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RF Link Budget & Range

RF & Wireless

How much margin does this link have, how far will it reach, and is the power legal?

Inputs

Hz
2.44 GHz
Conducted power at the radio's antenna pin, from its datasheet or settings.
dBm
From the antenna datasheet: gain toward the receiver, or peak gain.
dBi
Cable, connectors, filter and switch between the radio and the antenna.
dB
From the antenna datasheet.
dBi
From the receiver datasheet, at your data rate and error rate.
dBm
Your allowance for fading and shadowing.
dB
Total EIRP or conducted power only. Duty cycle, power density and the other conditions are not checked.
Rx cable and other losses
Cable, connectors, filter and switch between the antenna and the radio.
dB
Walls, body, polarisation.
dB
From L-Network Impedance Matching ("Mismatch loss at f"), or 0 if matched. A mismatch at the Rx antenna goes in Other losses.
dB

Results

Link margin M
23.26dB
Pass

Checked: M ≥ your 15 dB fade margin, failing below 0 dB, where the signal is under the sensitivity, with 1 dB Rx cable, 0 dB other and 0 dB mismatch loss
Show working
  1. Free-space path lossFSPL = 20 log d + 20 log f − 147.552 = 20 log 30 + 20 log 2.44e9 − 147.552 = 29.542 + 187.748 − 147.552 = 69.738 dB
  2. Received powerP_rx = P_tx − L_tx − L_mis + G_tx − PL − L_x + G_rx − L_rx = 0 − 1 − 0 + 0 − 69.738 − 0 + 0 − 1 = −71.738 dBm
  3. Link marginM = P_rx − S = −71.738 − (−95) = 23.262 dB
  4. Range at the fade marginPL_max = P_tx − L_tx − L_mis + G_tx + G_rx − L_rx − L_x − S − F = 0 − 1 − 0 + 0 + 0 − 1 − 0 − (−95) − 15 = 78 dB; d_max = 10^((PL_max − 20 log f + 147.552) / 20) = 10^((78 − 187.748 + 147.552) / 20) = 77.66 m
Received power Prx
−71.74dBm
Range at the fade margin dmax
77.66m
EIRP
−1dBm
All results (5)
Path loss PL
69.738dB
Wavelength λ
122.9mm
Allowed path loss PLmax

the path loss that leaves your fade margin
78dB
Range at zero margin
436.7m
ERP 

EIRP less 2.15 dB, the gain of a half-wave dipole
−3.15dBm
Margin, free space

Accuracy

Source
  • H. T. Friis
  • T. S. Rappaport

H. T. Friis, A Note on a Simple Transmission Formula, Proc. IRE the equation

T. S. Rappaport, Wireless Communications: Principles and Practice the equation

Checked against: ETSI EN 300 328, Wideband transmission systems; Data transmission equipment operating in the 2,4 GHz band; CEPT ERC Recommendation 70-03, Relating to the use of Short Range Devices (SRD); FCC Part 15, Radio Frequency Devices

Precision
Exact arithmetic on the Friis free-space formula, or on the log-distance model with your exponent.

Free space is a clear line of sight with nothing else in the path. A measured link scatters about either model by several dB as people, walls and the ground shadow it, which is what the fade margin is for. The path model, and its exponent n, usually dominate the range.

Verified against

2 independent cases. See the working.

This is a design aid. The engineer remains responsible for the design and for checking the standard itself.

Parameter sweep

Vary one input over a range and see the answer and verdict at each step, as a table and a curve.Pro

Worst-case corners

Put a tolerance on each input and get the worst-case band around the answer.Pro

Give at least one input a tolerance above zero.

Circuit

The principle

A link budget adds up every gain and loss between the radio's antenna pin and the receiver's input. What arrives, less the receiver's sensitivity, is the link margin: the dB the path can lose before the link drops. This page works out the margin and the range at your fade margin, or the Tx power a distance needs, and checks the radiated power against the rule you choose.

Wavelength
λ=cf\lambda = \frac{c}{f}
c = 299 792 458 m/s, exact.
Free-space path loss
FSPL(d)=20log⁡104πdλ=20log⁡10d+20log⁡10f−147.55\t{FSPL}(d) = 20\log_{10}\frac{4\pi d}{\lambda} = 20\log_{10} d + 20\log_{10} f - 147.55
Friis, between unity-gain antennas, with d in m and f in Hz. With d in km and f in MHz the constant is 32.45 dB. It holds in the far field only, d ≫ λ (Rappaport).
Log-distance path loss
PL(d)=FSPL(d0)+10 nlog⁡10dd0d≥d0\t{PL}(d) = \t{FSPL}(d_0) + 10\, n \log_{10}\frac{d}{d_0} \qquad d \geq d_0
Rappaport. n = 2 is free space. Below d0 the page uses free space, FSPL(d).
Received power
Prx=Ptx−Ltx−Lmis+Gtx−PL−Lx+Grx−LrxP_{rx} = P_{tx} - L_{tx} - L_{mis} + G_{tx} - \t{PL} - L_x + G_{rx} - L_{rx}
Every term in dB, dBm or dBi.
Link margin
M=Prx−SM = P_{rx} - S
Radiated power
EIRP=Ptx−Ltx−Lmis+GtxERP=EIRP−2.15 dB\t{EIRP} = P_{tx} - L_{tx} - L_{mis} + G_{tx} \qquad \t{ERP} = \t{EIRP} - 2.15\,\t{dB}
The mismatch loss counts as Tx loss, so it lowers the EIRP as well as the margin. 2.15 dBi is the gain of a half-wave dipole.
Range
PL(dmax)=Ptx−Ltx−Lmis+Gtx+Grx−Lrx−Lx−S−F\t{PL}(d_{max}) = P_{tx} - L_{tx} - L_{mis} + G_{tx} + G_{rx} - L_{rx} - L_x - S - F
Solved for dmax in closed form, from whichever model applies. With F = 0 it gives the range at zero margin.
Tx power for a distance
Ptx=S+F+PL(d)+Ltx+Lmis+Lx+Lrx−Gtx−GrxP_{tx} = S + F + \t{PL}(d) + L_{tx} + L_{mis} + L_x + L_{rx} - G_{tx} - G_{rx}
The power at the antenna pin that leaves exactly your fade margin at d.
  • fffrequency
  • λ\lambdawavelength
  • ccspeed of light in vacuum
  • dddistance between the antennas
  • d0d_0reference distance of the log-distance model
  • nnpath-loss exponent
  • PtxP_{tx}Tx power, conducted, at the radio's antenna pin
  • Gtx,GrxG_{tx}, G_{rx}antenna gains, in dBi
  • Ltx,LrxL_{tx}, L_{rx}cable, connector and filter losses on each side
  • LmisL_{mis}mismatch loss at the Tx antenna
  • LxL_xother losses: walls, body, polarisation
  • PL\t{PL}path loss
  • PrxP_{rx}received power
  • SSreceiver sensitivity
  • FFfade margin, your allowance for fading
  • MMlink margin
  • dmaxd_{max}range at the fade margin
  • EIRP,ERP\t{EIRP}, \t{ERP}radiated power against an isotropic antenna, and against a half-wave dipole
More detail

The margin and the fade margin

The received power moves as the path fades: people walk through it, doors close, a reflection cancels the direct wave. The fade margin is your allowance for that. Pass needs at least that much margin. Check means the link closes on average but has less than your allowance, so it will drop out at times. Fail means the received power is below the sensitivity.

Free space and log-distance

Free space is a clear line of sight, well above the ground. Most real paths lose more, and the loss grows faster with distance, though in a building with a line of sight it can grow a little slower. The log-distance model takes the free-space loss at a reference distance d0 and adds 10·n dB for each decade of distance beyond it. Rappaport gives the model, and measured exponents from about 1.6 to 6. The page marks a value outside that span Unverified. Measure n on your own site when you can: it sets the range more than any other input.

The power rules

The check is on total power only. EN 300 328 allows 20 dBm mean EIRP at 2.4 GHz for wideband equipment other than frequency hopping. It also limits the density to 10 dBm/MHz, which the page does not check: on a channel about 1 MHz wide it caps the EIRP near 10 dBm. ERC/REC 70-03 allows 25 mW ERP, 13.98 dBm, from 868.0 to 868.6 MHz, with a 1 % duty cycle, or listen-before-talk with adaptive frequency agility, that the page does not check. FCC Part 15 allows 1 W conducted for digital modulation at 2.4 GHz, less 1 dB for each dB of antenna gain above 6 dBi. It also limits the conducted density to 8 dBm in any 3 kHz, which the page does not check. The relaxations for fixed point-to-point links are not applied. Out of a rule's band the page gives no verdict. Consult the regulation itself before you rely on the answer.

Friis assumes the far field and a clear path. Measure the link on site, at the edge of its range, before you trust the range.
References: H. T. Friis, "A Note on a Simple Transmission Formula", Proc. IRE. T. S. Rappaport, Wireless Communications: Principles and Practice: the free-space and log-distance models, and measured path-loss exponents. ETSI EN 300 328: RF output power and power spectral density. CEPT ERC Recommendation 70-03. FCC Part 15. Related: L-Network Impedance Matching, for the mismatch loss at the Tx antenna.

Engine version ⁨1.26.4⁩