31 Path Loss and Link Budgets

31.1 In 60 Seconds

Prove One Installed Radio Link

Picture a loading-bay sensor that works with the door open but loses reports when a truck parks nearby. A range claim alone cannot tell the operator whether the installed path is safe to use.

A gateway means the boundary system that joins local devices to another network or service. Received signal strength means the radio power that arrives at a receiver. RSSI means received signal strength indicator, the radio’s reported estimate of that power.

Send marked packets over the real route, then change the door, vehicle position, channel, and antenna angle. Keep place, time, radio settings, RSSI, retries, delivery, and remaining margin so another person can repeat the test.

This check covers one route and set of conditions, not every season or obstruction. The deeper sections build the loss model, link-budget ledger, fade margin, and field validation plan.

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.

31.2 Start With the Story

You will estimate received power and margin, then compare the calculation with delivery evidence from the site. Start by recording the radio terms, path assumptions, and reliability requirement.

Follow one link-budget promise across four beats to see how every gain, loss, and reserve must survive field measurement.

31.3 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.

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.

Make What a Link Budget Promises traceable: inspect Figure 31.1 for Free-Space Path Loss Formula. Focus next on path loss in dB, the companion label anchoring Free-space path loss grows with the logarithm of both distance and frequency; doubling either adds about 6 dB.

Read the formula in Figure 31.1, then match each symbol to its unit below. Both distance and frequency contribute logarithmic loss, so increasing either increases attenuation.

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.

The mathematical gist. The log-distance model $PL(d)=PL(d_0)+10n\log_{10}(d/d_0)$ grows the chapter’s 2.4 GHz, 1 m reference of about 40 dB to 69.5 dB at 30 m in free space or 87.3 dB for $n=3.2$ indoors. Its separate reviewed ledger predicts $-105$ dBm, 21.0 dB raw margin above $-126$ dBm sensitivity, and 9.00 dB after reserving 12 dB for fading and shadowing.

Math Bridge · guided foundationsWhere does every decibel in the link budget go?Let Phoebe derive distance loss, received power, and the chapter's remaining 9 dB reserve step by step. Learn the maths

The One-Minute Link Decision

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.

31.4 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 reliable Walkthrough: From Radio Terms to a Release Number review needs the figure Figure 31.2. Its Link Budget Waterfall and TX power markers reveal where A link budget is a waterfall: add gains, subtract losses, and confirm the received power stays above receiver sensitivity after a reserved fade margin enters the running decision.

Inspect Figure 31.2 at Link Budget Waterfall and note that it uses Link Budget Waterfall to locate a communication boundary. Compare TX power, which uses TX power to expose operating cost, before reading +14 dBm as the place that highlights +14 dBm. The comparison turns A link budget is a waterfall: add gains, subtract losses, and confirm the received power stays above receiver sensitivity after a reserved fade margin into a bounded Walkthrough: From Radio Terms to a Release Number choice.

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

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

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

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.

31.5 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:

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.

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(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.

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

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.

A reliable The Log-Distance Model (and the n/2 Trap) review needs the figure Figure 31.3. Its Raw margin is not the release decision and stronger markers reveal where Margin layers: raw margin above sensitivity, the part reserved for variation, and the verified headroom that remains after measurement enters the running decision.

Within the visual Figure 31.3, Raw margin is not the release decision establishes the opening checkpoint because it uses Raw margin is not the release decision to mark a decision point. stronger develops the The Log-Distance Model (and the n/2 Trap) reading by showing how it highlights stronger; weaker completes it by showing where it highlights weaker. The sequence makes Margin layers: raw margin above sensitivity, the part reserved for variation, and the verified headroom that remains after measurement auditable for The Log-Distance Model (and the n/2 Trap).

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.

Before RSSI Is Not a Universal Grade, inspect the figure Figure 31.4. Compare Link-budget review record with Requirement; their difference reveals The link-budget review record ties the requirement to reviewed radio terms, a path estimate, site validation, and an explicit release decision. This gives RSSI Is Not a Universal Grade evidence to revisit.

Read Figure 31.4 downward from the requirement through the radio terms and predicted margin to site validation. The final branch accepts or redesigns the link using measured conditions; the calculation alone does not approve deployment.

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.

31.6 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.

31.7 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.

31.8 See Also