Practical_Antenna_Handbook_0071639586

150 p a r t I I : F u n d a m e n t a l s
where E RXorig = field strength at distant receiving antenna
I TXorig = feedpoint current of transmitting antenna
k = constant that collects in a single number the total proportionality
between E and I resulting from the specific characteristics of antennas,
the orientation of the two antennas with respect to each other, and the
attenuation along the path between them.
Suppose we now excite a second transmitting antenna with feedpoint current I TXorig
identical in all respects to the current in the first antenna; that is, a current having the
same magnitude and phase (at the second feedpoint) as the first current. Further, let’s
suppose we locate this second TX antenna at l/2 from the first but place it at exactly the
same distance (Fig. 5.1B) from the receiving point so that the peak amplitudes of the
two signals reach a maximum at the receive point at the same exact time. The principles
of superposition and linearity tell us that the net, or total, received signal will now be
twice that of the original because the receive antenna is intercepting two electromagnetic
fields (that happen to be in phase) instead of one. Twice the current or voltage at
the receiver input corresponds to a signal increase of 6 dB. (See App. A for an explanation
of the use of logarithms and decibels to describe ratios of power, voltage, and current.)
Now let’s cut the power to each of the two TX antennas in half, thus keeping the
total power to the two antennas the same as the original power to the first TX antenna.
At each TX antenna, then, P TXnew = ½ P TXorig . But since P = I 2 R,
PTXnew
ITXnew
= (5.2)
R
where R is the feedpoint resistance of each antenna and I TXnew is the feedpoint current
resulting from the new input power, P TXnew , to each element.
Putting the old and the new equations for power in a ratio, we obtain for the new
feedpoint current in each TX antenna
I
TXnew
2
P / 2 I R / 2
TXorig
TXorig
= = = ITXorig
/ 2 = 0.707I
(5.3)
TXorig
R R
2
I 1
))))
I 1
= I 2
= I TXnew
I 2
))))
Array axis
r
r
r
A
E RXnew
= 2KI TXnew
Figure 5.1B Received signal at a distant
point from two identical transmitting
antennas.