RANGE CALCULATION EXAMPLE
What is the maximum theoretical range of a
wireless system that transmits 600 mW on 900
MHz with isotropic receive and transmit antennas?
First, calculate the wavelength in meters:
Pretty small signal,
which is not unusual.
LINE OF SIGHT
wireless devices nearby or it could
even be spurious radiations like
harmonics from some other source.
Interference keeps you from making
sense of the received information,
strong signal or not.
λ = 300/fMHz = 300/900 = 0.333 meter
d = √ (PtGtGrλ2) / (16π2 Pr)
d = √ [(0.6)(1)(1)(0.333)
2 / 16( 3.14159)
2( 9. 55 x 10-12)]
Note that I used antenna gains of one since the
path loss calculation assumed that isotropic
antennas are used.
d = 6640 meters
Since there are 1609 meters per mile, the range is:
Most VHF, UHF, and
microwave signals are
line-of-sight as indicated
earlier. The actual LOS
range depends on antenna
height. If you try to go too
far without the necessary
antenna height, you will
not establish a link. The
formula below shows the
relationship between range
and antenna heights.
• Multipath — Multipath is the
phenomenon of the transmitted signal
being reflected from objects in the path
to the receiver. For example, signals will
bounce off buildings, cars, trees, even
people. As a result, multiple signals
reach the receiver along with the directly transmitted signal. These multipath
signals are delayed a bit so add to and
subtract from the main signal producing fading and signal cancellation.
d = 6640/1609 = 4.126 miles
d = √(2ht) + √(2hr)
That is pretty close to the four mile range assumed
in the original path loss calculation above, given
all the rounding of numbers during the calculations. Using practical antennas — even simple
ground planes or dipoles — the actual possible
range would be even greater because of the gain.
You can see that the calculations are pretty reliable.
In this case, d is the
range as usual in miles, ht is
the transmit antenna height
in feet, and hr is the receive
antenna height in feet. This
is the maximum possible
range with those heights.
given transmit power and the calculated path loss, you will need a receiver
sensitivity of at least - 80. 2 dBm to get
a reliable connection. Luckily, most
receivers have a sensitivity much
better than that.
At this point, you could calculate
the minimum receive power using the
sensitivity value in dBm. It involves taking the anitlog (log-1). The formula is:
NOW A REALITY CHECK
Pr = 0.001 log-1 (dBm/10)
Use the antilog buttons on your
calculator to get the value.
All the above is theoretical, but it
does work out pretty close to that in
the real world, assuming you are
operating in an open, free space
environment. Yet there are some
other factors that come into play you
have to be aware of.
In wireless, nothing is perfect. You
always have stuff beyond your control
that will keep the signal from getting
from point A to point B. Here are the
Pr = 0.001 log-1 ( 80.2/10) = 9. 55 x
10-12 or 9. 55 picowatt (p W)
ANTENNA HEIGHT EXAMPLE
Assume a transmitter antenna height
of 70 feet and a receive antenna height
of six feet. The maximum range is:
d = √(2ht) + √(2hr)
d = √( 2)( 70) + √( 2)( 6)
d = √(140) + √( 12) = 15. 3 miles
• Noise — Noise is that random variation caused by the atmosphere and
man-made sources that add to the
signal and reducing its intelligibility at
the receiver. The goal of course is a
high signal to noise power ratio (SNR).
If noise is too high it can obliterate the
signal meaning no reception.
• Interference — Interference is made
up of signals from other sources
on or near the same operational
frequency. It could come from other
• Obstacles — Radio signals travel
freely in open space. But when you
use wireless devices indoors (as most
of us do these days), obstacles like
walls, ceilings, and floors — not to
mention furniture or other devices like
machines — really mess up the signal.
These obstacles won’t usually stop the
signal completely, they will greatly
attenuate the signal. The attenuation is
particularly high when multiple walls
have to be penetrated. The type of
wall makes a difference, too. That is
why it is so difficult to reliably predict
any kind of range indoors. These
indoor obstacles also add to the multipath effects, also greatly limiting range.
The main solution to these
problems is to use as much transmit
power as the FCC regulations allow
and the application can afford. Also,
be sure your receiver has the best
sensitivity possible. Some really good
cell phone and other wireless chips
have sensitivities up to -140 dBm.
The other great solution is to use
a gain or directional antenna such as a
Yagi, collinear, or patch array. This not
only gives the signal a real power
boost, it also narrows the signal beam
making multipath problems less of
If you are putting together a wireless product or system, use these calculations as they will indeed get you into
the ball park. Then, just be sure to
include a little extra margin in transmit
power, receiver sensitivity, and antenna
gain and it will work very reliably. NV