Page 396 - Complete Wireless Design

Communications System Design

Communications System Design 395

(for instance, if the distance from the transmitter source is doubled, the
receiver will receive only a quarter of the energy it would have received at
half this distance). This means that no matter how directional, and thus
high-gain, an antenna may be, the power will still drop off commensurate
to the inverse square law, and will decrease in field strength over distance.
Thus, if a transmitter is sending at equal powers into two antennas—one
low gain, the other high gain—the high-gain directional antenna merely
started off with a higher field strength than would have been possible with
the use of the low gain, omnidirectional antenna. By following the formula
below, and working it out for various distances, we can obviously see that
for every time the distance between the receiver and transmitter is doubled,
a further 6 dB of path loss occurs:

L 32.4 20 log f 20 log d
P
where L path loss, dB
P
f frequency, MHz
d distance, km
2. Decide on the fade margin. The higher the frequency, the longer the link
path, and the greater the desired reliability, the more fade margin is
required. Fade margins of 10 to 20 dB in 20-km digital microwave links are
quite common, while higher frequencies and longer links may require up to
a 30-dB margin.
3. Since the magnitude of the noise floor of a receiver will set the minimum
signal level that will still be easily detectable above this noise—or a signal
that will have a positive SNR—we can calculate the signal strength
required at a receiver’s antenna inputs, at a receiver’s particular NF, to
obtain a desired SNR at the receiver’s output:

S 174 SNR NF (10 log BW )
dBm 10 N
where S signal strength, in dBm, needed at the receiver’s antenna
dBm
inputs (at the receiver’s front end), to obtain an output IF
signal at a desired SNR in a 50-ohm system
SNR required signal-to-noise ratio, in dB, for the type of modulation
used, at the output IF (i.e., at the detector or modem input)
NF noise figure, in dB, of the receiver
BW The 6-dB bandwidth of the IF, in Hz (or, more accurately, the
N
noise bandwidth)
4. Calculate the power that will be present at the receiver’s input after its own
antenna, and after its trip across the link from the transmitter.

P P G G PL
r t t r dB
where P power, in dBm, present at the receiver’s input
r

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