# Chapter 9 Radiation and Antennas

# Chapter Contents

1. Overview

2. 9.1 The Hertzian Dipole

3. 9.2 Antenna Radiation Characteristics

4. 9.3 Half-Wave Dipole Antenna

5. 9.4 Dipole of Arbitrary Length

6. 9.5 Effective Area of a Receiving Antenna

7. 9.6 Friis Transmission Formula

8. TB 17 Health Risks of EM Fields

9. 9.7 Radiation by Large-Aperture Antennas

10. 9.8 Rectangular Aperture with Uniform Aperture Distribution

11. 9.9 Antenna Arrays

12. 9.10 N-Element Array with Uniform Phase Distribution

13. 9.11 Electronic Scanning of Arrays

1. Chapter 9 Summary

2. Problems

# Objectives

Upon learning the material presented in this chapter, you should be able to:

1. Calculate the electric and magnetic fields of waves radiated by a dipole antenna.

2. Characterize the radiation of an antenna in terms of its radiation pattern, directivity, beamwidth, and radiation resistance.

3. Apply the Friis transmission formula to a free-space communication system.

4. Calculate the electric and magnetic fields of waves radiated by aperture antennas.

5. Calculate the radiation pattern of multi-element antenna arrays.

# Overview

An antenna is a transducer that converts a guided wave propagating on a transmission line into an electromagnetic wave propagating in an unbounded medium (usually free space), or vice versa. Figure 9-1 shows how a wave is launched by a hornlike antenna with the horn acting as the transition segment between the waveguide and free space.

# Figure 9-1 Antenna as a transducer between a guided electromagnetic wave and a free-space wave, for both transmission and reception.

(a) Transmission mode

Figure 9 1-a Full Alternative Text

(b) Reception mode

Figure 9 1-b Full Alternative Text

Antennas are made in various shapes and sizes (Fig. 9-2) and are used in radio and television broadcasting and reception, radio-wave communication systems, cellular telephones, radar systems, anticollision automobile sensors, and many other applications. The radiation and impedance properties of an antenna are governed by its shape, size, and material properties. The dimensions of an antenna are usually measured in units of λ of the wave it is launching or receiving; a 1-m long dipole antenna operating at a wavelength λ=2 m exhibits the same properties as a 1-cm long dipole operating at λ=2 cm. Hence, in most of our discussions in this chapter, we refer to antenna dimensions in wavelength units.

# Figure 9-2 Various types of antennas.

(a) Thin dipole

(b) Biconical dipole

(c) Loop

(d) Helix

(e) Log-periodic

Figure 9 2-e Full Alternative Text

(f) Parabolic dish reflector

(g) Horn

(h) Microstrip

Figure 9 2-h Full Alternative Text

(i) Antenna array

# Reciprocity

The directional function characterizing the relative distribution of power radiated by an antenna is known as the antenna radiation pattern (or simply the antenna pattern). An isotropic antenna is a hypothetical antenna that radiates equally in all directions, and it is often used as a reference radiator when describing the radiation properties of real antennas.

Reciprocity means that, if in the transmission mode a given antenna transmits in direction A 100 times the power it transmits in direction B, then when used in the reception mode it is 100 times more sensitive to electromagnetic radiation incident from direction A than from B. All of the antennas shown in Fig. 9-2 obey the reciprocity law, but not all antennas are reciprocal devices. Reciprocity may not hold for some solid-state antennas composed of nonlinear semiconductors or ferrite materials. Such nonreciprocal antennas are beyond the scope of this chapter; hence, reciprocity is assumed throughout. The reciprocity property is very convenient because it allows us to compute the radiation pattern of an antenna in the transmission mode—even when the antenna is intended to operate as a receiver.

To fully characterize an antenna, one needs to study its radiation properties and impedance. The radiation properties include its directional radiation pattern and the associated polarization state of the radiated wave when the antenna is used in the transmission mode, which is also called the antenna polarization.

The second aspect, the antenna impedance, pertains to the transfer of power from a generator to the antenna when the antenna is used as a transmitter and, conversely, the transfer of power from the antenna to a load when the antenna is used as a receiver, as will be discussed later in Section 9-5. It should be noted that throughout our discussions in this chapter it will be assumed that the antenna is properly matched to the transmission line connected to its terminals, thereby avoiding reflections and their associated problems.

# Radiation Sources

Radiation sources fall into two categories: currents and aperture fields. The dipole and loop antennas (Fig. 9-2(a) and (c)) are examples of current sources; the time-varying currents flowing in the conducting wires give rise to the radiated electromagnetic fields. A horn antenna (Fig. 9-2(g)) is an example of the second group because the electric and magnetic fields across the horn’s aperture serve as the sources of the radiated fields. The aperture fields are themselves induced by time-varying currents on the surfaces of the horn’s walls. Therefore, all radiation ultimately is due to time-varying currents. The choice of currents or apertures as the sources is merely a computational convenience arising from the structure of the antenna. We will examine the radiation processes associated with both types of sources.

# Far-Field Region

The wave radiated by a point source is spherical in nature, with the wavefront expanding outward at a rate equal to the phase velocity u p (or the velocity of light c if the medium is free space). If R, which is the distance between the transmitting antenna and the receiving antenna, is sufficiently large enough for the wavefront across the receiving aperture to be considered planar (Fig. 9-3), then the receiving aperture is said to be in the far-field (or far-zone) region of the transmitting point source. This region is of particular significance because—for most applications—the location of the observation point is indeed in the far-field region of the antenna. The far-field plane-wave approximation allows the use of certain mathematical approximations that simplify the computation of the radiated field and, conversely, provide convenient techniques for synthesizing the appropriate antenna structure that would give rise to the desired far-field antenna pattern.

# Figure 9-3 Far-field plane-wave approximation.

Figure 9 3 Full Alternative Text

# Antenna Arrays

When multiple antennas operate together, the combination is called an antenna array (Fig. 9-2(i)), and the array as a whole behaves as if it were a single antenna. By controlling the magnitude and phase of the signal feeding each antenna, it is possible to shape the radiation pattern of the array and to electronically steer the direction of the beam electronically. These topics are treated in Sections 9-9 to 9-11.