Introduction to Antennas and Radiating Systems

Caleb Wherry∗

Austin Peay State University Department of Computer Science

William Cooke†

Austin Peay State University Department of Physics and Astronomy

(Dated: May 1, 2011)

Abstract

A basic overview of antennas and radiating systems is presented. The concept of radiation from

accelerating charges and basic antenna concepts and design are explained. An example half-wave

dipole is analyzed.

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INTRODUCTION

Antennas are everywhere. From the depths of space to the depths of Earth’s oceans.

With the recent emphasis on wireless devices antennas have taken on an ever-increasing

importance. In this paper we will briefly overview what an antenna is, how they work and

some performance criteria, and analyze a simple example.

WHAT IS AN ANTENNA

To understand how an antenna works, it is important to first understand its purpose. An

electromagnetic wave can radiate through free space and an electric current can flow through

a conductive path. The antenna’s purpose is to serve as an interface, or transducer, between

the current and the free space wave. It transforms the wave to and from the current[1].

The current flows in a transmission line or other circuit. A transmission line may be

coaxial cable or parallel wires or some other medium with a well defined, complex impedance.

It is an important part of the antenna system.

A free space wave consists of fields instead of currents. The energy is carried in the fields.

Just as the transmission line has a characteristic impedance, so does free space. As shown

by Kraus[1], it is a pure resistance of

√

µ0/ǫ0 = 377Ω. (1)

To convert the current to a wave or vice-versa requires an antenna. A wave imposed on

an antenna causes a current to flow within the conductor. The current is proportional to

the field strength at a given time and location. Conversely, when a current oscillates in the

conductor the accelerating charges emit radiation.

HOW AN ANTENNA WORKS

Consider an electric dipole separated by a distance, d[2]. By driving the charges to and

from opposite ends in a sinusoidal motion with angular frequency ω, E and B fields will

be created that follow the charges. The E field is parallel to the movement, the B field is

perpendicular, and they are in phase. After each complete cycle, the ends of the field lines

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Dipole axis

FIG. 1. Energy Radiated from oscillating dipole

connect, creating a loop, that radiates away from the dipole, carrying energy with it. That

energy is provided by the driving force.

The Poynting vector determines the energy radiated from the dipole:

S =1

µ0

(E×B) =µ0

c

[

p0ω2

4π

(

sin θ

r

)

cos[

ω(

t−r

c

)]

]2

r (2)

. The waves have a wavelength of λ = 2πc/ω. There is no radiation along the axis of the

dipole, as shown in figure 1.

Longer conductors can be considered a series of connected dipoles. The E and B fields

add to increase the amount of energy radiated.

The waves radiated are transverse, in phase, and perpendicular. They radiate away

from the antenna at velocity c. There are non-radiating fields whose strength drops off

rapidly away from the antenna. The area near the antenna where the non-radiating fields

are strongest is designated the near field, the area further away the far field, or radiation

zone. There is no strict defining border between the two, but typically it is considered to

be one wavelength from the antenna.

By convention, the polarization of an antenna is defined as the plane of the E field

component. In a linear antenna such as the dipole the polarization is restricted to one

plane. If two perpendicular linear antennas are driven with currents 90 out of phase, the

vector sum of the waves will form a helix. This polarization is elliptical, or circular if the

amplitudes are equal. The vector can rotate clockwise or counter-clockwise. See figure 2.

For maximum energy transfer between a wave and a receiving antenna, the polarization

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FIG. 2. vertical(blue), horizontal(red), and circular(black) polarization

must be the same. If the polarization of the incident wave is unknown or not constant,

circular polarization becomes the most efficient. For instance, satellites may be oriented

in any direction relative to antennas on Earth and waves may also change polarization by

reflection or refraction of a non-constant medium such as the ionosphere. A helical antenna

creates circular polarization directly and is often used for space communication[1].

An isotropic radiator is an antenna that radiates power equally in all directions. It is a

reference only and is not physically realizable. It was shown in 2 that even the simple dipole

oscillator radiation varies with the angle from the axis. Variation in the radiation pattern

can be useful to increase signal power in a desired direction while minimizing it in others.

The radiation pattern is the same for transmission and reception.

To complete the interface, the antenna must be connected to an electric circuit. En-

ergy must transfer between the circuit and the antenna, therefore the antenna presents an

impedance to the electric circuit. The impedance of the antenna is controlled by several

factors.

Radiation resistance comes from power radiating away from the antenna. Kraus shows

that a dipole in air or vacuum has a radiation resistance:

Rr = 80π2(

L

λ

)2

. (3)

The radiation resistance is a pure resistance.

The conductors of the antenna have ohmic losses. Power dissipated in the ohmic losses

will be converted to heat.

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If the antenna is not electrically resonant power will be reflected. In that case the antenna

will have a reactive component: capacitive if the antenna is too short, and inductive if too

long.

The impedance presented by the antenna is the complex sum of the three components.

The environment surrounding the antenna alters the characteristics, especially the resonance.

Environmental factors such as nearby conductors, including the Earth, play an important

role in determining the characteristics, as well as the radiation pattern.

THE λ/2 DIPOLE

As a concrete example, we will now discuss the half-wavelength, center-fed dipole an-

tenna. It is a fundamental antenna, often used alone or as the basis of many more complex

configurations. It serves as a starting point in antenna analysis. The calculations here are

for air or vacuum and will differ in other media.

The half-wave dipole has two elements, each λ/4 in length, arranged linearly, for a specific

frequency f = ω/2π. At the center are terminals attached to other circuitry. When excited

by a driving current or an incident wave, a current will flow in the elements. The current

will be delayed by the propagation time at distance r of r/c. The retarded current is then:

[I] = I0ejω(t−r/c). (4)

For a dipole of length L, the retarded current at distance z from the terminals is

[I] = I0 sin[

2π

λ

(

L

2± z

)]

ejω(t−r/c). (5)

. By integrating each length dz as an independent dipole the fields for the entire antenna

can be calculated. After integrating and simplifying, the far fields are:

Hφ =j[I0]

2πr

[

cos [(βL cos θ) /2]− cos (βL/2)

sin θ

]

(6)

Eφ = HφZ = Hφ120π (7)

where β = ω/c, r the distance from center of the antenna, and θ the angle from the axis of

the antenna.

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By using the relation

P =

(

I0√2

)2

R0 (8)

we can find R0, the radiation resistance. The power, P , is the integral over a large sphere

of the Poynting vector

The radiation resistance is shown by Kraus to be 73Ω in free space.

CONCLUSION

Antenna theory and design is a large subject but very important to current technology.

Here we have provided only a brief overview. With an understanding of what an antenna

does and how it works, one can better prepare for the effects of electromagnetic radiation,

intended or unintended, into or out of any electronic device or experiment.

∗ calebwherry@gmail.com; www.calebwherry.com

† wrcooke@wrcooke.net; www.wrcooke.net

[1] J. D. Kraus, Antennas, 2nd ed. (McGraw-Hill, New York, 1988).

[2] D. J. Griffiths, Introduction to Electrodynamics, 3rd ed. (Prentice-Hall, Upper Saddle River,

NJ, 1999).

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