Monthly Archives: February 2014
Antenna Performance Measures
(1) 
Poynting Vector and Radiation Power Density. In an electromagnetic wave, energy is stored in equal amounts in the electric and magnetic fields, which together constitute the wave. The power flow is found by making use of the Poynting vector, S, defined as
S=ExH
where E (V/m) and H (A/m) are the field vectors. Since the Poynting vector represents a surface power density (W/m2), the integral of its normal component over a closed surface always gives the total power through the surface. That is,
where P is the total power (W) flowing out of closed surface A, and dA = ndA, и being the unit vector normal to surface. The Poynting vector S and the power P in the above relations are instantaneous values.
Normally, it is the timeaveraged Poynting vector Sav, which represents the average power density, that is of practical interest. It is given by
where Re stands for the real part of the complex number and the asterisk denotes the complex conjugate. Note that /? and H in Eq. (3) are the electric and magnetic fields written as complex numbers to include the change with time. That is, for a plane wave traveling in the positive г direction with electric and magnetic field components in the x and у directions, respectively, the electric field is E =xEx0e’coT while in Eq. (1) it is E =xEx0. The factor  appears because the fields represent peak values; it should be omitted for rms values. The average power Pav flowing outward through a closed surface can now be obtained by integrating Eq.
(3):
Consider the case that the electromagnetic wave is radiated by an antenna. If the closed surface is taken around the antenna within the farfield region, then this integration results in the average power radiated by the antenna. This is called radiation power, Prad, while Eq. (3) represents the radiation power density, Sav, of the antenna. The imaginary part of Eq. (3) represents the reactive power density stored in the near field of an antenna. Since the electromagnetic fields of an antenna in its farfield region are predominately real, Eq. (3) is enough for our purposes.
The average power density radiated by the antenna as a function of direction, taken on a large sphere of constant radius in the farfield region, results in the power pattern of the antenna.
РГ /*2тг /*7Т Pr&d = II Si’dA= I I [rSi(r)l • [fr2sinedBd<t>] = 4;7T2Sj JJa Jо Jo 
As an example, for an isotropic radiator, the total radiation power is given by
Here, because of symmetry, the Poynting vector Si =! Stir) is taken independent of the spherical coordinate angles в and ф, having only a radial component.
From Eq. (5) the power density can be found:
The above result can also be reached if we assume that the radiated power expands radially in all directions with the same velocity and is evenly distributed on the surface of a spherical wavefront of radius r.
As we will see later, an electromagnetic wave may have an electric field consisting of two orthogonal linear components of different amplitudes, Ex0 and Ey0, respectively, and a phase angle between them, S. Thus, the total electric field vector, called an elliptically polarized vector, becomes
which at г = 0 becomes
So i£is a complex vector (phasorvector), which is resolvable into two components хЁх and >’ЁУ. The total H vector associated with/?, at г = 0, is then
where f is the phase lag of Hy with respect to Ёх. From Eq. (9) the complex conjugate magnetic field can be found changing only the signs of exponents.
Now the average Poynting vector can be calculated using the above fields:
It should be noted that Sav is independent of S, the phase angle between the electric field components.
In a lossless medium t;= 0, because the electric and magnetic fields are in time phase and Ex0/Hx0 = Exl,/Hxl,
j/£’2 /£2 jJJ2 , JJ2
= i], where i] is the intrinsic impedance of the medium, which is real. If E = V *() J’11 and H = V
are the amplitudes of the total E and H fields respectively, then 
(11)
The above expressions are the most general form of radiation power density of an elliptically polarized wave or of an elliptically polarized antenna, respectively, and hold for all cases, including the linear and circular polarization cases, that we will introduce later on.
Radiation Intensity. Radiation intensity is a farfield parameter, in terms of which any antenna radiation power pattern can be determined. Thus, the antenna power pattern, as a function of angle, can be expressed in terms of its radiation intensity as (2,3)
ЩЄ, ф) = S^vr2
r2 л
= ~Е(гв, ф)2 2ц
(12) 
= ^[Е, Лг,9,ф)2 + Еф(г, Є,ф)*] ~ 2~ 0)2 + Еф{$, 0)2
where
U(Q, ф) = radiation intensity (W/unit solid angle)
Sav = radiation density, or radial component of Poynting vector (W/m2)
E(r,0,ф) = total transverse electric field (V/m)
H(r,6,ф) = total transverse magnetic field (A/m) r = distance from antenna to point of measurement (m)
П = intrinsic impedance of medium (^/square)
In Eq. (12) the electric and magnetic fields are expressed in spherical coordinates.
What makes radiation intensity important is that it is independent of distance. This is because in the far field the Poynting vector is entirely radial, which means the fields are entirely transverse and E and H vary as 1/r.
Since the radiation intensity is a function of angle, it can also be defined as the power radiated from an antenna per unit solid angle. The unit of solid angle is the steradian, defined as the solid angle with its vertex at the center of a sphere of radius r that is subtended by an area on the sphere equal to r2. But the area of a sphere of radius r is given by A = 4nr2, so in the whole sphere there are 4nr2/r2 = 4n sr. For a sphere of radius r, an infinitesimal area dA on the surface of it can be written as
(13) 
dA = r2 sin вdвdф (ш2)
Thus, the total power can be obtained by integrating the radiation intensity, as given by Eq. (12), over the entire solid angle of 4n as
and therefore the element of solid angle dQ of a sphere is given by 
dA dSl = —5 = sin в d в d ф (sr) rB 
As an example, for the isotropic radiator ideal antenna, the radiation intensity и(в, ф) will be independent of the angles в and ф, and the total radiated power will be
Prad = §CiUld^ = Ui f f sm6d6d^ = Ui$iidn = 4xUi (16) Jo Jo
or Ui = Prad/4n, which is the power density of Eq. (6) multiplied by r2.
Dividing и(в, ф) by its maximum value Umax(e, ф), we obtain the normalized antenna power pattern,
A term associated with the normalized power pattern is the beam solid angle QA defined as the solid angle through which all the power from a radiating antenna would flow if the power per unit solid angle were constant over that solid angle and equal to its maximum value (Fig. 8). This means that, for typical patterns, the beam solid angle is approximately equal to the halfpower beamwidth (HPBW), that is,
If the integration is done over the main lobe, the mainlobe solid angle, QM, results, and the difference of QA – QM gives the minorlobe solid angle. These definitions hold for patterns with clearly defined lobes. The beam efficiency (BE) of an antenna is defined as the ratio QM/QA and is a measure of the amount of power in the major lobe compared to the total power. A high beam efficiency means that most of the power is concentrated in the major lobe and that minor lobes are minimized.
Directivity and Gain. A very important antenna parameter, which indicates how well an antenna concentrates power into a limited solid angle, is its directivity D, defined as the ratio of the maximum radiation intensity to the radiation intensity averaged over all directions. The average radiation intensity is calculated
Fig. 8. Power pattern and beam solid angle of an antenna. 
by dividing the total power radiated by 4n sr. Hence,
since from Eq. (16), Prad/4n = Ui. So, alternatively, the directivity of an antenna can be defined as the ratio of its radiation intensity in a given direction (which usually is taken to be the direction of maximum radiation intensity) to the radiation intensity of an isotropic source with the same total radiation intensity. Equation
(19) can also be written
Thus, the directivity of an antenna is equal to the solid angle of a sphere, which is 4n sr, divided by the antenna beam solid angle QA. We can say that by this relation the value of directivity is derived from the antenna pattern. It is obvious from this relation that the smaller the beam solid angle, the larger the directivity, or, stated in a different way, an antenna that concentrates its power in a narrow main lobe has a large directivity.
Obviously, the directivity of an isotropic antenna is unity. By definition an isotropic source radiates equally in all directions. If we use Eq. (20), QA = 4n, since Un(e, ф) = 1. This is the smallest directivity value that one can attain. However, if we consider the directivity in a specified direction, for example D(e, ф), its value can be smaller than unity.
As an example let us calculate the directivity of the very short dipole. We can calculate its normalized radiated power using the electric or the magnetic field components, given in Table 1. Using the electric field Ee for the farfield region, from Eq. (12) we have
and
Alternatively, we can work using power densities instead of power intensities. The power flowing in a particular direction can be calculated using Eq. (3) and the electric and magnetic farfield components given in Table 1:
By integrating over all angles the total power flowing outwards is seen to be 
The directivity is the ratio of the maximum power density to the average power density. For the very short dipole antenna, the maximum power density is in the в = 90° direction (Fig. 2), and the average power density is found by averaging the total power PT from Eq. (24) over a sphere of surface area 4n r2. So
Thus, the directivity of a very short dipole is 1.5, which means that the maximum radiation intensity is 1.5 times the power of the isotropic radiator. This is often expressed in decibels:
dB 
(26) 
D = 10 log10d dB = 10 log10(1.5) = 1.76
Here, we use a lowercase letter for the absolute value and a capital letter for the logarithmic value of the directivity, as is a common in the field of antennas and propagation.
The gain of an antenna is another basic property for its characterization. Gain is closely associated with directivity, which is dependent upon the radiation patterns of an antenna. The gain is commonly defined as the ratio of the maximum radiation intensity in a given direction to the maximum radiation intensity produced in the same direction from a reference antenna with the same power input. Any convenient type of antenna may be taken as the reference. Many times the type of the reference antenna is dictated by the application area, but the most commonly used one is the isotropic radiator, the hypothetical lossless antenna with uniform radiation intensity in all directions. So
where the radiation intensity of the reference antenna (isotropic radiator) is equal to the power in the input, Pin, of the antenna divided by 4n.
Real antennas are not lossless, which means that if they accept an input a power Pin, the radiated power Prad generally will be less than Pin. The antenna efficiency k is defined as the ratio of these two powers:
where Rr is the radiation resistance of the antenna. Rr is defined as an equivalent resistance in which the same current as that flowing at the antenna terminals would produce power equal to that produced by the antenna. Rioss is the loss resistance, which allows for any heat loss due to the finite conductivity of the materials used to construct the antenna or due to the dielectric structure of the antenna. So, for a real antenna with losses, its radiation intensity at a given direction U(e, ф) will be
where U0(e, ф) is the radiation intensity of the same antenna with no losses.
Using Eq. (29) in Eq. (27) yields the expression for the gain in terms of the antenna directivity:
(30) 
(6’Ф) _ Щnax(£. Ф) _ kD
Vi 
Thus, the gain of an antenna over a lossless isotropic radiator equals its directivity if the antenna efficiency is k = 1, and it is less than the directivity if k < 1.
The values of gain range between zero and infinity, while those of directivity range between unity and infinity. However, while the directivity can be computed from either theoretical considerations or measured radiation patterns, the gain of an antenna is almost always determined by a direct comparison of measurement against a reference, usually a standardgain antenna.
Gain is expressed also in decibels:
where, as in Eq. (26), lowercase and capital letters mean absolute and logarithmic values, respectively. The reference antenna used is sometimes declared in a subscript; for example, dBi means decibels over isotropic.
AIRCRAFT FLEET
To handle the swelling number of air travelers, the air carrier fleets need to be upgraded with larger aircraft. Most of the growth in fleet size of the major U. S. carriers will occur after 2000, when aging aircraft are replaced with newer, more efficient aircraft. The fleet size, with its upswing after 2000, is shown in Fig. 5 (1).
Table 3. Forecast Passenger Enplanements at the 10 Busiest US Airports 1995 2010 % Rank CityAirport Enplanements Enplanements Growth

6000 
5000 
4000 
3000 
2000 
1000 
Figure 5. Jet aircraft forecast to be in 0 service by US air carriers 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 
7000 
At the end of 1995, U. S. air carriers had firm orders placed for 604 new aircraft and options on an additional 799 aircraft. The price tag for the firm orders was $35.5 billion. The firm orders were distributed among aircraft from Airbus Industries, Boeing Commercial Aircraft Company, McDonnell – Douglas Aircraft Company, and the Canadian Regional Jet. The most popular aircraft on order was the Boeing 737, with 218 firm orders and 260 options.
ColdWorked Microstructures
In order to achieve high critical current densities a fine and homogeneous dispersion of flux pinning material must be introduced that is of sufficient volume for significant pinning but does not deleteriously affect the other Hc2 or Tc. The process by which the first high critical current density microstructures were achieved was arrived at empirically before the resulting microstructures were characterized (12). The processing involved a high coldwork strain followed by three or more heat treatments in the a + в phase range, each separated by additional cold work with the final heat treatment being followed by another large cold – work strain. An understanding of the microstructural development was key, however, to the further optimization of NbTi and the reproducible production of high critical current strand. Initial observation of the microstructure was hindered by the difficulty in preparing transverse cross sections of micronsized filaments suitable for examination by transmission electron microscopy (TEM). Once techniques had been developed to prepare the TEM specimens, it became clear that folded sheets of aTi precipitates were the dominant microstructural features of the final strand (see Ref. 13). Systematic analysis of the production process (as in Ref. 14) revealed that the high prestrain heat treatments produced aTi precipitates only at the intersections of grain boundaries. The location of precipitation at the grain boundary triple points meant that the precipitation was homogeneously distributed if alloy composition and grain size were uniform. The grain boundary triplepoint aTi was also sufficiently ductile that it could be drawn down to the nanometer scale with breaking up or causing the strand itself to become difficult to draw. This contrasted with the other commonly observed aTi precipitate morphology, Widmanstatten aTi, which formed in densely packed rafts in the interior of grains and resulted in a great increase in the filament hardness. The next section reviews each step of the process in more detail.
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 farfield 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 threedimensional pattern of an antenna can be obtained by taking a few twodimensional 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
і2 
Fig. 2. Radiation field pattern of far field from an ideal (very short) dipole: (a) threedimensional pattern plot, (b) Eplane radiationpattern polar plot, and (c) Hplane radiationpattern polar plot (HPBW, Hplane 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 threedimensional farfield pattern for the ideal dipole, while the patterns in Fig. 2(b, c) are twodimensional and represent cross sections of the threedimensional pattern, showing the dependence of the fields on the angles в and ф.
All farfield 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(mter), 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 broadcasttype—is used for many broadcast or communication services where all directions are to be covered equally well. The horizontalplane pattern is generally circular, while the verticalplane pattern may have some directivity in order to increase the gain.
Other forms of directional patterns are pencilbeam, fanbeam, and shapedbeam 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 fanbeam pattern is similar to the pencilbeam 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 pencilbeam pattern, the fanbeam pattern generally implies a rather substantial amount of gain. The shapedbeam 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. Threedimensional 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 pencilbeam 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 wellknown figureofeight pattern, the cardioid pattern, splitbeam 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 uniformamplitude array of five isotropic sources with 0.5wavelength 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 0.5wavelength 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 Eplane 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 Hplane 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 Hplane patterns, in general, are referred to as the principalplane 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 principalplane 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 principalplane 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 halfpower beamwidth and the sidelobe level in the two principal planes specify the important characteristics of the patterns. The halfpower beamwidth (HPBW) is defined in a plane containing the major maximum beam, as the angular width within which the radiation intensity is at least onehalf 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 halfpower (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 halfpower 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 nearfield region and the farfield region. The nearfield 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 nearfield region. Of all the regions, it is the smallest. It derives its name from the reactive field, which lies close to every currentcarrying 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 onesixth
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 nearfield region and farfield regions lies the radiating nearfield 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 nearfield 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 nearfield region (r >
0.62 V ■ " ) and the starting distance of the farfield region (r < 2D2/X)(2).
The outer boundary of the nearfield 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 farfield or radiation region begins at the outer boundary of the nearfield 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 farfield 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.