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Loop Antennas

EE-4382/5306 - Antenna Engineering

Outline• Introduction

• Small Circular Loop

• Circular Loop of Constant current

2Linear Wire Antennas

Constantine A. Balanis, Antenna Theory: Analysis and Design 4th Ed., Wiley, 2016.

Stutzman, Thiele, Antenna Theory and Design 3rd Ed., Wiley, 2012.

Introduction

3

Loop Antennas - Introduction

Slide 4

Loop antennas are also simple, cheap, and very versatile.It is the equivalent to the magnetic dipole, in comparison to the electrical dipole.They are classified into electrically small and electrically large.

Linear Wire Antennas

Small Circular Loop

5

Slide 6Linear Wire Antennas

𝑎 ≪ 𝜆𝐼 = 𝐼0

Small Circular Loop - Fields

Introduction to Antennas Slide 7

𝐻𝑟 = 𝑗𝑘𝑎2𝐼0 cos 𝜃

2𝑟21 +

1

𝑗𝑘𝑟𝑒−𝑗𝑘𝑟

𝐻𝜃 = −(𝑘𝑎)2𝐼0 sin 𝜃

4𝑟1 +

1

𝑗𝑘𝑟−

1

𝑘𝑟 2𝑒−𝑗𝑘𝑟

𝐻𝜙 = 0

𝐸𝑟 = 𝐸𝜃 = 0

𝐸𝜙 = 𝜂(𝑘𝑎)2𝐼0 sin 𝜃

4𝑟1 +

1

𝑗𝑘𝑟𝑒−𝑗𝑘𝑟

Small Circular Loop- Fields

Slide 8Linear Wire Antennas

Power Density and Radiation Resistance

Slide 9Linear Wire Antennas

𝑅𝑟 = 𝜂𝜋

6𝑘2𝑎2 2 = 𝜂

2𝜋

3

𝑘𝑆

𝜆

2

= 20𝜋2𝐶

𝜆

4

≅ 31,171𝑆2

𝜆4

𝑅𝑟 = 𝜂2𝜋

3

𝑘𝑆

𝜆

2

𝑁2 = 20𝜋2𝐶

𝜆

4

𝑁2 ≅ 31,171𝑁2𝑆2

𝜆4

𝑆 = 𝜋𝑎2

𝐶 = 2𝜋𝑎

Effect of turns on circular loop antenna

Introduction to Antennas Slide 10

As with the inf/short dipole, the short loop suffers from very small radiation resistance and big radiation losses. However this can be accounted for by multiturn loop antennas.Current distribution in multiturn antennas is complex and experiments are employed to measure the radiation efficiencies.The total ohmic resistance for an N-turn circular-loop antenna is

𝑅𝑜ℎ𝑚𝑖𝑐 =𝑁𝑎

𝑏𝑅𝑠

𝑅𝑝

𝑅0+ 1

𝑎 = loop radius𝑏 = wire radius

2𝑐 = loop separationRp = ohmic resistance per unit length based on proximity effect

𝑅0 =𝑁𝑅𝑠2𝜋𝑏

= ohmic skin effect resistance per unit length

Effect of turns on circular loop antenna

Introduction to Antennas Slide 11

Small Circular Loop Antenna –Examples

Introduction to Antennas Slide 12

Find the radiation resistance of a single-turn and eight-turn small

circular loop. The radius of the loop is 𝜆

25and the medium is free-

space.

Small Circular Loop Antenna –Examples

Introduction to Antennas Slide 13

Find the radiation efficiency of a single-turn and an eight-turn

small circular loop at 𝑓 = 100 MHz. The radius of the loop is 𝜆

25,

the radius of the wire is 10−4𝜆. The turns are spaced 4 × 10−4𝜆apart. Assume the wire is copper with conductivity of 5.7 ×

107𝑆

𝑚and the antenna is radiating into free-space.