Introduction to Antennas and Radiating Systems

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 fromaccelerating charges and basic antenna concepts and design are explained. An example half-wavedipole is analyzed. 1

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-increasingimportance. In this paper we will briefly overview what an antenna is, how they work andsome 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. Anelectromagnetic wave can radiate through free space and an electric current can flow througha conductive path. The antenna’s purpose is to serve as an interface, or transducer, betweenthe 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 becoaxial 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 shownby Kraus[1], it is a pure resistance of µ0 / 0 = 377Ω. (1) To convert the current to a wave or vice-versa requires an antenna. A wave imposed onan antenna causes a current to flow within the conductor. The current is proportional tothe field strength at a given time and location. Conversely, when a current oscillates in theconductor the accelerating charges emit radiation.HOW AN ANTENNA WORKS Consider an electric dipole separated by a distance, d[2]. By driving the charges to andfrom opposite ends in a sinusoidal motion with angular frequency ω, E and B fields willbe created that follow the charges. The E field is parallel to the movement, the B field isperpendicular, and they are in phase. After each complete cycle, the ends of the field lines 2

Dipole axis FIG. 1. Energy Radiated from oscillating dipoleconnect, creating a loop, that radiates away from the dipole, carrying energy with it. Thatenergy is provided by the driving force. The Poynting vector determines the energy radiated from the dipole: 2 1 µ0 p 0 ω 2 sin θ r S = (E × B) = cos ω t − ˆ r (2) µ0 c 4π r c. The waves have a wavelength of λ = 2πc/ω. There is no radiation along the axis of thedipole, as shown in figure 1. Longer conductors can be considered a series of connected dipoles. The E and B fieldsadd to increase the amount of energy radiated. The waves radiated are transverse, in phase, and perpendicular. They radiate awayfrom the antenna at velocity c. There are non-radiating fields whose strength drops offrapidly away from the antenna. The area near the antenna where the non-radiating fieldsare strongest is designated the near field, the area further away the far field, or radiationzone. There is no strict defining border between the two, but typically it is considered tobe one wavelength from the antenna. By convention, the polarization of an antenna is defined as the plane of the E fieldcomponent. In a linear antenna such as the dipole the polarization is restricted to oneplane. If two perpendicular linear antennas are driven with currents 90◦ out of phase, thevector sum of the waves will form a helix. This polarization is elliptical, or circular if theamplitudes 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 3

FIG. 2. vertical(blue), horizontal(red), and circular(black) polarizationmust 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 orientedin any direction relative to antennas on Earth and waves may also change polarization byreﬂection or refraction of a non-constant medium such as the ionosphere. A helical antennacreates 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 areference only and is not physically realizable. It was shown in 2 that even the simple dipoleoscillator radiation varies with the angle from the axis. Variation in the radiation patterncan 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 animpedance to the electric circuit. The impedance of the antenna is controlled by severalfactors. Radiation resistance comes from power radiating away from the antenna. Kraus showsthat a dipole in air or vacuum has a radiation resistance: 2 L Rr = 80π 2 . (3) λThe radiation resistance is a pure resistance. The conductors of the antenna have ohmic losses. Power dissipated in the ohmic losseswill be converted to heat. 4

If the antenna is not electrically resonant power will be reflected. In that case the antennawill have a reactive component: capacitive if the antenna is too short, and inductive if toolong. 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 importantrole 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 complexconfigurations. It serves as a starting point in antenna analysis. The calculations here arefor 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 specificfrequency f = ω/2π. At the center are terminals attached to other circuitry. When excitedby a driving current or an incident wave, a current will flow in the elements. The currentwill be delayed by the propagation time at distance r of r/c. The retarded current is then: [I] = I0 ejω(t−r/c) . (4)For a dipole of length L, the retarded current at distance z from the terminals is 2π L [I] = I0 sin ±z ejω(t−r/c) . (5) λ 2. By integrating each length dz as an independent dipole the fields for the entire antennacan be calculated. After integrating and simplifying, the far fields are: j[I0 ] cos [(βL cos θ) /2] − cos (βL/2) Hφ = (6) 2πr sin θ Eφ = Hφ Z = Hφ 120π (7)where β = ω/c, r the distance from center of the antenna, and θ the angle from the axis ofthe antenna. 5

By using the relation 2 I P = √0 R0 (8) 2we can find R0 , the radiation resistance. The power, P , is the integral over a large sphereof 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 antennadoes 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). 6

Introduction to Antennas and Radiating Systems

by J. Caleb Wherry

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