The Installed-Link Margin

The Installed-Link Margin

Ada re-derives this chapter’s own numbers step by step, at full precision

foundations
math-foundations
calculation-audit
wifi-mobile
Ada ADA · CALCULATION AUDIT

The Installed-Link Margin

A deployed 10 m, 2.44 GHz link starts with 0 dBm transmit power and a −95 dBm receiver, giving a comfortable 35 dB margin in line of sight — but routing it through three drywall partitions and one brick wall adds 24 dB of loss and cuts the margin to just 11 dB. A stronger parent recovers 7 dB, and a node reporting every five minutes turns three retries into 36 extra attempts an hour. This audit rebuilds the received-power ledger and asks whether that remaining headroom can survive walls, doors, and carts, or whether battery life stays unproven until those attempts are tied to measured radio-on time.

Companion to the chapter 802.15.4 Deployment Practices — every number here comes from that chapter.

One path-loss ledger, one retry warning, ~4 minutes

The physics is not hidden in the join result. Ada keeps the deployed link as a received-power ledger, then asks whether the remaining dB headroom can survive walls, doors, carts, and retries.

See the relationship before changing it

The figure reads from left to right. The blue card is wall loss. The middle card applies this page's rule. The green card is installed link margin. Walk the arrows once: set the input, apply the rule, then read the result with its unit.

The retained audit below checks several chapter fixtures. This model keeps those stated values fixed and changes only wall loss, so the numeric fixture does not switch without explanation.

Wall loss changes installed link margin An input card leads through the rule margin = 35 dB line-of-sight margin - wall loss to the installed link margin result. INPUT PAGE INPUT APPLY THE RULE predict calculate check units OUTPUT RESULT
Walk the arrows. Each measured wall-loss decibel removes one decibel of installed margin.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline is 24 dB.

  2. 2

    Name the relationship. margin = 35 dB line-of-sight margin - wall loss

  3. 3

    Substitute with units. 35 dB - 24 dB = 11.0 dB

  4. 4

    Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.

Predict, then change wall loss

Try Predict the direction of margin = 35 dB line-of-sight margin - wall loss. Test another wall loss, then compare installed link margin.

24 dB
Chapter baseline
Installed link margin

Observe Each measured wall-loss decibel removes one decibel of installed margin. Reset wall loss to 24 and compare installed link margin.

Explain Each measured wall-loss decibel removes one decibel of installed margin.

Check yourself

What should you do before trusting a moved-control result?
Answer: Predict its direction, apply the shown relationship, keep the units, and reset to the worked baseline.
What does this small model leave out?
Answer: Only wall loss moves here. Field effects named in the technical boundary stay fixed.

Honesty note. This teaching model changes only wall loss. It is not a field prediction.

Rebuild the received-power ledger

The chapter’s 10 m, 2.44 GHz example starts with 0 dBm transmit power, near-0 dBi antennas, about 60 dB path loss, and −95 dBm receiver sensitivity.

line_of_sight_rx = 0 + 0 + 0 - 60 = -60 dBm
line_of_sight_margin = -60 - (-95) = 35 dB
wall_loss = 3 x 4 dB + 12 dB = 24 dB
through_walls_rx = -60 - 24 = -84 dBm
through_walls_margin = -84 - (-95) = 11 dB

Compare parents before accepting

The parent comparison uses the same sensitivity, so the stronger parent can be checked without inventing a new radio model.

parent_a_margin = -84 - (-95) = 11 dB
parent_b_margin = -77 - (-95) = 18 dB
extra_headroom = 18 - 11 = 7 dB

Parent B still needs LQI and retry evidence, but the link-budget math shows why it is the better first commissioning candidate.

Turn retries into a power gate

A node that reports every five minutes sends 12 reports per hour. Three extra retries per report become a measurable radio-on burden.

reports_per_hour = 60 / 5 = 12
extra_retry_attempts_per_hour = 12 x 3 = 36

The chapter does not state current or airtime for each retry, so Ada stops at the count. Battery life can be claimed only after those 36 attempts/hour are tied to measured radio-on time and current.

Every number above is taken from the chapter’s own installed-link example and re-derived step by step.

TrySelect Check audit after subtracting 24 dB of wall loss from the original 35 dB link margin.
ObserveThe received-power ledger ends at 11 dB margin, while the alternate parent restores 7 dB before Reset.
ExplainThree walls and one brick subtract 24 dB directly from margin; retries affect battery only after their radio-on energy is measured.
Technical boundaries. The link ledger uses fixed path and wall losses at one distance and frequency. It does not model fading, antenna orientation, people, doors, carts, interference, receiver implementation, retry airtime, current draw, or temporal variation.
Audit result

After 24 dB of partition loss, 11 dB remains. The 36 extra attempts per hour cannot be converted to battery life without measured energy per attempt.