Prof. Girish KumarElectrical 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

𝐴 = 𝐴𝑧 𝑧 =𝜇

4𝜋𝐼𝑜𝑑𝑙

𝑒−𝑗𝑘𝑟

𝑟𝑒𝑗𝑤𝑡 𝑧

𝑖(𝑡) = 𝐼𝑜𝑒𝑗𝑤𝑡 𝑖𝑧

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

of the antenna

Far Field Region (kr>>1)

Uniform Current - Radiation Pattern

max

0

34

2rad

UD

P

Directivity

E-plane radiation pattern

H-plane radiation pattern

3-D radiation pattern

𝐸𝜃 = 𝑗𝜂𝑘𝐼𝑜𝑙

4𝜋𝑟sin𝜃

𝐻𝜙 = 𝑗𝑘𝐼𝑜𝑙

4𝜋𝑟sin𝜃

𝐸𝜃

𝐻𝜙= 𝜂 = 120𝜋

𝑅𝑟 = 80𝜋2𝑙

𝜆

2

𝐸𝑟 ≃ 𝐸𝜙 = 𝐻𝑟 = 𝐻𝜃 = 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

𝐼𝑒 𝑥′, 𝑦′, 𝑧′ = 𝑎𝑧𝐼0 1 −2

𝑙𝑧′ , 0 ≤ 𝑧′ ≤ 𝑙 2

𝑎𝑧𝐼0 1 +2

𝑙𝑧′ , − 𝑙 2 ≤ 𝑧′ ≤ 0

𝐴 𝑥, 𝑦, 𝑧 =𝜇

4𝜋 𝑎𝑧

− 𝑙 2

0

𝐼0 1 +2

𝑙𝑧′

𝑒−𝑗𝑘𝑅

𝑅𝑑𝑧′

+ 𝑎𝑧

0

𝑙 2

𝐼0 1 −2

𝑙𝑧′

𝑒−𝑗𝑘𝑅

𝑅𝑑𝑧′

𝐸𝜃 ≃ 𝑗𝜂𝑘𝐼0𝑙𝑒

−𝑗𝑘𝑟

8𝜋𝑟sin𝜃

𝐸𝑟 ≃ 𝐸𝜙 = 𝐻𝑟 = 𝐻𝜃 = 0

𝐻𝜙 ≃ 𝑗𝑘𝐼0𝑙𝑒

−𝑗𝑘𝑟

8𝜋𝑟sin𝜃

𝑅𝑟 =2𝑃𝑟𝑎𝑑

|𝐼0|2 = 20𝜋2

𝑙

𝜆

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: 𝑍𝐿= 0, → Z𝑖𝑛= 𝑗𝑍0tan𝛽𝑙

Case 2: 𝑍𝐿= ∞, → Z𝑖𝑛 =𝑍0

𝑗tan𝛽𝑙

Case 3: 𝑍𝐿= 𝑍0, → Z𝑖𝑛 = 𝑍0

Where, 𝛽 =2𝜋

𝜆

𝑖𝑓 𝑙 <𝜆

4→ tan𝛽𝑙 = +𝑣𝑒

𝜆

4< 𝑙 <

𝜆

2→ tan𝛽𝑙 = −𝑣𝑒

𝑍0 𝑍L

𝑍in

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 dipoleElectric 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.

𝑙 + 𝑑 = 0.48𝜆, where, d is the diameter of wire and d<𝜆/10

𝐸𝜃 ≃ 𝑗𝜂𝐼0𝑒

−𝑗𝑘𝑟

2𝜋𝑟

cos𝜋2 cos𝜃

sin𝜃

𝐻𝜙 ≃ 𝑗𝐼0𝑒

−𝑗𝑘𝑟

2𝜋𝑟

cos𝜋2 cos𝜃

sin𝜃

𝑅𝑟 =2𝑃𝑟𝑎𝑑

|𝐼0|2 ≃ 73

𝐷0 = 4𝜋𝑈max

𝑃𝑟𝑎𝑑≃ 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

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

Coaxial line

Shorted

together

𝜆 4

𝑙 𝑙

𝜆 4

Outer

conductor

of coax

Inner

conductor

of coax

Metal

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

Sleeve or bazooka balun

Narrow BW

)𝑍1(balanced

)𝑍1(unbalanced

Ferrite core

Metal sleeve

Shorted to coax’s

outer conductorCoaxial 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

𝑍𝑖𝑛 = 22𝑍𝑟

𝑍𝑖𝑛 = 4𝑍𝑟

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)