Antenna height vs transmit power: which actually extends your range?

Height, in almost every case. Over open ground, doubling your antenna height is worth about 6 dB, while doubling your transmit power is worth 3 dB. And when a hill sits in the path, height is the only lever that reduces the loss instead of paying for it. Here are the numbers behind that, and the cases where power really is the right answer.

The short answer, in three numbers

Three figures settle most of the argument before you spend anything.

• Twice the power is +3 dB. In free space that stretches your range by 41 %. Over real ground it is closer to 19 %.
• Twice the height is +6 dB. Over open ground the received signal grows with the square of each antenna height, so a doubling is worth twice as many decibels as a doubling of power, and it counts in both directions of the link.
• A ridge in the path is 16 dB. That is what it costs when the crest stands one Fresnel radius above the direct line, and it is a factor of 40 in power. Multiplying a transmitter by 40 is a serious undertaking where it is permitted at all.

The rest of this article is where those numbers come from.

What does extra link budget actually buy?

Decibels are a poor unit for thinking about distance, because the same decibels buy wildly different amounts of range depending on the path. Signal strength falls with distance raised to the power n, where n is 2 in free space and climbs towards 4 over ordinary ground with low antennas. Extra budget multiplies your range by ten to the power of the gain divided by ten n.

Read the last row again. Going from 5 W to 500 W means a different radio, a different power supply and often a different licence, and in the real world it moves your usable range by a factor of about three. That is the honest ceiling on brute force.

What height buys you, first: the horizon

The earth curves away underneath your signal. Radio waves also bend slightly downwards in the lower atmosphere, which is normally modelled by pretending the earth has four thirds of its real radius. That puts the radio horizon at 4.12 times the square root of your height in metres, in kilometres. Add both ends together and you have the geometric limit of the link.

Nothing from the link budget appears in that table, and that is the point. Beyond the horizon the earth itself is the obstacle and the signal has to diffract around the bulge. That loss climbs so steeply with distance that watts buy very little extra reach. It is why a modest repeater on a hill usually beats a high-power station in a valley.

What height buys you, second: the ground reflection

Even on a flat, clear path your signal arrives twice. Once directly, and once bounced off the ground in between. The reflection arrives with its phase reversed, so the two largely cancel. The lower the antennas, the more completely they cancel.

The two-ray model over plane earth puts numbers on that. Past a break point that at VHF is only tens of metres away, received power grows with the square of each antenna height and falls with the fourth power of distance. Doubling either antenna is +6 dB. Doubling the transmit power is +3 dB. A metre of mast is worth more than a watt, and unlike the watt it works on receive as well. There is a ceiling on that, and we come to it below.

When something is in the way, the argument changes shape

Everything above assumes a clear path. Put a ridge in the middle and the loss stops being a smooth curve and turns into a cliff. The signal has to diffract over the edge, and the price depends on where the crest sits relative to the direct line, measured against the first Fresnel zone. That last phrase does the real work here, so it is worth unpacking before any numbers.

What is a Fresnel zone, and what is its radius?

Radio does not travel down a pencil-thin ray. Energy leaving the antenna reaches the far end by a whole family of slightly longer paths, and each one arrives with its own phase. Paths whose detour is under half a wavelength arrive broadly in step with the direct one and add to what you receive. The surface where the detour is exactly half a wavelength is an ellipsoid with an antenna at each focus, and that ellipsoid is the first Fresnel zone. It is the volume of space actually carrying the link, which is why the question is never whether you can see the far end. It is whether that volume is clear.

The first Fresnel radius is how fat that ellipsoid is at one place along the path, measured square out from the direct line. It is zero at each antenna, widest halfway along, and it grows with both wavelength and path length. It is a length in metres and nothing more, which is what makes it the natural yardstick for saying how far above or below the direct line something sits.

So the two words are not interchangeable, though they get swapped constantly. The zone is the whole ellipsoid. The radius is its half-width at one place along the path, and it is a different number at every place.

The direct line is the straight geometric line between the two antennas, and it exists whether or not the ground is in the way. Once a crest rises above it you have lost line of sight, and everything past that is diffraction. Nothing stops a hill standing well above that line, so the Fresnel radius in the table is a yardstick rather than a limit. It is simply the natural unit of length for this path at this frequency. Measure it where the obstacle actually stands, which is why the same crest costs you more near one of the antennas than at midpath.

Wider than most people expect, which is why "I can see it from here" is not the same as a clear path. At the midpoint of a link the first zone has a radius of 8.66 times the square root of the path length in kilometres divided by the frequency in gigahertz, in metres.

A 30 km link on 868 MHz wants roughly 30 m of clearance at midpath to keep 60 % of the first zone free, and that is before the earth bulge. A treeline you could walk through is enough to cost real decibels at VHF. It is also why the same path behaves so differently at 145 MHz and at 5.8 GHz, even though nothing about the geometry has moved.

What does an obstruction cost?

Those are ideal knife edges taken one at a time. Real hills are rounded and rarely come alone, so read the figures as a floor rather than a forecast. Sixteen decibels is forty times the power. Twenty-eight is more than six hundred times. This is also where the two levers stop behaving alike. Power buys margin on top of the diffraction loss and has to pay all of it. Height attacks the loss itself, because lifting an antenna lifts the direct line at the crest and reduces the intrusion with it. How much mast that takes is set by the same Fresnel radius. A crest that merely grazes needs very little. One a full radius up needs the direct line raised by about that much where it stands, which is a serious mast at VHF and a few metres at 5.8 GHz.

When does more height stop paying?

The six decibels per doubling do not run forever. That bonus exists only because the ground reflection arrives out of phase and cancels part of the direct ray, and because lifting the antenna weakens the cancellation. Once the antennas stand high enough that the reflection no longer sets itself against the direct path, there is nothing left to recover. The link goes back to behaving like free space, with the two rays adding and cancelling in lobes as the geometry shifts.

The height at which that happens is a number you already have. Once each antenna stands roughly one first Fresnel radius above the reflecting ground, the return on a doubling collapses from 6 dB to very little. Read it straight off the Fresnel table above: on a 5 km link at 868 MHz the ceiling is around 21 m, at 145 MHz over 30 km it is about 125 m, and at 5.8 GHz over 1 km it is under 4 m. Below the ceiling a metre of mast is worth more than a watt. Above it, height still buys horizon and still clears terrain, which are usually the real reasons you wanted it, but it no longer pays 6 dB per doubling.

So when does power win?

It genuinely does, in four situations. Being honest about them is what makes the rule useful.

• The path is already clear. With line of sight, Fresnel clearance and nothing but a shortage of margin, decibels are decibels and an amplifier does exactly what it says.
• You cannot move the antenna. Handhelds, vehicles, drones and rented rooftops cap your height at whatever you were given. With the geometry fixed, decibels are the only variable you still control.
• You only need it on transmit. A beacon or a telemetry downlink that nobody answers has no return path to protect, so asymmetric power is not wasted.
• Gain is cheaper than watts anyway. Six decibels of antenna gain equals four times the power, costs nothing to run, and helps on receive too. It also narrows the beam, so check the pattern still covers what you need. Reach for the antenna before the amplifier, and for height before either.

The order to spend your effort in

1. Raise the antenna. It is the only change that alters the geometry rather than the budget, and the cheapest decibels on the list.
2. Buy clearance, not just sight. Aim for 60 % of the first Fresnel zone free over every obstacle, not a line that merely scrapes the ridge.
3. Fix the receive side. Feedline loss, a tired connector and a noisy site cost you on every contact, and no transmit power repairs any of them.
4. Add antenna gain. It works in both directions, costs nothing to run, and puts your energy where you actually want it.
5. Add watts last. By this point you know exactly how many decibels you still need, and an amplifier is the most expensive way to buy them.

Check the path before you buy anything

All of this is arithmetic on a path you have not looked at yet. Drop two points on the map, read the terrain profile, then raise the transmitter a few metres and watch the obstruction clear. That takes about a minute in the browser and answers the question for your path rather than the average one. For the difference between what is visible and what a signal actually does, we pulled those apart in a viewshed for radio. For getting the heights themselves right, there is a short guide on AGL and AMSL.

Figures from standard propagation theory: the four-thirds effective earth radius for the radio horizon, the two-ray plane-earth model for ground reflection, and the ITU-R P.526 knife-edge formulation for diffraction loss. All three describe idealised paths. Real terrain, clutter and weather move the numbers, which is precisely what a terrain-based model is for.