗푘푅 r + 푎 퐼 1 − 푧′ 푑푧′ 푧 0 푙 푅 0 also have reactive impedance Input Impedance of

l

푍0 푍L Case 1: 푍퐿= 0, → Z푖푛= 푗푍0tan훽푙

푍 Case 2: 푍 = ∞, → Z = 0 퐿 푖푛 푗tan훽푙

푍in Case 3: 푍퐿= 푍0, → Z푖푛 = 푍0

2휋 Where, 훽 = 휆 휆 For Short-circuit, ZL = 0, Zin is inductive, so T-Line represents inductance 푖푓 푙 < → tan훽푙 = +푣푒 Open-circuit, Z = , Z is capacitive, so T-Line represents 4 L in 휆 휆 < 푙 < → tan훽푙 = −푣푒 4 2 Half wavelength Dipole

Electric and magnetic fields of Directivity of half- dipole a half-wavelength dipole 휋 푈max 퐼 푒−푗푘푟 cos cos휃 퐷0 = 4휋 ≃ 1.643 퐸 ≃ 푗휂 0 2 푃푟푎푑 휃 2휋푟 sin휃 휋 D = 2.1 dB 퐼 푒−푗푘푟 cos cos휃 퐻 ≃ 푗 0 2 휙 2휋푟 sin휃

λ/2 Dipole Radiation 2푃 Note: Input impedance for λ/2 dipole is 73+j42.5Ω. 푅 = 푟푎푑 ≃ 73 Resistance 푟 |퐼 |2 To make imaginary part equal to zero, the antenna 0 length is reduced until the input impedance becomes real. Design of Dipole Antenna 푙 + 푑 = 0.48휆, where, d is the diameter of wire and d<휆/10 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

D0 = 3.25

Rr Flat Dipole Antenna

BW for |S11| < 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: εr = 4.4, tanδ = BW = 1.14 to 1.28 GHz (140 MHz, 11.6%) 0.02, h = 1.6mm Broadband Dipole Antenna

Bandwidth of dipole antenna is directly proportional to its diameter

Cylindrical dipole antenna Biconical dipole antenna (can use hollow pipe also) (can use wire grid also) Design

Devices that can be used to balance inherently unbalanced systems by cancelling or choking the outside current, are known as (balance to unbalance).

푙 푙

Coaxial line 휆 4 Metal 휆 4

Outer Inner conductor Shorted conductor of coax together of coax

휆 4 Coaxial Balun (1:1)- Narrow Bandwidth Balun Design (Contd.)

Ferrite core maintains high impedance levels over a wide 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 푍1(unbalanced)

푍1(balanced)

Shorted to coax’s Coaxial line outer conductor Ferrite core balun Sleeve or bazooka balun Wide BW Narrow BW Microstrip Balun Dipole Antenna for GSM900

Microstrip Balun Dipole Antenna BW for |S11| < 10 dB is from 881 to 967 MHz L = 127 mm, w = 4 mm (covers GSM900 band of 890 to 960 MHz)

FR4 substrate: εr = 4.4, tanδ = 0.02, h = 1.6mm Folded Dipole Antenna

The impedance of the N fold folded dipole is N2 times greater than that of an isolated dipole of the same length as one of its side.

Impedance for 2-fold dipole antenna is 2 푍푖푛 = 2 푍푟 푍푖푛 = 4푍푟

2-fold dipole antennas are used in Yagi-Uda Antennas for

TV reception using of Z0 = 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 Zin = 750 Ω)