Dipole Antennas Prof. Girish Kumar Electrical Engineering - - PowerPoint PPT Presentation

• Prof. Girish Kumar

Electrical Engineering Department, IIT Bombay

gkumar@ee.iitb.ac.in (022) 2576 7436

Dipole Antennas

Infinitesimal Dipole

An infinitesimally small current element is called the Hertz Dipole (Length L< λ/50)

Dipole and its field components in spherical polar co-ordinate

𝐵 = 𝐵𝑨 𝑨 = 𝜈 4𝜌 𝐽𝑝𝑒𝑚 𝑓−𝑘𝑙𝑠 𝑠 𝑓𝑘𝑥𝑢 𝑨 𝑗(𝑢) = 𝐽𝑝𝑓𝑘𝑥𝑢 𝑗𝑨 where, k =

2π λ

Assume an infinitesimal current element of length dl carrying an alternating current Io. The instantaneous current is

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 Far Field Region

Near Reactive Field Region Near Radiative Field Region

r >

where d is the maximum dimension

• f the antenna

Far Field Region (kr>>1)

Uniform Current - Radiation Pattern

max

3 4 2

rad

U D P   

Directivity

E-plane radiation pattern H-plane radiation pattern 3-D radiation pattern 𝐹𝜄 = 𝑘𝜃 𝑙𝐽𝑝𝑚 4𝜌𝑠 sin𝜄 𝐼𝜚 = 𝑘 𝑙𝐽𝑝𝑚 4𝜌𝑠 sin𝜄 𝐹𝜄 𝐼𝜚 = 𝜃 = 120𝜌 𝑆𝑠 = 80𝜌2 𝑚 𝜇

2

𝐹𝑠 ≃ 𝐹𝜚 = 𝐼𝑠 = 𝐼𝜄 = 0

Note : Infinitesimal antenna is not an efficient radiator

Impedance of free-space

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

Far Field Region (kr>>1)

Small Dipole – Radiation Resistance

Small dipole current distribution Small dipole vector potential

𝐽𝑓 𝑦′, 𝑧′, 𝑨′ = 𝑏𝑨𝐽0 1 − 2 𝑚 𝑨′ , 0 ≤ 𝑨′ ≤ 𝑚 2 𝑏𝑨𝐽0 1 + 2 𝑚 𝑨′ , − 𝑚 2 ≤ 𝑨′ ≤ 0 𝐵 𝑦, 𝑧, 𝑨 = 𝜈 4𝜌 𝑏𝑨

− 𝑚 2

𝐽0 1 + 2 𝑚 𝑨′ 𝑓−𝑘𝑙𝑆 𝑆 𝑒𝑨′ + 𝑏𝑨

𝑚 2

𝐽0 1 − 2 𝑚 𝑨′ 𝑓−𝑘𝑙𝑆 𝑆 𝑒𝑨′ 𝐹𝜄 ≃ 𝑘𝜃 𝑙𝐽0𝑚𝑓−𝑘𝑙𝑠 8𝜌𝑠 sin𝜄 𝐹𝑠 ≃ 𝐹𝜚 = 𝐼𝑠 = 𝐼𝜄 = 0 𝐼𝜚 ≃ 𝑘 𝑙𝐽0𝑚𝑓−𝑘𝑙𝑠 8𝜌𝑠 sin𝜄 𝑆𝑠 = 2𝑄𝑠𝑏𝑒 |𝐽0|2 = 20𝜌2 𝑚 𝜇

2

For l = λ / 10, Rr = 2 Ω l = λ / 4, Rr = 12.3 Ω Dipoles also have reactive impedance

Input Impedance of Transmission Line

Case 1: 𝑎𝑀= 0, → Z𝑗𝑜= 𝑘𝑎0tan𝛾𝑚 Case 2: 𝑎𝑀= ∞, → Z𝑗𝑜 =

𝑎0 𝑘tan𝛾𝑚

Case 3: 𝑎𝑀= 𝑎0, → Z𝑗𝑜 = 𝑎0 Where, 𝛾 =

2𝜌 𝜇

𝑗𝑔 𝑚 < 𝜇 4 → tan𝛾𝑚 = +𝑤𝑓 𝜇 4 < 𝑚 < 𝜇 2 → tan𝛾𝑚 = −𝑤𝑓

𝑎0 𝑎L 𝑎in

l

For Short-circuit, ZL = 0, Zin is inductive, so T-Line represents inductance Open-circuit, ZL = , Zin is capacitive, so T-Line represents capacitance

Half wavelength Dipole

Directivity of half-wavelength dipole

Electric and magnetic fields of a half-wavelength dipole

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.

𝑚 + 𝑒 = 0.48𝜇, where, d is the diameter of wire and d<𝜇/10 𝐹𝜄 ≃ 𝑘𝜃 𝐽0𝑓−𝑘𝑙𝑠 2𝜌𝑠 cos 𝜌 2 cos𝜄 sin𝜄 𝐼𝜚 ≃ 𝑘 𝐽0𝑓−𝑘𝑙𝑠 2𝜌𝑠 cos 𝜌 2 cos𝜄 sin𝜄 𝑆𝑠 = 2𝑄𝑠𝑏𝑒 |𝐽0|2 ≃ 73 𝐸0 = 4𝜌 𝑉max 𝑄𝑠𝑏𝑒 ≃ 1.643

D = 2.1 dB

λ/2 Dipole Radiation Resistance

Design of Dipole Antenna 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

Length of each segment = 50 mm Width = 4mm, Gap = 2mm BW for |S11| < 10 dB is from 1.39 to 1.54 GHz (150 MHz, 10.2%)

Flat Dipole Antenna Pattern and Directivity

Directivity of 4.8 dB is maximum at 3.75 GHz where length of dipole is approx. 1.25 λ Radiation Pattern at 1.5, 3.75 and 4.5 GHz

Printed Dipole Antenna

BW = 1.14 to 1.28 GHz (140 MHz, 11.6%)

Length of each segment = 50 mm Width = 4mm, Gap = 2mm FR4 substrate: εr = 4.4, tanδ = 0.02, h = 1.6mm

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

• r choking the outside current, are known as baluns (balance to unbalance).

Coaxial line Shorted together

𝜇 4 𝑚 𝑚 𝜇 4

Outer conductor

• f coax

Inner conductor

• f coax

Metal

𝜇 4 Coaxial Balun (1:1)- Narrow Bandwidth

Sleeve or bazooka balun Narrow BW

) 𝑎1(balanced ) 𝑎1(unbalanced Ferrite core Metal sleeve Shorted to coax’s

• uter conductor

Coaxial line

Ferrite core balun Wide BW

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.

Microstrip Balun Dipole Antenna for GSM900

Microstrip Balun Dipole Antenna L = 127 mm, w = 4 mm FR4 substrate: εr = 4.4, tanδ = 0.02, h = 1.6mm BW for |S11| < 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 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

𝑎𝑗𝑜 = 22𝑎𝑠 𝑎𝑗𝑜 = 4𝑎𝑠

2-fold dipole antennas are used in Yagi-Uda Antennas for TV reception using balanced line of Z0 = 300 Ω

Dipole Antenna Applications

Compact Dipole Antenna for RFID Chip Folded Broadband Dipole Antenna for RF Harvesting (Triangular shape for broadband and multi-fold gave Zin = 750 Ω)