Math Bridge: RFID Portal EIRP

← Back to RFID Industry Applications
Math BridgeRFID portalRegulated ceiling

How does a portal power setting reach the tag?

Connect EIRP, reader antenna gain, tag sensitivity, free-space range, and measured zone margin without turning an ideal ceiling into a read claim.

Eddie, the electronics guideEddie guides
The one targetTranslate portal EIRP into amplifier demand and an ideal forward-link screen.
The chapter case915 MHz, a 9 dBi reader antenna, 2 dBi tag gain, and −18 dBm wake threshold.
What it buys youA bounded starting point for a dock-door pilot.

A field team faces an unresolved physical question: How does a portal power setting reach the tag? They must answer it before changing portal eirp 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 portal eirp. The middle card applies this page's relationship. The green card is eirp in watts. 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.

Portal EIRP changes eirp in watts An input card leads through the page relationship to the eirp in watts result. SET INPUT ONE CONTROL APPLY RULE predict calculate check units READ RESULT
Walk the arrows. EIRP sets the forward field. Gain changes the amplifier split; only a changed EIRP changes this free-space range calculation.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline for portal eirp is 36.

  2. 2

    Name the relationship. P_tx = 36 - 9 = 27 dBm = 0.501 W λ = 3.00e8 / 915e6 = 0.3279 m d_max = λ/(4π) x sqrt(EIRP x G_tag / P_th) = 16.46 m

  3. 3

    Substitute the chapter fixture. Set portal eirp to 36. The page ledger gives eirp in watts as 3.981 W.

  4. 4

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

Predict, then change portal eirp

Try Predict the direction of eirp in watts. Move one control, calculate, then check your prediction.

36
Chapter baseline
EIRP in watts

Observe EIRP sets the forward field. Gain changes the amplifier split; only a changed EIRP changes this free-space range calculation. Reset the control to 36 and compare eirp in watts.

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

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

1. Start with the physical story

EIRP is the power the portal appears to radiate in its favoured direction. Antenna gain reduces the conducted amplifier power needed for the same EIRP but does not evade the regulatory ceiling.

Eddie: The ideal range is deliberately larger than the intended zone; that gap is why zone containment must be measured.

2. Name every algebra move

1

Split EIRPSubtract antenna gain from EIRP to find conducted reader power.

2

Convert dBmUse 10^((dBm−30)/10) for watts.

3

Find wavelengthUse λ = c/f at 915 MHz.

4

Solve FriisSet received power to the tag threshold and solve for distance.

5

Check the zoneCalculate loss, received level, and margin at the pilot boundary.

3. Reproduce the chapter case

P_tx = 36 − 9 = 27 dBm = 0.501 W
λ = 3.00e8 / 915e6 = 0.3279 m
d_max = λ/(4π) × sqrt(EIRP × G_tag / P_th) = 16.46 m

The 36 dBm free-space ceiling is far beyond a 2.4 m pilot zone. At that boundary the ideal forward-link margin is about 16.73 dB before material, orientation, coupling, and return-link effects.

4. Try one real input

TryMove the portal EIRP. Conducted power, ideal range, and zone margin recompute from the same chain.

Portal EIRP
EIRP in watts
Conducted power
Conducted watts
Wavelength
Tag gain
Ideal range ceiling
Ceiling / pilot zone
Zone free-space loss
Zone received level
Zone margin

ObserveAt 36 dBm EIRP, a 9 dBi panel needs 27 dBm conducted power while the ideal tag ceiling remains 16.46 m.

ExplainEIRP sets the forward field. Gain changes the amplifier split; only a changed EIRP changes this free-space range calculation.

Technical boundaries.

This is an ideal forward-link screen, not a portal read-range model.

Regulation
The allowed EIRP, channel plan, duty, and measurement method depend on jurisdiction and equipment.
Tag
Threshold and gain vary with IC, inlay, material, orientation, and polarisation.
Portal
Multipath, shielding, return-link sensitivity, collisions, and middleware filtering require pilot evidence.

Correct, not complete: this ledger does not approve a portal or certify a read zone.

5. Use the result in the pilot

Start below the applicable ceiling, measure intended, missed, duplicate, and adjacent-zone reads, and tune power, aim, shielding, and filtering together.

6. Record the evidence state

Keep region, channel, conducted power, cable loss, antenna gain and beam, tag lot and orientation, zone geometry, trace, filters, and retest trigger.

7. Check yourself

Does a 9 dBi antenna add 9 dB above the allowed EIRP?
Answer: No. Conducted power must be reduced so the gain-inclusive EIRP stays within the applicable limit.
Why is the ideal ceiling much larger than the portal zone?
Answer: Friis omits the installed losses and containment mechanisms that define a real portal.
Does a positive tag margin prove the event is correct?
Answer: No. Decoding, collisions, return link, zone identity, and middleware state remain separate evidence.
Honesty boundary.

The ledger exposes one ideal forward-link chain.

Computed
EIRP split, wavelength, Friis ceiling, and free-space zone margin are reproducible.
Observed
Actual tag reads, misses, duplicates, and adjacent-zone spillover must be measured.
Governed
Regional rules and equipment declarations determine the lawful operating state.

Correct, not complete: use the result to design a pilot, not to declare one passed.

Return to RFID industry applications with the portal maths unpacked →