Hack 91. The Passive Repeater

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

Everyone you know is getting wireless signals across 5, 10, 15, or even more miles per hop. You need to go only four miles, but there's a hill in the middle; it'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 halfway 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?

6.10.1. Why a Passive Repeater Won't Work

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 [Hack #97]). 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 #97] to find a rough estimate of loss for a given distance.

How much signal is available over our unobstructed 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 two-mile path, which is -68 dB. (Do the calculation and you'll see for yourself.)

The calculation is simple, because 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 two-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 four-mile unobstructed path, we get -51 dBm for our receivera 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.

6.10.2. An Example that Almost Works

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 four-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 four-mile minus 500 feet path, since it's virtually the same as the full four-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.

6.10.3. A Working Example

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-connnector 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 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