Math Bridge: RFID Tag Power-Source Range

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Math BridgeRFID linkThreshold screen

Which threshold limits the forward link?

Hold reader hardware fixed and expose what changes when the tag powers its own chip.

Eddie, the electronics guideEddie guides
The one targetConnect tag power source to the limiting forward-link threshold.
The chapter case915 MHz, 36 dBm EIRP, 9 dBi reader gain, and 2 dBi tag gain.
What it buys youAn ideal ceiling to challenge with installed-location evidence.

A field team faces an unresolved physical question: Which threshold limits the forward link? They must answer it before changing tag threshold 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 tag threshold. The middle card applies this page's relationship. The green card is threshold power (mw). 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.

Tag threshold changes threshold power (mw) An input card leads through the page relationship to the threshold power (mw) result. SET INPUT ONE CONTROL APPLY RULE predict calculate check units READ RESULT
Walk the arrows. Range scales with the square root of the power ratio, so 12 dB becomes 10^(12/20), not 10^(12/10), in distance.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline for tag threshold is -30.

  2. 2

    Name the relationship. λ = 3x10⁸ / 915x10⁶ = 0.328 m dpassive = λ/(4π) x 10^(56/20) = 16.46 m dBAP = λ/(4π) x 10^(68/20) = 65.54 m dBAP/dpassive = 10^(12/20) = 3.98

  3. 3

    Substitute the chapter fixture. Set tag threshold to -30. The page ledger gives threshold power (mw) as 1.00e-3.

  4. 4

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

Predict, then change tag threshold

Try Predict the direction of threshold power (mw). Move one control, calculate, then check your prediction.

-30
Chapter baseline
Threshold power (mW)

Observe Range scales with the square root of the power ratio, so 12 dB becomes 10^(12/20), not 10^(12/10), in distance. Reset the control to -30 and compare threshold power (mw).

Explain Only tag threshold 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 tag threshold moves. Field effects named in the page's technical boundary stay fixed.

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

1. Start with the physical story

A passive tag must harvest enough reader power to wake its chip; a BAP tag can move that limiting threshold without changing reader EIRP.

Eddie: The battery changes the tag-side energy condition, not the lawful reader ceiling.

2. Name every algebra move

1

Find wavelengthUse λ = c/f.

2

Split EIRPSubtract reader antenna gain to get conducted power.

3

Budget lossUse EIRP + tag gain − threshold.

4

Solve rangeInvert free-space loss for distance.

3. Reproduce the chapter case

λ = 3×10⁸ / 915×10⁶ = 0.328 m
dpassive = λ/(4π) × 10^(56/20) = 16.46 m
dBAP = λ/(4π) × 10^(68/20) = 65.54 m
dBAP/dpassive = 10^(12/20) = 3.98

The ratio follows the 12 dB threshold advantage; it is not an installed read-range promise.

4. Try one real input

TryMove the tag-side limiting threshold while reader EIRP and both antenna gains stay fixed.

Tag threshold
Threshold power (mW)
Wavelength
Conducted power
Conducted watts
Passive loss budget
Passive ideal ceiling
Candidate loss budget
Candidate ideal ceiling
Threshold advantage
Range ratio

ObserveA −30 dBm limiting threshold adds 12 dB of loss budget and makes the ideal ceiling 3.98 times the passive wake screen.

ExplainRange scales with the square root of the power ratio, so 12 dB becomes 10^(12/20), not 10^(12/10), in distance.

Technical boundaries.

This is a one-way ideal free-space screen.

Return link
Backscatter detectability, reader noise, modulation, and protocol timing can become limiting.
Installation
Polarisation, tag orientation, materials, cable loss, multipath, collisions, and lawful regional settings remain separate.
Threshold
Use measured or vendor-qualified thresholds for the exact chip, tag, state, and temperature.

Correct, not complete: this ledger does not select a tag or release a read zone.

5. Use the result in the lab

Lay out boundary tags at the calculated fractions, then test orientation, material, traffic, and power one controlled variable at a time.

6. Record the evidence state

Keep reader, antenna, cable, EIRP, tag model, threshold basis, geometry, read trace, misses, stray reads, and retest trigger.

7. Check yourself

Did the BAP battery raise reader EIRP?
Answer: No. The reader ceiling and antenna split stayed fixed.
Why does 12 dB make range 3.98 times larger?
Answer: Free-space power falls with distance squared, so distance uses 20 in the dB exponent.
Is 65.5 m a portal acceptance distance?
Answer: No. It is an ideal one-way ceiling before the installed return link and environment.
Honesty boundary.

The ledger isolates how a tag-side threshold changes one ideal forward link.

Computed
Wavelength, loss budget, conducted power, range ceiling, and ratio are reproducible.
Specified
Certified reader settings and qualified tag thresholds replace the illustrative constants.
Observed
Installed intended, missed, duplicate, and stray reads decide the usable zone.

Correct, not complete: validate both link directions on the real object.

Return to RFID System Components with the threshold maths unpacked →