FUNDAMENTALS OF ELECTROMAGNETIC RADIATION

2.4 SOME BASIC ANTENNA PARAMETERS

 Radiation from a short current filament is commonly called dipole radiation. Since a short current filament may be viewed as an elementary antenna, it has associated with it a number of basic characteristics described by parameters used to characterize antennas in general. In this section we will introduce these parameters and illustrate them using the short current filament as an example.

 Radiation Pattern

 The relative distribution of radiated power as a function of direction in space is the radiation pattern of the antenna. For the elementary dipole the radiated power varies according to , as Eq. (2.31) shows. The radiation pattern is similar to the figure 8 revolved about an axis, as shown in Fig. 2.7a. It is common practice to show planar sections of the radiation pattern instead of the complete three�dimensional surface. The two most important views arc those of the principal E-plane and H-plane patterns. The E-plane pattern is a view of the radiation pattern obtained from a section containing the maximum value of the radiated field and in which the electric field lies in the plane of the chosen sectional view. Similarly, the H-plane pattern is a sectional view in which the H field lies in the plane of the section, and again the section is chosen to contain the maximum direction of radiation. The E and H-plane patterns for the dipole antenna are shown in Fig. 2.76 and 2.7c.

 The half-power beam width is usually given for both the principal E and H-plane patterns and is the angular width between points at which the radiated power per unit area is one-half of the maximum. For the dipole the E-plane half-power beam width is 90�, while the H plane does not show a half-power beam width, since the pattern is a constant circular pattern in the H plane.

 Directivity and Gain

 An antenna does not radiate uniformly in all direction. The variation of the intensity with direction in space is described by the directivity function

�

Figure 2.7 (a) Power radiation pattern for short current filament. (b) Principle E‑‑plane pattern. (c) Principal H-�plane pattern.

for the antenna. The intensity of radiation is the power radiated per unit solid angle, and this is obtained by multiplying the Poynting vector flux density by r`. For the dipole we obtain

for the power radiated per unit solid angle. The definition of the directivity function �is�

where �is the total radiated power. For the dipole we can compute the total radiated power by integrating the Poynting‑vector power flux through a closed spherical surface surrounding the dipole. This is equivalent to integrating the intensity over the solid angle of a sphere; thus from Eq. (2.33),

since . The integration is readily done after replacing �by �to give

 It is now found that by using Eqs. (2.33) and (2.34)

The maximum directivity is 1.5 and occurs in the H = ‑rr/2 plane.

The maximum directivity,, which often is referred to simply as the directivity, is a measure of the ability of an antenna to concentrate the radiated power in a given direction. For the same amount of radiated power, the dipole produces 1.5 times the power density in the �direction that an isotropic radiator would produce. An isotropic radiator or antenna is a fictitious antenna that radiates uniformly in all directions and is commonly used as a reference.

The gain of an antenna is defined in a manner similar to that for the directivity, except that the total input power to the antenna rather than the total radiated power is used as the reference. The difference is a measure of the efficiency of the antenna; that is,

where 71 is the efficiency, P,n is the total input power, and P, is the total radiated power. Most antennas have an efficiency close to unity. The gain of an antenna may be stated as follows:

The maximum gain, or simply gain, of an antenna is a more significant parameter in practice than the directivity, even though the: two arc closely related.

The gain of an antenna is often incorporated into a parameter called the efective isotropic radiated power, or EIRP, which is the product of the input power and the maximum gain. Its significance is that an antenna with a gain of 10 and 1 W of input power is just as effective as an antenna with a gain of ? and an input power of 5 W. Both have the same 10 W of effective isotropic radiated power. Thus input power can be reduced by using an antenna with a higher gain. In later chapters we will find that the gain of an antenna is proportional to its cross‑sectional area measured in wavelengths squared. Thus, very high gain antennas are usually found only in the microwave hand. where a wavelength is it few centimeters or less.

 Radiation Resistance

 The radiation resistance of an antenna is that equivalent resistance which would dissipate the same amount of power as the antenna radiates when the current in that resistance equals the input current at the antenna terminals. For the dipole antcnna the radiation resistance , is found from the relation

  . When we use Eq. (2.35) for we find that

upon using , . As an example, consider dl = 1 m and , corresponding to a frequency of 1 MHz. The radiation resistance equals 0,0084 , which is very small. Although the dipole is not a practical antenna, the above example does illustrate the general result that the radiation resistance of an antenna that is a small fraction of a wavelength long is very small. Such antennas usually also exhibit a verv high reactance and a very poor efficiency, which in turn means very low gain. In small antennas most of the input power is dissipated in ohmic losses instead of being radiated. An efficient antenna must be comparable to a wavelength in size. It is for this reason that antennas at low frequencies are of necessity simple structures such as the very high towers used in the radio broadcast band 500 to 1500 kHz, where the wavelength ranges from 600 down to 200 m.