DRAFT Recommended Practice for Measurements and ...

1/29/98 52 C95.3-1991 Revision — 2 nd Draft
10/98 Draft
Fig 4.4 Estimated Gain Reduction for a Representative Antenna
There are also problems in experimentally determining the near-field gain. The usual farfield
gain measurement approach involves measuring the power transmitted between a
pair of antennas and applying the equation
G G
T
R
PR
=
P
T
⎛
⎜
⎝
4πd⎞
⎟
λ ⎠
2
(Eq 4.2)
where P R is the received power, G T and G R are the gains of the transmitting and
receiving antennas, respectively, and d is the distance between the antennas. Equation
4.2 holds rigorously only in the far field. At shorter distances, G T and G R cannot be
separated into the individual factors [B114]. Nevertheless, since one can measure
P R /P T , it is tempting to apply Eq 4.2 to the case of two identical antennas in the near
field and obtain G a 2 = (P R /P T ) (4πd/λ) 2 , where G a is the measured apparent near-field
gain of the two antennas. However, G a obtained in this manner is not the correct nearfield
gain. In other words, G a will not yield the correct on-axis power density when used
in Eq 4.1. This fact can perhaps be seen intuitively. P R is the result of an integration (or
averaging) of the incident field distribution over the receiving aperture and unless the
incident field is a plane wave, there is no simple relationship between G a and the desired
on-axis power density. The error decreases as d becomes smaller. The near-field gain
error can be approximated empirically by plotting measured data (smoothed to eliminate
standing wave oscillations) and comparing it with a theoretical curve that falls off as 1/d 2 .
By determining the deviation from 1/d 2 , the smoothed, experimental data can be
evaluated.
For rectangular apertures,
PT
⎛ b
W = ⎜ ⎞ 2
η
n A ⎝ a⎠ ⎟
(Eq 4.3)
2
where W is the power density at the receiving aperture, A = ab is the physical area of the
aperture, a and b are the aperture dimensions (a being the larger), and η is the aperture
efficiency defined as A e /A, with A e the effective aperture area. Equation 4.3 is simply a
modified form of Eq 4.1 obtained by use of the relations G = 4πA e /λ 2 and
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