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Wireless

Radio Links & Antennas: The Link Budget

A radio link is one big sum: power you transmit, losses along the way, antenna gains. If the result leaves margin, the link lives; if not, it drops with the first rain. Let’s learn to add.

≈ 12 min read

The link went up in the dry season and it was glorious. Solid signal, 2 ms ping, happy customer, photo for the company feed. Then winter arrived, and the link started dropping every rainy afternoon. Bad luck? No — arithmetic nobody did. A point-to-point radio link is not something you "install and see if it works"; you calculate it first, with math that fits on a napkin. This guide is that napkin, with every number shown.

The link budget: one sum on a napkin

Think of the link like your paycheck at the end of the month. Transmit power is income, the path charges tolls, and the antennas are bonuses paid at both ends. What reaches the receiver is:

Prx = Ptx + Gtx − Lcables − FSPL + Grx

Here Ptx is the radio's power in dBm, Gtx and Grx are the antenna gains in dBi, Lcables covers coax and connector losses, and FSPL is free-space path loss — the big toll. Everything is in decibels, and that's precisely the point: dB turn horrible multiplications into grade-school addition. Mind the units, though: dBm is absolute power (referenced to 1 mW), dB is a ratio, and dBi is gain relative to an isotropic antenna. They add up cleanly exactly because ratios scale absolute power. If dBm still gives you the side-eye, spend two minutes with the dBm/mW converter: 23 dBm is about 200 mW, 30 dBm is 1 W, and up it goes.

There is exactly one rule of survival: if Prx − receiver sensitivity ≥ margin, the link lives. Sensitivity is the floor the manufacturer declares for each modulation, and margin is your cushion against the real world — aim for 10–15 dB, not less. Everything else in this guide exists to fill that inequality with honest numbers.

FSPL: the toll the vacuum charges

"Free-space path loss" sounds like the air soaks up your signal, but nothing gets absorbed: it's pure geometry. Energy leaves the antenna and spreads over an ever-growing sphere, while your receiving antenna always captures the same little window of it. Farther away, bigger sphere, smaller slice. The formula, with frequency in MHz and distance in km:

FSPL = 32.45 + 20·log10(f) + 20·log10(d)

redzilla — fspl
$ fspl --freq 5800 --dist 10
FSPL = 32.45 + 20·log10(5800) + 20·log10(10)
     = 32.45 + 75.27 + 20.00
     = 127.7 dB

That 127.7 dB means roughly one part in six trillion of what you transmitted actually arrives. Sounds apocalyptic, but modern receivers hear −90 dBm signals without breaking a sweat, so the math works out. Two properties of the formula let you think fast in the field:

  • Doubling the distance always costs +6 dB. And the logarithm does something curious: the first kilometer at 5.8 GHz already costs 107.7 dB; the other nine add barely 20 dB more. Existing is expensive; traveling is cheap.
  • Going up in frequency costs too: moving from 2.4 to 5.8 GHz adds 7.7 dB of loss over the same path. In exchange you get cleaner spectrum and more compact antennas for the same gain — at 5.8 GHz the wave is about 5.2 cm long, versus 12.5 cm at 2.4 GHz (play with the frequency and wavelength converter).

EIRP: what actually leaves the antenna

An antenna amplifies nothing — it has no watts to give — but it concentrates. A 14 dBi antenna takes energy that would go everywhere and squeezes it into a beam, like going from a bare bulb to a flashlight. The "apparent" power in the beam's direction is the EIRP:

EIRP = Ptx + Gantenna − Lcables

With a 23 dBm radio, a 14 dBi antenna and a 1 dB jumper: 23 + 14 − 1 = 36 dBm ≈ 4 W equivalent, out of a device that draws less than a light bulb. The antenna and RF converter does these sums for you, including the dBi↔dBd conversions that catalogs use to keep you humble.

On the legal side, two sentences and no more: unlicensed bands carry EIRP limits set by each country's regulator — in Chile, SUBTEL — typically around 36 dBm for point-to-multipoint, with more headroom for point-to-point links using directional antennas. Before cranking up power, check the current rules for your band: the fine always costs more than the better antenna.

The Fresnel zone: the invisible sausage

This is where most "properly installed" links go to die. A radio signal doesn't travel along a string between the two antennas: it occupies a volume shaped like an ellipsoid — an invisible sausage, fat in the middle and tapered at the ends. If anything pokes into that sausage, part of the energy diffracts and arrives out of phase, subtracting from the direct signal. The result: you can see the far tower through binoculars and the link still performs like dial-up.

Profile of a 10 km radio link: first Fresnel zone ellipse between two towers, with a tree intruding into the minimum 60% clearance Tower A · Tx Tower B · Rx 1st Fresnel zone · r ≈ 11.4 m line of sight (10 km) minimum clearance: 60% of r r tree inside the 60% = sick link
Fig. 1 — The 10 km path at 5.8 GHz: the ellipse needs 6.8 m of clear air below the line of sight at midpoint. The tree respects the line of sight — and still ruins the sausage.

The first-zone radius at the middle of the path, with d in km and f in GHz:

r = 8.657 × √(d / f)

For our 10 km at 5.8 GHz: r = 8.657 × √(10/5.8) ≈ 11.4 m. In practice you clear 60% of that radius — about 6.8 m of nothing below the line of sight at mid-path — because inside the 60% core, diffraction doesn't bite yet. And note where frequency sits in the formula: dividing. At 2.4 GHz the sausage fattens to a 17.7 m radius. Lower frequencies forgive rain, not obstacles.

Two details separate the engineer who calculates from the one who prays. First, the Earth is curved: over a 10 km path the planet pushes a bulge of about a meter and a half into the midpoint, stacked on top of whatever obstacle is there. Second, obstacles grow: a young pine or eucalyptus gifts you one or two meters per year. The clearance that looks generous today is a support ticket in three winters. The wireless link calculator hands you the Fresnel radius along with the rest of the budget so you don't eyeball it.

"I can see the other tower, we're good" is the most expensive sentence in this trade. Visual line of sight is a zero-width line; the signal needs the whole ellipse. A metal-roofed shed or a row of poplars grazing the sausage — without touching the line — leaves you a link that passes the test and gasps with wind, wet leaves, or the neighbor's new barn. Calculate clearance before quoting towers, not after.

Worked example: 10 km at 5.8 GHz, step by step

Let's put it all together. A typical rural link: 10 km between a hilltop and a plant, 5.8 GHz band, integrated radios mounted right at the antenna (cable loss ≈ 0).

  1. Write down the inputs. Ptx = 23 dBm, 14 dBi antennas on both ends, sensitivity = −85 dBm for the modulation you need. Careful here: datasheets brag about the sensitivity of the slowest modulation; use the one for the data rate you actually plan to deliver.
  2. Compute the toll. FSPL = 32.45 + 20·log10(5800) + 20·log10(10) = 32.45 + 75.27 + 20 = 127.7 dB.
  3. Climb the ladder. You leave at 23 dBm, the antenna lifts you to 23 + 14 = 37 dBm of EIRP, the path drops you to 37 − 127.7 = −90.7 dBm, and the receiving antenna pulls you back up: −90.7 + 14 = Prx ≈ −76.7 dBm.
  4. Measure the cushion. Margin = −76.7 − (−85) = 8.3 dB.
  5. Pass the verdict. The link lights up and looks splendid on a sunny day… but 8.3 dB is below the recommended 10–15 dB. This is, precisely, the link from the first paragraph of this guide: the one that drops when winter shows up.
  6. Fix it on paper, where it's free. 20 dBi antennas on both ends add 12 dB to the budget: a 20.3 dB margin, a link built for winter. The other lever is shortening the hop with a repeater; raising Ptx is usually capped by regulation.
Link budget ladder: 23 dBm plus 14 dBi, minus 127.7 dB of FSPL, plus 14 dBi, yields −76.7 dBm received against a −85 dBm sensitivity 0 −40 −80 dBm +14 −127.7 +14 +23 dBm 37 dBm −90.7 −76.7 Prx −76.7 dBm sensitivity −85 dBm margin 8.3 dB Ptx +Gtx 14 dBi −FSPL +Grx 14 dBi Prx
Fig. 2 — The budget ladder: gains lift you, FSPL drops you off a cliff, and what matters is how much air is left between Prx and the sensitivity floor.

Fade margin, VSWR and the coax that charges by the meter

Why 10–15 dB of margin and not 3? Because FSPL is the only polite term in the equation; the rest of the world moves. Reflections off water or metal roofs arriving out of phase (multipath), foliage that doubles its weight in winter water, atmospheric ducts that bend the beam. Dinner-table fact: below 10 GHz, rain itself barely attenuates — at 5.8 GHz, fractions of a dB per kilometer even in a downpour — but everything that comes with the rain (soaked leaves, fresh reflections, wind shaking the dish) absolutely does. Above 10 GHz, in the licensed bands, rain becomes the main character of the calculation. Margin is your insurance against all of it at once.

VSWR: the signal that bounces before leaving

Between the radio and the antenna there's another battlefield. VSWR measures how much signal bounces back at an impedance mismatch: at VSWR 1.5, 4% of the power reflects (you lose 0.18 dB); at 2.0, 11% reflects (0.5 dB). The number looks innocent, and that's the trap: the loss isn't the problem — the symptom is. A climbing VSWR means a badly crimped connector, water inside the cable, or a damaged antenna, and those get worse before they get better. The antenna and RF converter translates between VSWR, return loss and reflection coefficient.

Coax: every meter has a price tag

And the silent classic: the cable. Coax charges by the meter, raises its rates with frequency (proportional to √f), and never negotiates:

CableAttenuation @ 2.4 GHz10 m costs you
RG-58≈ 51 dB / 100 m≈ 5.1 dB
RG-213≈ 20 dB / 100 m≈ 2.0 dB
LMR-400≈ 12.7 dB / 100 m≈ 1.3 dB
LMR-600≈ 8.2 dB / 100 m≈ 0.8 dB

Approximate nominal values; at 5.8 GHz multiply by ~1.55. Translation: 20 m of RG-58 at 2.4 GHz is 10.1 dB — more than the entire margin of our worked example, burned inside a plastic tube. The coax loss calculator interpolates by cable type, frequency and exact length.

Mount the radio at the top, right behind the antenna, and come down with Ethernet + PoE instead of coax: network cable loses zero RF dB even at 80 m. Save coax for jumpers under a meter, and seal every connector as if the cable were going scuba diving — in a proper southern winter, it basically is.

Now it's your turn: run your next path through the wireless link calculator with real coordinates and real hardware, demand a double-digit margin and 60% Fresnel clearance with the trees three years older. If the sum doesn't work on paper, it won't work on the roof.

Tools to practice with