27  Path Loss and Link Budgets

Turn Radio Physics Into a Link Decision

27.1 In 60 Seconds

A wireless range claim is only useful when the budget behind it can be inspected. Path-loss and link-budget work turns radio terms into an auditable decision: what the link must achieve, what each gain or loss contributes, how much margin remains, and what site evidence proves it.

27.2 Start With the Story

Start with a sensor that works on the bench but fails after a wall, a shelf, interference, or a longer distance changes the radio path. The core idea in Path Loss and Link Budgets is simple: wireless propagation is about link margin, obstacles, frequency, fading, interference, antennas, and measured delivery rather than hope. This page focuses that idea on Wireless-propagation free-space path loss, log-distance models, the link-budget ledger, fade margin, RSSI interpretation. In everyday IoT, RSSI, SNR, retries, packet delivery, placement, and fade margin explain why a gateway location or band choice succeeds or fails. Start simple: write the distance, band, obstacles, antenna assumptions, and measured margin before choosing the radio plan.

27.3 What a Link Budget Promises

Path loss is the signal a radio link spends while crossing distance, frequency, walls, clutter, and motion. A link budget is the accounting that turns that loss into a deployment decision: start with transmitter power, add antenna gains, subtract every loss, then check whether the predicted receive level still sits comfortably above the receiver’s sensitivity.

The important idea is not “use the most powerful radio.” The important idea is margin: a link should still work after the site behaves like a real site, with people, weather, metal, and interference all spending part of the budget.

If you only need the intuition, this layer is enough: a link budget is a bank account in decibels. Power and antenna gain are deposits, every path and installation loss is a withdrawal, and the receiver sensitivity is the minimum balance. You want money left over (fade margin) for a rainy day.

Think of shouting across a field. Double the distance and your voice is noticeably harder to hear; add a wall, a crowd, or wind and it gets worse fast. Radio behaves the same way, except we can put numbers on each effect in decibels and add them up before anyone installs hardware.

Free-space path loss grows with the logarithm of both distance and frequency; doubling either adds about 6 dB.

Two rules of thumb fall straight out of the physics and are worth memorizing:

• Doubling distance in free space adds about 6 dB of loss.
• Doubling frequency at the same distance adds about 6 dB of loss.

That is why a 2.4 GHz link generally reaches less far than a 900 MHz link at the same power, and why moving a gateway twice as far away is a real cost, not a rounding error.

Phoebe’s Field Notes: Where the Link Budget Comes From

Phoebe the physics guide

27.3.1 Phoebe’s Why

Path loss is not a mysterious radio tax. In free space, the same transmit power is spread over a larger spherical wavefront as distance grows, so a small receive antenna catches a smaller slice. Frequency enters because the antenna’s effective capture area is set by wavelength. The link budget then turns every multiplication or division in that physical chain into addition or subtraction in dB, which is why the ledger can be audited row by row.

27.3.2 The Derivation

An isotropic transmitter spreads power \(P_t\) over a sphere:

\[S(d) = \frac{P_t}{4\pi d^2}\]

For an isotropic receive antenna,

\[A_e = \frac{\lambda^2}{4\pi}\]

so received power is density times aperture:

\[P_r = S(d)A_e\]

\[P_r = P_t\left(\frac{\lambda}{4\pi d}\right)^2\]

The free-space path-loss ratio is therefore

\[L_{fs} = \frac{P_t}{P_r}\]

\[L_{fs} = \left(\frac{4\pi d}{\lambda}\right)^2\]

Using \(\lambda = c/f\) gives

\[L_{fs} = \left(\frac{4\pi df}{c}\right)^2\]

Convert that power ratio to dB:

\[L_{fs,dB} = 10\log_{10}L_{fs}\]

\[L_{fs,dB} = 20\log_{10}\frac{4\pi df}{c}\]

Because dB is logarithmic, multiplied gains and loss ratios become additions:

\[ \begin{aligned} P_{rx} ={}& P_{tx} + G_{tx} - L_{tx} \\ &+ G_{rx} - L_{rx} - L_{path} - L_{misc} \end{aligned} \]

and the release question is the remaining headroom after sensitivity and reserve:

\[M_{avail} = P_{rx} - P_{sens} - M_{reserved}\]

27.3.3 Worked Numbers: This Chapter’s Budget

• Why doubling costs about 6 dB: \(20\log_{10}(2) = 6.02\) dB, so doubling distance or frequency in the FSPL equation adds the same 6.02 dB toll.
• 1 km reference points: with \(d = 1\) km, \(L_{fs,dB} = 20\log_{10}(d_{km}) + 20\log_{10}(f_{MHz}) + 32.45\). At 900 MHz, \(0 + 59.1 + 32.45 = 91.5\) dB. At 2.4 GHz, \(0 + 67.6 + 32.45 = 100\) dB. At 5 GHz, \(0 + 74.0 + 32.45 = 106\) dB, which is why the chapter rounds it to about 107 dB.
• 30 m log-distance check: the chapter uses about 40 dB at 2.4 GHz and 1 m. Free space at 30 m gives \(40 + 10(2.0)\log_{10}(30) = 40 + 29.5 = 69.5\) dB. A light indoor exponent \(n = 3.2\) gives \(40 + 10(3.2)\log_{10}(30) = 40 + 47.3 = 87.3\) dB. The indoor model spends \(17.8\) dB more margin before any explicit wall-loss row.
• Reviewed ledger: using the chapter’s terms, \(P_{rx} = 14 + 0 - 1 + 3 - 1 - 118 - 2 = -105\) dBm. Raw margin is \(-105 - (-126) = 21.0\) dB. After the 12 dB fade and shadowing reserve, \(M_{avail} = 21.0 - 12.0 = 9.00\) dB.

The One-Minute Link Decision

Name the link requirement

Start with the packet delivery, latency, and availability the application actually needs, not a range number in isolation.

Add the deposits and withdrawals

Transmit power and antenna gains are deposits; path loss, cable, body, wall, and installation losses are withdrawals.

Keep a reserve

Leave fade margin above receiver sensitivity so normal site variation does not drop the link.

Beginner Examples

• A short outdoor sensor with clear line of sight may close its budget easily and only needs a quick margin check.
• An indoor sensor through two walls can lose tens of decibels to the building alone, so the same radio may not reach.
• A higher transmit power does not fix a link that fails on receiver sensitivity, antenna placement, or interference.

Link Budget Knowledge Check

If this gives you enough to reason about why a link reaches or fails, you can stop here. Continue to Practitioner when you need to build and defend an actual budget.

27.4 Apply It: Build the Link-Budget Ledger

A link budget is an accounting ledger. Gains are positive, losses are negative, and the result is compared with receiver sensitivity and a reserved margin. The workflow below produces a number you can defend in review.

Walkthrough: From Radio Terms to a Release Number

1. State the requirement. Name the packet delivery, latency, and availability target the link must meet.
2. Start with the clean path. Estimate path loss for the distance and frequency before adding any site-specific loss.
3. Add every gain and loss. Transmit power, antenna gains, cable and connector loss, body or enclosure loss, wall loss, and installation loss.
4. Compare with receiver sensitivity. Use the sensitivity for the actual data rate, bandwidth, coding, and packet target, not a best-case headline.
5. Reserve and verify margin. Hold margin for fading and interference, then compare the prediction with measured RSSI, SNR, and delivery.

A link budget is a waterfall: add gains, subtract losses, and confirm the received power stays above receiver sensitivity after a reserved fade margin.

The receive level and available margin come from two short equations:

P_rx = P_tx + G_tx - L_tx + G_rx - L_rx - L_path - L_misc

Available margin = P_rx - P_sensitivity - M_reserved

Term

Meaning

Review action

Transmit power

Radio output power before the antenna, usually in dBm.

Use the configured value; confirm legal and product power limits separately.

Antenna gain

Directional or installation gain in dBi, at both ends.

Use realistic mounted-antenna data, not a marketing peak without placement context.

Cable and connector loss

Loss between radio and antenna.

Include both ends when external antennas, pigtails, or adapters are used.

Path loss

Distance, frequency, and environment loss.

Start with free-space loss, then use a defensible model or site measurement.

Miscellaneous loss

Body, enclosure, polarization mismatch, installation error, and detuning.

Add a term only when the deployment actually carries that risk.

Receiver sensitivity

Minimum receive level for the chosen data rate, bandwidth, coding, and packet target.

Use the exact mode that will ship, not a best-case headline from another mode.

Reserved margin

Reserve for fading, shadowing, interference, aging, and measurement error.

Set it from the reliability need and validate it in the real site.

Worked Budget Example

Suppose a low-rate outdoor sensor has these reviewed terms:

• Transmit power: +14 dBm
• Sensor antenna gain: 0 dBi; sensor cable/enclosure loss: 1 dB
• Gateway antenna gain: +3 dBi; gateway cable loss: 1 dB
• Estimated path loss for the planned route: 118 dB
• Miscellaneous installation loss: 2 dB
• Receiver sensitivity in the selected mode: -126 dBm
• Reserved fade and shadowing margin: 12 dB

P_rx = 14 + 0 - 1 + 3 - 1 - 118 - 2 = -105 dBm

Raw link margin is -105 - (-126) = 21 dB. After reserving 12 dB for fading and shadowing, 21 - 12 = 9 dB remains.

This model closes, but it is not a release by itself. The team should validate the route under expected mounting, traffic, weather, occupancy, and interference. If the application is critical or the site is variable, a thin remaining margin should trigger better placement, antenna work, a gateway move, a lower data rate, or a different link choice.

Try It: Wireless Range and Path-Loss Explorer

Use the explorer to move frequency, distance, environment, and the radio terms. Watch how doubling distance or frequency each adds roughly 6 dB, how a harsher environment exponent eats margin, and where the predicted receive level crosses the receiver sensitivity line.

Incremental Practice

Beginner

Draft a ledger for a clear-line-of-sight outdoor link and confirm whether it closes with at least 10 dB reserved margin.

Intermediate

Add two interior walls and an enclosure loss to the same link; record which row changed the decision.

Advanced

For a mobile tag near metal, plan measurements at the worst expected locations because reflections can make the average path misleading.

Why Cable and Enclosure Losses Get Their Own Rows

Separate rows make the decision auditable. If a field measurement fails, the team can see which assumption to retest instead of hiding losses inside one optimistic number. A ledger that collapses everything into a single “path loss” figure cannot be debugged later.

Available Margin Knowledge Check

Order the Review

If your job is to produce a defensible budget and a release number, you can stop here. Continue to Under the Hood for the path-loss math and the failure modes behind each row.

27.5 Under the Hood: Path-Loss Math and Failure Modes

The deeper layer explains where the ledger numbers come from and how each one fails. Path loss is the row most often estimated wrongly, so it gets the most attention here.

The formulas are useful only when the assumptions are visible. Record the units, reference distance, receiver mode, antenna context, and environment class beside the number, because those choices decide whether another engineer can reproduce the estimate or find the mistake.

Free-Space Path Loss

Free-space path loss (FSPL) is the clean-air baseline: a clear line of sight, no walls, no reflectors, no people, and no detuning. For distance in kilometers and frequency in megahertz:

FSPL_dB = 20 log10(d_km) + 20 log10(f_MHz) + 32.45

Useful reference points at 1 km:

• A 900 MHz-class signal: about 91.5 dB.
• A 2.4 GHz signal: about 100 dB.
• A 5 GHz signal: about 107 dB.

These are not range promises. They are clean-air reference points used before adding environment, antenna, installation, and reliability terms. The 20 log10 terms are exactly why doubling either distance or frequency adds about 6 dB.

Unit check. The constant 32.45 assumes kilometers and megahertz. If distance is in meters, convert first (30 m = 0.03 km). A correct equation with inconsistent units produces a wrong budget that still looks reasonable.

The Log-Distance Model (and the n/2 Trap)

Real environments grow loss faster than free space. The path-loss exponent n describes how quickly loss grows after a reference point. It does not mean “multiply the whole free-space loss by n / 2.” The safe review model is:

PL(d) = PL(d0) + 10 n log10(d / d0) + X_sigma

• PL(d0) is measured or calculated loss at a reference distance such as 1 m.
• n is the environment’s path-loss exponent.
• X_sigma is shadowing variation from walls, people, vehicles, shelves, terrain, and layout changes.

Clear or Outdoor LOS

Use n near 2 only with a credible line-of-sight path and a mostly clear Fresnel region.

Office or Light Indoor

Use a larger exponent when furniture, partitions, people, and reflections make the path worse than clean air.

Obstructed or Industrial

Metal, dense walls, equipment, vehicles, and non-line-of-sight routes consume margin quickly and must be measured.

Example at 2.4 GHz, where free-space loss at 1 m is about 40 dB, evaluated at 30 m:

PL_free = 40 + 10(2.0) log10(30) = 69.5 dB PL_indoor = 40 + 10(3.2) log10(30) = 87.3 dB

The environment changes the distance-growth term. It does not turn 69.5 dB into 111 dB by multiplying the whole free-space result by 3.2 / 2.

Margin Has Three Layers

Margin layers: raw margin above sensitivity, the part reserved for variation, and the verified headroom that remains after measurement.

Raw Margin

P_rx - P_sensitivity. Only says the estimate is above the decode threshold.

Reserved Margin

The part held back for fading, shadowing, interference, antenna error, weather, and measurement uncertainty.

Verified Margin

The headroom left after realistic site measurements confirm the model under peak and normal conditions.

A negative available margin is a fail. A barely positive margin is a lab pass, not a robust deployment. Strong predicted margin still needs validation when the site has moving objects, metal, people, weather, interference, or changing layouts.

RSSI Is Not a Universal Grade

dBm is an absolute power unit. RSSI is a receiver-reported strength indicator that may be calibrated differently across chipsets and radio families, so the same RSSI can be healthy for one link and unusable for another.

• Compare RSSI with the sensitivity of the exact receiver mode.
• Compare RSSI with SNR, retry count, packet delivery, and time-of-day behavior.
• Do not copy alert thresholds from a different radio technology.
• Treat a single RSSI reading as a clue, not a deployment proof.

Example: -85 dBm means very different things at sensitivity -92 dBm (raw margin 7 dB) versus -120 dBm (raw margin 35 dB). High RSSI with poor delivery often points to interference or receiver overload; low RSSI with poor delivery points toward path loss, antenna, placement, or sensitivity.

The Review Record

The link-budget review record ties the requirement to reviewed radio terms, a path estimate, site validation, and an explicit release decision.

A useful record answers: what delivery, latency, and availability must the link meet; what radio terms and receiver mode were used; which model or measurement supports the path-loss row; what margin was reserved; where and when RSSI, SNR, retries, and delivery were measured; and what condition forces a redesign.

Interactive Review

Log-Distance Knowledge Check

Common Pitfalls

1. Multiplying FSPL by the path-loss exponent. Use the log-distance model from a reference point; multiplying the whole FSPL result by n / 2 greatly overstates loss and hides the assumption.
2. Treating a closed spreadsheet as a released link. A spreadsheet shows the link might close; it does not prove mounting, clutter, interference, delivery, or seasonal variation.
3. Forgetting receiver mode. Sensitivity changes with data rate, bandwidth, coding, and error target. Use the mode that ships.
4. Copying RSSI thresholds across radios. A value that is weak for one link can be healthy for another with different sensitivity, bandwidth, modulation, and SNR.

At this depth, a link is a chain of limits: transmit power, antenna gain, path loss, environment, receiver sensitivity, reserved margin, and measured evidence. A trustworthy decision records each limit instead of trusting one optimistic range number.

27.6 Summary

• Path loss is the baseline cost of distance, frequency, and environment; free-space loss is the clean-air reference and doubling distance or frequency each adds about 6 dB.
• The log-distance model describes how loss grows from a reference distance in a real site; the exponent belongs in the distance term, never as an n / 2 multiplier on total FSPL.
• A link budget adds gains, subtracts path and installation losses, compares the result with receiver sensitivity, and reserves margin for variation.
• Margin has three layers: raw, reserved, and verified; only verified margin reflects real site evidence.
• RSSI is meaningful only against the specific receiver’s sensitivity, SNR, and delivery, not as a universal grade.

27.7 Key Takeaway

A link budget connects transmit power, antenna gain, path loss, receiver sensitivity, and fade margin into one auditable decision. It is the first sanity check before promising wireless range, and the site measurement is the proof.

27.8 See Also

Radio Wave Basics for IoT

Review frequency, wavelength, and antennas before calculating loss.

Fading and RF Interference

See why reserved margin can disappear in the field and how to tell coverage from coexistence problems.

Practical Wireless Lab

Validate path-loss and margin assumptions against measured evidence.