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Hack 78 The Passive Repeater

Use a passive device that requires no power to
shoot around obstacles.

Everyone you know is getting signals
5, 10, 15, or even more miles per hop. You need only to go four
miles, but there's a hill in the
middleit's not distance,
it's the obstacle that's killing
you. You know you could put a repeater station on the hill, but
there's no power, and you can't
afford the cost of a solar power system big enough to ride out a few
cloudy days. What you need is a passive
repeater.

Suppose the hill is right at the half-way point. Just to make sure
you get a big enough signal, you buy two 24 dBi parabolic dishes, mount
them on a 20-foot pole, and have lots of clearance in the now
line-of-sight paths to the end stations. Both ends are also provided
with 24 dBi dishes. You anticipate the joy of getting high speed down
to your house for the first time, but when you turn your gear on,
there's no signal to be seen. Argh! What went wrong?

Let's think about how our system is supposed to
work. If we didn't have the obstacle in the middle
of the path, our endpoint antennas would ensure that we had a strong
signal over our four-mile path. Our signal from the originating end
had to go only half the distance, so we know the signal at the
two-mile point is four times bigger than it would be at four miles
(due to the inverse square law; see [Hack #81]). Our thinking is that this signal
in the cable is supposed to get launched from the second antenna and
beam strongly to your house, since it has to go only a relatively
easy two-mile hop.

Well, actually the system is working just the way you thought. The
reason you can't see a signal is that
it's just too weak. First, let's
predict how much signal we'd see if we had a clear
four-mile path.

At 2.4 GHz, the
free space path attenuation (loss) can
be calculated like this:

Loss (in dB) = 104.2 + 20 log d

where d is in miles (if
you'd rather use kilometers, use 92.4 as the
constant instead of 104.2, or substitute 32.4 if you prefer your
distance in meters). With an algebraic (scientific) calculator, get
the path loss for four miles by keying in:

      104.2 [plus key (+)] 20 [times key (x)] [log key] 4 [equals key (=)]

you'll see 116.24 in the display. For the terminally
lazy (or those without a calculator), consult the precomputed lookup
table [Hack #81] to find a rough
estimate of loss for a given distance.

How much signal is available over our nonobstructed four-mile path?
Let's assume that we have 24 dBi antennas on each
end and that our radios are in a box near each antenna.
Let's allow a 3 dB loss for pigtails, connector
attenuation, and transmission line (coax).

We use dBs for our ratios since it makes it easy to calculate total
path gains and losses. Just add the dB
for each element in the path, and the sum is the effective path.

Coax  +  Antenna  +  Free Space Loss  +  Antenna  +  Coax 
-3   +     24    +       -116        +     24    +   -3  =  -74

It looks like we'll get 74 dB less out of the
connector at our receiver than we put in at the transmitter.
That's about 25 million times smaller, so
it's a good thing that our receivers can detect weak
signals!

Now let's put the hill back in place and put the
passive repeater on top, coupling the antenna leads directly into
each other with an appropriate
"barrel" connector. To calculate
our signal, we note that the distance is half, so
we'll see 6 dB more signal over a 2-mile path, which
is -68 dB. (Do the calculation and you'll see for
yourself.)

The calculation is very simple since we have the same antennas
everywhere. When we connect our two antennas together on the hill, we
just add the connector-to-connector loss for the two 2-mile paths,
and we get -136 dB less at the receiver than we put in at the
transmitter when our passive repeater is in place.

If we have a 200 mW transmitter (23dBm) when we have the 4-mile
unobstructed path, we get -51 dBm for our receiver. A great signal,
as we expected. But with the passive repeater in the middle of the
obstructed path, we get only -113dB and, sorry to say, we
won't get any bandwidth. Even the thermal noise of
the antenna would exceed the tiny signal provided by our passive
repeater. In fact, if the hill is about 500 feet high, diffraction
over the top is likely to give us a path loss 35 or 45 dB worse than
free space loss. So the signal from the passive repeater is about 200
times smaller than what just falls over the hill.

So have we proven that passive repeaters don't work?
While it looks pretty bad, let's look at another
example. Let's keep the 4-mile distance, but say
that we live just 500 feet from the ridge. We are still obstructed
and can't get a direct signal, but
let's do the calculation for a passive repeater on
this ridge.

We don't have to recalculate the 4-mile minus 500
feet path, since it's virtually the same as the full
4-mile path, or -74 dB. Our second hop is now about 1/10 mile, so
this hop gives us -84 dB. Adding up our components in this hop, we
get -3 + 24 + -74 + 24 + -3 = -42 dB. Coupling our antennas together
at the passive repeater, we add the two paths and get -74 + -42 = 116
dB. Our 23 dBm transmitter now gets us -93 dBm at the receiver end.
Not a great signal, but we should be able to get 1 Mb/s connections
through the passive repeater. Of course, you could argue that you
should just put your radio on the peak and run 500 feet of cable, and
that might be a reasonable alternative. The passive repeater is just
barely working for us here.

However, there are situations where you can't just
run a cable. Let's say that you live in the city,
and across from you is a building 60 feet high. You can get
permission to put antennas on the roof of the obstructing building,
but there's no power there. You
can't run a cable across the street, and you
can't build a tower tall enough to get over the
building. In this case, we have a 100 foot path from the passive
repeater to your house (approximately .02 mile). Our

free
space loss for this path is -70 dB and
the connector-to-connector loss is -28 dB. Assuming that the
originating station is still 4 miles away, our total
connector-to-connector loss is 102 dB. Now our +23 dBm transmitter
gets a very respectable -79-dBm signal to the receiver. Yay! we can
get our full 11 Mb/s speed and still have an 8 dB fade margin.

So in certain circumstances, a passive repeater can give you great
results. It works best when the two path lengths are vastly
different. The absolute poorest result occurs when the obstruction is
in the middle of the path. In this case, you have to use an active
repeater to get the signal through.

Ron Wickersham