Antnrfld

ANTENNA NEAR FIELD

As noted in the sections on RF propagation and the radar equation, electromagnetic radiation expands
spherically (Figure 1) and the power density at a long range (R) from the transmitting antenna is:
PtGt
PD ' [1]
4BR 2
When the range is large, the spherical surface of uniform power density appears flat to a receiving antenna
which is very small compared to the surface of the sphere. This is why the far field wave front is considered planar and
the rays approximately parallel. Also, it is apparent that at some shorter range, the spherical surface no longer appears
flat, even to a very small receiving antenna.

The distances where the planer, parallel ray approximation breaks down is known as the near field. The
crossover distance between near and far fields (Rff) is taken to be where the phase error is 1/16 of a wavelength, or
about 22.5E.
2D 2 where 8 is the wavelength and D is the largest dimension of the transmit antenna. [2]
Rff '
8
If the same size antenna is used for multiple frequencies, Rff will increase with increasing frequency. However,
if various size antennas are used for different frequencies and each antenna is designed with D as a function of 8 (8/2 to
1008), then Rff will vary from c/2f to 20000c/f. In this case Rff will decrease with increasing frequency. For example:
a 108 antenna at 3 GHZ has a D of 100 cm and corresponding Rff of 20 m, while a 108 antenna at 30 GHz has a D of
10 cm and corresponding Rff of 2 m.

While the above analogy provides an image of
the difference between the near and far fields, the
relationship must be defined as a characteristic of the
transmitting antenna.

Actual antennas, of course, are not ideal point
source radiators but have physical dimensions. If the
transmitting antenna placed at the origin of Figure 1 2
occupies distance D along the Z-axis and is boresighted
along the Y-axis (N = 90), then the geometry of point P
on the sphere is represented in two dimensions by N
Figure 2. For convenience, the antenna is represented by
a series of point sources in an array.

Figure 1 - Spherical Radiation to point "P" from an ideal
point source.

3-5.1

When point P is close to the antenna, as in Z
Figure 2, then the difference in distance of the two rays r
and R taken respectively from the center of the antenna
and the outer edge of the antenna varies as point P P(y,z)
changes. R
(z-zt)

Derivation of equation [2] is given as follows: r
zt 2
From Figure 2, the following applies: N = 90E

r2 = z2 + y2 [3] D Y

z = r cos 2 [4]
y = r sin 2 and [5]
[6] Figure 2 - Near Field Geometry of point "P" for a non-
R ' y 2%(z&z ))2 ' y 2%z 2&2zz )%(z ))2
ideal radiator with dimension D.

Substituting [3] and [4] into [6] R ' r 2%[&2(r cos 2)z ) %(z ))2] [7]

which puts point P into spherical coordinates.

Equation [7] can be expanded by the binomial theorem which for the first three terms, reduces to:
(z ))2sin2 2
R ' r & z ) cos 2 % % ....... [8]
2r

In the parallel ray approximation for far field calculations (Figure 3) the third term of [8] is neglected.

The distance where the far field begins (Rff) (or where the near field ends) is the value of r when the error in R
due to neglecting the third term of equation [8], equals 1/16 of a wavelength.

Rff is usually calculated on boresight, so 2 = 90E and the second term of equation [8] equals zero (Cos 90E =
0), therefore from Figure 3, where D is the antenna dimension, Rff is found by equating the third term of [8] to 1/16
wavelength.
(z ))2 sin2 2 8
'
2Rff 16

D 2
Sin 2 ' Sin 90 ' 1 and z ) ' D/2 so: 2 8
'
2Rff 16

16(D/2)2 2D 2 [9]
Rff ' '
28 8
Equation [9] is the standard calculation of far field given in all references.
Besides [9] some general rules of thumb for far field conditions are:
r >> D or r >> 8

3-5.2

If the sphere and point P are a very great distance from the antenna, then the rays are very nearly parallel and
this difference is small as in Figure 3.
Z

zt 2
N = 90E
D Y

ztcos 2

Figure 3 - Far Field Parallel Ray Approximation for Calculations.

The power density within the near field varies as a function of the type of aperture illumination and is less than
would be calculated by equation [1]. Thus, in the antenna near field there is stored energy. (The complex radiation
field equations have imaginary terms indicating reactive power.) Figure 4 shows normalized power density for three
different illuminations.

Curve A is for reference only and shows how power density would vary if it were calculated using
equation [1].
Curve B shows power density variations on axis for an antenna aperture with a cosine amplitude distribution.
This is typical of a horn antenna in the H-plane.
Curve C shows power density variations on axis for a uniformly illuminated antenna aperture or for a line
source. This is typical of a horn antenna in the E-plane.
Curve D shows power density variations on axis for an antenna aperture with a tapered illumination.
Generally the edge illumination is approximately -10 dB from the center illumination and is typical of a parabolic dish
antenna.
Point E - For radiation safety purposes, a general rule of thumb for tapered illumination is that the maximum
safe level of 10 mW/cm2 (-200 V/m) is reached in the near field if the level at Rff reaches 0.242 mW/cm2 as can be
verified by computing the power density at point E in Figure 4. (10 mW/cm2 at point E extrapolates to 0.242 mW/cm2
[16 dB lower] at R=Rff , or Y axis value =1). Figure 1 in Section 3-6 depicts more precise values for radiation hazard
exposure.
Point F - Far Field Point. At distances closer to the source than this point (near field), the power density from
any given antenna is less than that predicted using Curve A. At farther distances, (far field) power densities from all
types of antennas are the same.

3-5.3

X = Power Density in dB Normalized to Y = 1, i.e. Y = R / R ff for Near Field Measurements

Y = Near Field Distance Normalized to Far Field
Transition Point I.e. Y = R/(2D 2 /8) = R/R ff

Y

Figure 4 - Antenna Near-Field On-Axis Power Density (Normalized)
For Various Aperture Illuminations

FOR FAR FIELD MEASUREMENTS:

ONE WAY SIGNAL STRENGTH (S) TWO WAY SIGNAL STRENGTH (S)
S 2R S 2R
S decreases by 6 dB S decreases by 12 dB
6 dB when the distance doubles 12 dB when the distance doubles
(1/4 pwr) R (1/16 pwr) R

6 dB R 12 dB R
(4x pwr) S increases by 6 dB (16x pwr) S increases by 12 dB
when the distance is half when the distance is half
S 0.5 R S 0.5 R

When free space measurements are performed at a known distance from a source, it is often necessary to know
if the measurements are being performed in the far field. As can be seen from Curve A on Figure 4, if the distance is
halved (going from 1.0 to 0.5 on the Y axis), the power density will increase by 6 dB (going from 0 to 6 dB on the X
axis). Each reduction in range by ½ results in further 6 dB increases. As previously mentioned, Curve A is drawn for
reference only in the near field region, since at distances less than Rff the power density increases less than 6 dB when
the range is halved. In the far field, all curves converge and Equation [1] applies.

When a measurement is made in free space, a good check to ensure that is was performed in the far field is to
repeat the measurement at twice the distance. The power should decrease by exactly 6 dB. A common error is to use 3
dB (the half power point) for comparison. Conversely, the power measurement can be repeated at half the distance, in
which case you would look for a 6 dB increase, however the conclusion is not as sure, because the first measurement
could have been made in the far field, and the second could have been made in the near field.

3-5.4

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