Math Bridge: ISA100 Link Margin

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Math BridgeISA100.11aLink budget

Why can a radio link budget be added?

Recompute the chapter's 100 m link in logarithmic and linear form, then reserve fading headroom without hiding the assumptions.

Eddie, the electronics guideEddie guides
The one targetConnect distance, free-space loss, received level, sensitivity, and reserved margin.
The chapter case2.4 GHz at 100 m with 10 dBm transmit power and 2 dBi antennas.
What it buys youAn auditable first-pass link state before site evidence.

A field team faces an unresolved physical question: Why can a radio link budget be added? They must answer it before changing distance on the real device. Predict the direction first.

See the relationship before changing it

The figure reads from left to right. The blue card is distance. The middle card applies this page's relationship. The green card is wavelength. 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 added model holds every other chapter fixture fixed, so the numeric fixture does not switch without explanation.

Distance changes wavelength An input card leads through the page relationship to the wavelength result. SET INPUT ONE CONTROL APPLY RULE predict calculate check units READ RESULT
Walk the arrows. Distance enters the loss logarithm. Every doubled distance adds about 6.02 dB free-space loss before site effects.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline for distance is 100.

  2. 2

    Name the relationship. FSPL = 20log10(100) + 20log10(2400) - 27.55 = 80.05 dB P_r = 10 + 2 + 2 - 80.05 = -66.05 dBm margin = -66.05 - (-95) = 28.95 dB remaining = 28.95 - 20 = 8.95 dB

  3. 3

    Substitute the chapter fixture. Set distance to 100. The page ledger gives wavelength as 0.125 m.

  4. 4

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

Predict, then change distance

Try Predict the direction of wavelength. Move one control, calculate, then check your prediction.

100
Chapter baseline
Wavelength

Observe Distance enters the loss logarithm. Every doubled distance adds about 6.02 dB free-space loss before site effects. Reset the control to 100 and compare wavelength.

Explain Only distance moves here. The other chapter fixtures remain fixed.

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 distance moves. Field effects named in the page's technical boundary stay fixed.

Honesty note. This teaching model changes only distance. It replays the chapter fixture; it is not a field prediction.

1. Start with the physical story

Decibels turn multiplication of power ratios into addition. dBm anchors that ratio to one milliwatt, allowing absolute transmit and receive levels to share a ledger with gains and losses.

Eddie: The short dB sum is only trustworthy when every sign, reference, and omitted loss stays visible.

2. Name every algebra move

1

Find wavelengthDivide wave speed by 2.4 GHz.

2

Find free-space lossUse the metre/MHz Friis form.

3

Add the linkTransmit power plus gains minus path loss gives received dBm.

4

Find marginSubtract receiver sensitivity from received power.

5

Reserve fadingSubtract the explicit fade budget and convert remaining dB to a power ratio.

3. Reproduce the chapter case

FSPL = 20log10(100) + 20log10(2400) − 27.55 = 80.05 dB
P_r = 10 + 2 + 2 − 80.05 = −66.05 dBm
margin = −66.05 − (−95) = 28.95 dB
remaining = 28.95 − 20 = 8.95 dB

The raw margin is about a 785-to-1 power ratio. After the chapter's 20 dB fade reserve, about 7.85-to-1 headroom remains.

4. Try one real input

TryMove the ideal distance. Loss, received level, linear power, raw margin, and reserved headroom recompute together.

Distance
Wavelength
Metre/MHz constant
Free-space loss
Received level
Received power (mW)
Raw margin
Raw power headroom
Margin after reserve
Reserved headroom
3 dB loss doublings left

ObserveAt 100 m, the ideal received level is −66.05 dBm and 8.95 dB remains after the 20 dB reserve.

ExplainDistance enters the loss logarithm. Every doubled distance adds about 6.02 dB free-space loss before site effects.

Technical boundaries.

This is a free-space ledger, not an ISA100 coverage prediction.

Radio
Power, gains, sensitivity, channel, rate, and certification state are explicit design inputs.
Site
Fresnel clearance, metal, multipath, interference, installation loss, and antenna orientation require measurements.
Reserve
A 20 dB fade budget is a planning assumption, not a universal acceptance threshold.

Correct, not complete: this ledger does not approve topology, reliability, or process traffic.

5. Use the result in design

Use the ideal ledger to expose the assumed budget, then replace free-space confidence with measured RSSI, retry, latency, and availability across operating states.

6. Record the evidence state

Keep channel, distance, power, antennas, mounting, losses, sensitivity and rate, reserve, site state, measurement method, and retest trigger.

7. Check yourself

Why can dBm, dBi, and dB appear in one sum?
Answer: dBm is an absolute level anchored to 1 mW; dBi and dB are logarithmic gain and loss ratios applied to it.
Is 29 dB margin the same as 29 times power?
Answer: No. 29 dB is roughly a 10^(29/10), or about 794-to-1, power ratio.
Does 9 dB remaining prove the industrial link?
Answer: No. The installed path and required service still need measured evidence.
Honesty boundary.

The ledger exposes the ideal arithmetic and the chosen reserve.

Exact
Log conversion, free-space loss, received level, and sensitivity margin are reproducible.
Assumed
The radio parameters and 20 dB reserve belong to this worked case.
Measured
Installed loss, interference, retries, latency, and availability belong to field acceptance.

Correct, not complete: use it to audit a link budget, not certify a deployment.

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