## RECEIVING ANTENNAS

 £ Figure 2. Coordinate system for radiation field.

An antenna can be used for both reception and transmission. This article discusses the properties of an antenna when it is used for the reception of an electromagnetic (EM) plane wave (1,2). Figure 1(a) shows an example of a receiving antenna, in which a half-wavelength dipole is used. A receiver, expressed as antenna load ZL, is connected to the center terminals of the dipole. The arrows in this figure show the flow of the power density (Poynting power) of an incident EM plane wave, which propagates toward the dipole antenna from the right side. It is observed that the power of the incident EM plane wave moves toward the center terminals and is absorbed in the antenna load ZL.

 (a)

 Figure 1. Reception of an electromagnetic plane wave. (a) Half­wavelength dipole antenna. (b) Array antenna on a circular cavity.

 X

 -1>h

 (1)

 1

 The point of interest of a receiving antenna is the power WL delivered to a receiver or antenna load ZL, as shown in an example of Fig. 1(a). To calculate WL, the induced current 10 at the antenna terminals must be obtained. For this, an equivalent circuit for the receiving antenna is introduced. The maximum value of WL is discussed on the basis of the vector effective height h. The receiving antenna is recognized as an electrical net for collecting an EM plane wave. For example, the power of the EM plane wave in Fig. 1(b) is collected by many elements on a circular cavity of area Aap (aperture) and transferred to the center port to which a receiver (ZL) is connected. Generally, the collected power WL at the center port is less than the power Wap given by Aap times the power density at the receiv­ing antenna aperture. In other words, 100% of Aap is not used for the reception of the EM plane wave. In the final section, the aperture efficiency ^ap as a measure of receiving antenna performance is defined after the discussion of the receiving cross section Ar. (Note that some fundamental relationships used in the discussion of receiving antennas are summarized in the last part of this article.)

 VECTOR EFFECTIVE HEIGHT Consider an antenna isolated in free space specified by per­mittivity e0 and permeability xo, as shown in Fig. 2, where spherical coordinates (R, в, ф) are used with unit vectors (R, в, ф). The antenna is driven by a voltage source of frequency f. The current I(s’) flows along the antenna conductor of length L = s2 — s1, radiating the electric field E expressed as

 E = — j 30k-

 e—jkR

 R

 where h, called the vector effective height, is defined as
 s =
 (3)
 (4)
 e-JkR ~R
 (5)
 (6)
 e~JkR — h • /02hd
 (7)
 (8)

with

/s2

1(s’)s’ejkr(s ) R ds’

The notations in Eqs. (1) to (3) are as follows: k(= wV^0f0 = 2w/A with ш = 2wf, where A is wavelength) is the phase con­stant, I0 is the input-terminal current [i. e., I0 = I(0)], s’ is the distance from the driving point to a source point along the antenna conductor, s’ is the unit vector tangential to the an­tenna conductor at the source point, and r(s’) is the position vector directed toward the source point from the coordinate origin.

Example. Let us consider an infinitesimal dipole antenna (kr « 0) on the z axis, assuming that the current has constant amplitude and phase over the antenna length l. Equation (3) is calculated to be S = I0ls’. From Eq. (2), h = l(s’ • в)в = —l sin вв. In the direction normal to the dipole axis (в = 90°), h = —le = lz = hd.