## Radiation From Antennas

Radiation Patterns. The radiation pattern of an antenna is generally its most basic requirement, since it determines the spatial distribution of the radiated energy. This is usually the first property of an antenna that is specified, once the operating frequency has been stated. An antenna radiation pattern, or antenna pattern, is defined as a graphical representation of the radiation properties of the antenna as a function of space coordinates. Since antennas are commonly used as parts of wireless telecommunication systems, the radiation pattern is determined in the far-field region where no change in pattern with distance occurs. Using a spherical coordinate system, shown in Fig. 1, with the antenna at the origin, the radiation properties of the antenna depend only on the angles ф and в along a path or surface of constant radius. A plot of the radiated or received power at a constant radius is called a power pattern, while the spatial variation of the electric or magnetic field along a constant radius is called the amplitude field pattern. In practice, the necessary information from the complete three-dimensional pattern of an antenna can be obtained by taking a few two-dimensional patterns, according to the complexity of radiation pattern of the specific antenna. For most applications, a number of plots of the pattern as a function of в for some particular values of ф, plus a few plots as a function of ф for some particular values of в, give the needed information.

Antennas usually behave as reciprocal devices. This is very important, since it permits the characterization of the antenna either as a transmitting or as a receiving antenna. For example, radiation patterns are often measured with the test antenna operating in the receive mode. If the antenna is reciprocal, the measured pattern is identical when the antenna is in the transmit mode. If nonreciprocal materials, such as ferrites and active devices, are not present in an antenna, its transmitting and receiving properties are identical.

The radiation fields from a transmitting antenna vary inversely with distance, whereas the variation with observation angles (ф, в) depends on the antenna type. A very simple but basic configuration antenna is the ideal, or very short, dipole antenna. Since any linear or curved wire antenna may be regarded as being composed of a number of short dipoles connected in series, knowledge of this antenna is useful. So we will use the fields radiated from an ideal antenna to define and understand the properties of radiation patterns. An ideal dipole positioned symmetrically at the origin of the coordinate system and oriented along the г axis is shown in Fig. 1. The pattern of electromagnetic fields, with wavelength k, around a very short wire antenna of length L << k, carrying a uniform current I0e^mt, is described by functions of distance, frequency, and angle. Table 1 summarizes the expressions for the fields from a very short dipole antenna as given in Refs. 2 and 3. We have Ev = Hr = He = 0 for r >k and L ^k. The variables shown in these relations are I0 = amplitude (peak value in time) of current (A), supposed to be constant along the dipole; L = length of dipole (m); ш = 2nf = radian frequency, where f is the frequency in hertz; t = time (s), в = 2n/k = phase constant (rad/m) в = azimuthal angle, (dimensionless); c = velocity of light « 3x 108 m/s; k = wavelength (m); j = complex operator

Fig. 1. Spherical coordinate system for antenna analysis. A very short dipole is shown with the directions of its nonzero field components. |

= v * — distance from center of dipole to observation point, (m) and e0 = permittivity of free space = 8.85

pF/m.

Note that Ee and Hф are in time phase in the far field. Thus, the electric and magnetic fields in the far field of the spherical wave from the dipole are related in the same manner as in a plane traveling wave. Both

і-2 |

Fig. 2. Radiation field pattern of far field from an ideal (very short) dipole: (a) three-dimensional pattern plot, (b) E-plane radiation-pattern polar plot, and (c) H-plane radiation-pattern polar plot (HPBW, H-plane beamwidth).

are also proportional to sin в. That is, both are at a maximum when в = 90° and a minimum when в = 0° (in the direction of the dipole axis). This variation of Ee or Hф with angle can be presented by a field pattern, shown in Fig. 2, the length r of the radius vector being proportional to the value of the far field (Ee or Hф) in that direction from the dipole. The pattern in Fig. 2(a) is the three-dimensional far-field pattern for the ideal dipole, while the patterns in Fig. 2(b, c) are two-dimensional and represent cross sections of the three-dimensional pattern, showing the dependence of the fields on the angles в and ф.

All far-field components of a very short dipole are functions of I0, the dipole current; L/k, the dipole length in wavelengths; 1/r, the distance factor; jej(mt-er), the phase factor; and sin в, the pattern factor, which gives

the variation of the field with angle. In general, the expression for the field of any antenna will involve these factors.

For longer antennas with complicated current distribution the field components generally are functions of the above factors, which are grouped into the element factor and the space factor. The element factor includes everything except the current distribution along the source, which is the space factor of the antenna. For example, consider the case of a finite dipole antenna. The field expressions are produced by dividing the antenna into a number of very short dipoles and summing all their contributions. The element factor is equal to the field of the very short dipole located at a reference point, while the space factor is a function of the current distribution along the source, the latter usually described by an integral. The total field of the antenna is given by the product of the element and space factors. This procedure is known as pattern multiplication.

A similar procedure is also employed in array antennas, which are used when directive characteristics are needed. The increased electrical size of an array antenna due to the use of more than one radiating element gives better directivity and special radiation patterns. The total field of an array is determined by the product of the field of a single element and the array factor of the array antenna. If we use isotropic radiating elements, the pattern of the array is simply the pattern of the array factor. The array factor is a function of the geometry of the array and the excitation phase. Thus, changing the number of elements, their geometrical arrangement, their relative magnitudes, their relative phases, and their spacing, we obtain different patterns. Figure 3 shows some of characteristic patterns of an array antenna with two isotropic point sources as radiating elements, using different values of the above quantities, which produce different array factors.

Common Types of Radiation Patterns. An isotropic source or radiator is an ideal antenna that radiates uniformly in all directions in space. Although no practical source has this property, the concept of the isotropic radiator is very useful, and it is often used as a reference for expressing the directive properties of actual antennas. It is worth recalling that the power flux density S at a distance r from an isotropic radiator is Р|/4лт2, Pi being the transmitted power, since all the transmitted power is evenly distributed on the surface

of a spherical wavefront with radius r. The electric field intensity is calculated as v > (using – the relation from electric circuits, power = E2/n, where n is the characteristic impedance of free space, 377 Q).

On the contrary, a directional antenna is one that radiates or receives electromagnetic waves more effectively in some directions than in others. An example of an antenna with a directional radiation pattern is that of an ideal or very short dipole, shown in Fig. 2. It is seen that this pattern, which resembles a doughnut with no hole, is nondirectional in the azimuth plane, which is the xy plane characterized by the set of relations Щф), в = п/2], and directional in the elevation plane, which is any orthogonal plane containing the г axis characterized by [g(в), ф = constant]. This type of directional pattern is called an omnidirectional pattern and is defined as one having an essentially nondirectional pattern in a given plane, which for this case is the azimuth plane, and a directional pattern in any orthogonal plane, in this case the elevation plane. The omnidirectional pattern—known also as broadcast-type—is used for many broadcast or communication services where all directions are to be covered equally well. The horizontal-plane pattern is generally circular, while the vertical-plane pattern may have some directivity in order to increase the gain.

Other forms of directional patterns are pencil-beam, fan-beam, and shaped-beam patterns. The pencil- beam pattern is a highly directional pattern, which is used when it is desired to obtain maximum gain and when the radiation pattern is to be concentrated in as narrow an angular sector as possible. The beamwidths in the two principal planes are essentially equal. The fan-beam pattern is similar to the pencil-beam pattern except that the beam cross section is elliptical in shape rather than circular. The beamwidth in one plane may be considerably broader than in the other plane. As with the pencil-beam pattern, the fan-beam pattern generally implies a rather substantial amount of gain. The shaped-beam pattern is used when the pattern in one of the principal planes is desired to have a specified type of coverage. A typical example is the cosecant pattern, which is used to provide a constant radar return over a range of angles in the vertical plane. The

Fig. 3. Three-dimensional graphs of power radiation patterns for an array of two isotropic elements of the same amplitude and (a) opposite phase, spaced 0.5k apart, (b) phase quadrature, spaced 0.5k apart, (c) opposite phase, spaced 0.25k apart, and (d) opposite phase, spaced 1.5k apart. |

Ec) w |

pattern in the other principal plane is usually a pencil-beam type, but may sometimes be circular, as in certain types of beacon antennas.

In addition to the above pattern types, there are a number of special shapes used for direction finding and other purposes. These include the well-known figure-of-eight pattern, the cardioid pattern, split-beam patterns, and multilobed patterns whose lobes are of substantially equal amplitude. For such patterns, it is generally necessary to specify the pattern by an actual plot of its shape or by a mathematical relationship.

Antennas are often referred to by the type of pattern they produce. Two terms, which usually characterize array antennas, are broadside and endfire. A broadside antenna is one for which the main beam maximum is in a direction normal to the plane containing the antenna. An endfire antenna is one for which the main beam

Fig. 4. Polar plots of a linear uniform-amplitude array of five isotropic sources with 0.5-wavelength spacing between the sources: (a) broadside radiation pattern (0° phase shift between successive elements), and (b) endfire radiation pattern (180° phase shift).

is in the plane containing the antenna. For example, the short dipole antenna is a broadside antenna. Figure 4 shows two cases of broadside and endfire radiation patterns, which are produced from a linear uniform array of isotropic sources of 0.5-wavelength spacing between adjacent elements. The type of radiation pattern is controlled by the choice of phase shift between the elements. Zero phase shift produces a broadside pattern, and 180° phase shift (for this case where the spacing between adjacent element is 0.5 k) leads to an endfire pattern, while intermediate values produce radiation patterns with the main lobes between these two cases.

Characteristics of simple patterns. For a linearly polarized antenna, such as a very short dipole antenna, performance is often described in terms of two patterns [Fig. 2(b, c)]. Any plane containing the г axis has the same radiation pattern, since there is no variation in the fields with angle ф [Fig. 2(b)]. A pattern taken in one of these planes is called an E-plane pattern, because it is parallel to the electric field vector E and passes through the antenna in the direction of the beam maximum. A pattern taken in a plane orthogonal to an E plane and cutting through the short dipole antenna (the xy plane in this case) is called an H-plane pattern, because it contains the magnetic field H and also passes through the antenna in the direction of the beam maximum [Fig. 2(c)]. The E – and H-plane patterns, in general, are referred to as the principal-plane patterns. The pattern plots in Fig. 2(b, c) are called polar patterns or polar diagrams. For most types of antennas it is a usual practice to orient them so that at least one of the principal-plane patterns coincides with one of the geometrical principal planes. An illustration is shown in Fig. 5, where the principal planes of a microstrip antenna are plotted. The xy plane (azimuthal plane, в = п/2) is the principal E plane, and the хг plane (elevation plane, ф = 0) is the principal H plane.

A typical antenna power pattern is shown in Fig. 6. In Fig. 6(a), a polar plot on a linear scale is depicted, and in Fig. 6(b), the same pattern is shown in rectangular coordinates in decibels. As can be seen, the radiation pattern of the antenna consists of various parts, which are known as lobes. The main lobe (or main beam or major lobe) is defined as the lobe containing the direction of maximum radiation. In Fig. 6(a) the main lobe is pointing in the в = 0 direction. In some antennas there may exist more than one major lobe. A minor lobe is any lobe except the main lobe. Minor lobes comprise sidelobes and back lobes. The term sidelobe is sometimes reserved for those minor lobes near the main lobe, but is most often taken to be synonymous with minor lobe. A back lobe is a radiation lobe in, approximately, the opposite direction to the main lobe. Minor lobes usually

Fig. 5. The principal-plane patterns of a microstrip antenna: the xy plane or E plane (azimuth plane, 0 = n/2), and the xz plane or H plane (elevation plane, ф = 0). |

represent radiation in undesired directions, and they should be minimized. Sidelobes are normally the largest of the minor lobes. The level of side or minor lobes is usually expressed as a ratio of the power density in the lobe in question to that of the main lobe. This ratio is often termed the sidelobe ratio or sidelobe level and desired values of it depend on the antenna application.

For antennas with simple patterns, the half-power beamwidth and the sidelobe level in the two principal planes specify the important characteristics of the patterns. The half-power beamwidth (HPBW) is defined in a plane containing the major maximum beam, as the angular width within which the radiation intensity is at least one-half the maximum value for the beam. The beamwidth between first nulls (BWFN) and the beam widths 10 dB or 20 dB below the pattern maximum are also sometimes used. All of them are shown in Fig. 6. However the term beamwidth by itself is usually reserved to describe the half-power (3 dB) beamwidth.

The beamwidth of the antenna is a very important figure of merit in the overall design of an antenna application. As the beamwidth of the radiation pattern increases, the sidelobe level decreases, and vice versa. So there is a tradeoff between the sidelobe ratio and beamwidth.

In addition, the beamwidth of the antenna is used to describe the resolution of the antenna: its ability to distinguish between two adjacent radiating sources or radar targets. The most common measure of resolution is half the first null beamwidth, which is usually used to approximate the half-power beamwidth. This means that two sources separated by angular distances equal to or greater than the HPBW of an antenna, with a uniform distribution, can be resolved. If the separation is smaller, then the antenna will tend to smooth the two signals into one.

Field Regions of an Antenna. For convenience, the space surrounding a transmitting antenna is divided into several regions, although, obviously, the boundaries of the regions cannot be sharply defined. The names given to the various regions denote some pertinent prominent property of each region.

In free space there are mainly two regions surrounding a transmitting antenna, the near-field region and the far-field region. The near-field region can be subdivided into two regions, the reactive near field and the radiating near field.

The first and innermost region, which is immediately adjacent to the antenna, is called the reactive or induction near-field region. Of all the regions, it is the smallest. It derives its name from the reactive field, which lies close to every current-carrying conductor. In this region the reactive field, which decreases with either the

Fig. 6. Antenna power patterns: (a) a typical polar plot on a linear scale, and (b) a plot in rectangular coordinates on a decibel (logarithmic) scale. The associated lobes and beamwidths are also shown. |

square or the cube of distance, dominates over all radiated fields, the components of which decrease with the

first power of distance. For most antennas, this region is taken to extend over distances r < 0.62 V ■ ‘ from the antenna as long as D > k, where D is the largest dimension of the antenna and к is the wavelength (2). For the case of an ideal or very short dipole, for which D = hz ^ k, this distance is approximately one-sixth

of a wavelength (k/2n). At this distance from the very short dipole the reactive and radiation field components are respectively equal in magnitude.

Between the reactive near-field region and far-field regions lies the radiating near-field region, which is the region where the radiation fields dominate, but the angular field distribution still depends on the distance from the antenna. For a transmitting antenna focused at infinity, which means that the rays at a large distance from the antenna are parallel, the radiating near-field region is sometimes referred to as the Fresnel region, a term taken from the field of optics. This is taken to be that between the end of reactive near-field region (r >

0.62 V ■ " ) and the starting distance of the far-field region (r < 2D2/X)(2).

The outer boundary of the near-field region lies where the reactive field intensity becomes negligible with respect to the radiation field intensity. This occurs at distances of either a few wavelengths or a few times the major dimension of the antenna, whichever is the larger. The far-field or radiation region begins at the outer boundary of the near-field region and extends outward indefinitely into free space. In this region the angular distribution of the field is essentially independent of the distance from the antenna. For example, for the case of a very short dipole, the sin в pattern dependence is valid anywhere in this region. The far-field region is commonly taken to be at distances r > 2D2/k from the antenna, and for an antenna focused at infinity it is sometimes referred to as the Fraunhofer region.

All three regions surrounding an antenna and their boundaries are illustrated in Fig. 7.

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