Thursday, May 15, 2008

Two meter handheld range

Here's another post inspired by a search hit. Some fine soul hit my blog today on a search for "expected range on a 2 meter handheld radio". This search would have brought our feckless reader to this post, which does not fairly answer the question. So, in the hopes that the next person to do this search actually learns something, I'll essay to answer this question.

The answer, of course, is "it varies". The amateur radio two-meter band is a VHF band, and as such is almost entirely line of sight. (Sporadic E skip, tropospheric ducting, meteor scatter, auroral skip, and earth-moon-earth are all quite difficult with an HT, so I won't dwell on them here.) So, basically, the range of any 2-meter radio is going to be limited by the horizon. However, because the atmosphere refracts radio waves considerably more than it does light, the effective radio horizon is about 15% further than visual horizon. So that establishes one of the limits on range: the receiver at the other end must be above the effective horizon. This is a function of four things: the altitude above ground of the transmitter, the altitude above ground of the receiver, the distance between the two, and the terrain between the two. The effective radio horizon for a given location, assuming flat terrain, is about 4.11 kilometers times the square root of the height of the antenna (in meters) above ground. So two stations with their antennas each one meter above ground will be in each others' horizons if they are closer than about 8 kilometers (a typical handheld-to-handheld case). If one of the stations is, instead, a repeater with its antenna 60 meters above ground, the range is nearly 36 kilometers. If one of you is atop the John Hancock Center in Chicago (344 meters), the range would be a whopping 80 kilometers. Of course, all of these are assuming flat terrain; if one of you in on top of a mountain, then that will also increase range, and if there's a mountain between you then you will be out of luck.

This isn't the end of the discussion, though. Not only do you have to have to be within each other's radio horizons, you also have to have enough power to survive path loss. Path loss represents the reduction in strength of the radio wave as it travels through space. Much of this is simply due to the inverse square law: as the wavefront grows in size, it occupies more space without having any more power, and thus has a lower power density. The receiving antenna's size doesn't change, so if it's moved further away it will receive less of the transmitted field. This is "freespace path loss", and if this is all you were facing loss would simply double twice with each doubling in distance (a loss of 6 dB for each doubling in distance, or octave). However, in real situations, other factors also contribute to loss, and in average conditions the effective loss in VHF is closer to 7 dB per octave, with a base at 1 km of about -71 dB. Most HTs will be able to just barely receive a signal at about -120 dBm, and should give suitable performance at about -100 dBm. This means that at 1 km, to have acceptable performance, you'll need to transmit a signal of -29 dBm. That's not even two microwatts. (In practice, you wouldn't get that far on two microwatts, because your HT's antenna probably sucks. More on that below.) Even at the 80 kilometers long-range case above, the path loss is only -115 dB; a signal of 15 dBm, or about 30 milliwatts, would be sufficient. Even with antenna losses, that's possibly within the typical 5 watt (37 dBm) capabilities of your average HT.

However, this discussion ignores one critical factor: the poor antennas that most HTs have. In practice the antenna of a handheld radio has negative gain in most operating environments, and you can expect to lose anywhere from 2 to 5 dB due to this issue alone. Obstacles (other than terrain) can also wreak havoc with the signal; if you're in a car, for example, expect to lose as much as 20 dB due to absorption from the car; other things that can reduce range include trees and buildings. Also, when transmitting within one wavelength of the ground (which for an HT is almost always) a significant portion of the signal is lost into the ground; this can account for up to 10 dB of loss.

However, it remains the case that in almost all cases, radio horizon, and not power, is the primary limitation on VHF range. So, in ordinary conditions, your 2m HT range is going to be about 8 km HT-to-HT simplex and about 25 to 40 km HT-to-repeater (depending mainly on the height of the repeater's antenna).

P.S. All numbers in this article may be wrong. I've tried to get them right but it's late and I may have made mistakes. If you do spot anything wrong, please feel free to hit me.