wilamowski-b-m-irwin-j-d-industrial-communication-systems-2011

2-12 Industrial Communication Systems
C = B log 2( 1+
SNR )
(2.4)
where B is the channel bandwidth and the signal to noise ratio (SNR) = P s /P n (signal power P s and noise
power P n ).
2.4.1.4 Free-Space Path Loss, Fresnel Zone
For determination of the required transmit power levels and/or receiver sensitivities, it is important to
know the attenuation of the air-link between transmit and receive antenna. In the most simple case of
two antennas that are in line of sight (e.g., point-to-point radio systems), the so-called free-space path
loss L 0 equals
L
0
4 d
= ⎛ ⎝ ⎜ π ⎞
⎟
λ ⎠
2
(2.5)
with d as the distance between the transmitter’s and receiver’s antenna. Note that the loss depends on
the frequency: Doubling the transmission frequency increases the path loss by four.
Having a direct line of sight path between both antennas is not the only prerequisite for applying
formula 2.5. Radio waves do not propagate only at a direct line from the transmitter to the receiver.
They occupy a certain volume defined by the concentric Fresnel ellipsoids. By ensuring no or almost
no obstacles (20% obstruction as a rule of thumb) to be within the first Fresnel ellipsoid/first Fresnel
zone, the wireless link can be assumed not to be influenced (no additional attenuation). This is shown
in Figure 2.10.
The first Fresnel zone’s radius, F 1 , at a given point can be calculated by
F =
1
λd1d2
. (2.6)
d + d
1 2
For example, if someone plans to run a point-to-point radio link at 2.45.GHz over a distance d = d 1 + d 2 = 1.km,
the maximum cross-section radius r (see Figure 2.10) becomes r = 5.5.m. This means that the antennas need to
be mounted 5.5.m higher than an obstacle in the middle of the radio link.
2.4.1.5 antennas
Each wireless transmission needs antennas for reception and transmission. An antenna is characterized
by lots of parameters like size, bandwidth, gain, return loss (matching to system impedance), and many
d 1
F 1 r
d
d 2
FIGURE 2.10
First Fresnel zone of a line of sight radio link.
© 2011 by Taylor and Francis Group, LLC