Loop Antennas - Home | EM Labemlab.utep.edu/ee4382_AntennaEngineering/Topic 4 -- … · ·...
Transcript of Loop Antennas - Home | EM Labemlab.utep.edu/ee4382_AntennaEngineering/Topic 4 -- … · ·...
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.