Math Bridge: Conducted Power versus Installed EIRP

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Math BridgeCellular IoTStruggle-friendly runway

Why can a 22.5 dBm bench pass become 20.0 dBm in the enclosure?

Separate conducted test-port power from installed EIRP before approving an NB-IoT design.

Radio Remi, the guideRadio Remi guides
The one targetCompare two different RF quantities without calling either one coverage.
The chapter case23.0 dBm radio; 0.500 dB cable; −3.00 dBi installed gain.
What it buys youA lab record that distinguishes modem, cable, antenna, and field path.

A field team faces an unresolved physical question: Why can a 22.5 dBm bench pass become 20.0 dBm in the enclosure? They must answer it before changing installed antenna gain 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 installed antenna gain. The middle card applies this page's relationship. The green card is installed eirp. 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.

Installed antenna gain changes installed eirp An input card leads through the page relationship to the installed eirp result. SET INPUT ONE CONTROL APPLY RULE predict calculate check units READ RESULT
Walk the arrows. The slider cannot change the conducted test because the antenna is outside that measurement plane. It changes only the installed radiated budget.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline for installed antenna gain is -3.

  2. 2

    Name the relationship. Pport=Pt-Lcable; EIRP=Pt+Ginstalled; R=10^((Pport-EIRP)/10)

  3. 3

    Substitute the chapter fixture. Set installed antenna gain to -3. The page ledger gives installed eirp as 20.00 dBm.

  4. 4

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

Predict, then change installed antenna gain

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

-3
Chapter baseline
Installed EIRP

Observe The slider cannot change the conducted test because the antenna is outside that measurement plane. It changes only the installed radiated budget. Reset the control to -3 and compare installed eirp.

Explain Only installed antenna gain 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 installed antenna gain moves. Field effects named in the page's technical boundary stay fixed.

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

1. Name the measurement plane

A cable into a test set ends before the antenna. An over-the-air budget includes the installed antenna. Both can be reported in dBm, but they describe different physical planes.

Radio Remi: Put the reference plane beside every RF number.

2. Name the algebra moves

1

Subtract cable lossPport=Pt−Lcable.

2

Add installed gainEIRP=Pt+Ginstalled.

3

Form the gapΔ=Pport−EIRP.

4

Undo decibelsR=10^(Δ/10).

3. Reproduce the bench and enclosure

Pport=23.0−0.500=22.5 dBm; EIRP=23.0−3.00=20.0 dBm

The 2.50 dB difference is a 1.78× bench-to-radiated power ratio. It does not say that the tower receives 1.78× less power, because the path and direction still need their own terms.

4. Try one controlled change

Pport=Pt−Lcable; EIRP=Pt+Ginstalled; R=10^((Pport−EIRP)/10)

TryChange only installed antenna gain. Radio output and cable loss stay fixed.

Test-port power
Installed EIRP
Bench minus EIRP
Bench-to-EIRP ratio
EIRP versus bench
Radio output

ObserveAt −3.00 dBi, the test port remains 22.5 dBm while EIRP is 20.0 dBm. The gap is 2.50 dB, a 1.78× ratio, and EIRP is 56.2% of the test-port power.

ExplainThe slider cannot change the conducted test because the antenna is outside that measurement plane. It changes only the installed radiated budget.

Technical boundaries.

A dBm comparison is useful only when its reference planes are explicit.

Conducted
Cable calibration, connector repeatability, bandwidth, and instrument uncertainty remain
Radiated
EIRP is directional and depends on installed pattern, mismatch, efficiency, and polarization
Coverage
Tower receive power also needs distance, obstruction, interference, and receiver terms

Pair the conducted result with installed over-the-air and current-trace evidence.

5. Avoid the ratio trap

The 1.78× ratio compares two local budget numbers. It is not a direct ratio of tower receive power, range, packet success, or battery life.

6. Build the lab record

Record reference plane, frequency, bandwidth, calibration date, cable and connector loss, radio setting, uncertainty, enclosure state, antenna match and pattern, orientation, RSRP, SINR, delivery, retries, and current.

7. Check yourself

Why does changing antenna gain not change the test-port output?
Answer: The conducted reference plane ends before the antenna.
What does −3 dBi mean in this example?
Answer: The installed antenna budget is 3 dB below the isotropic reference in the stated direction.
Does 20.0 dBm EIRP prove a field pass?
Answer: No. Path, interference, receiver, network, and energy evidence are still required.
Honesty boundary.

The page compares measurement planes without treating an illustrative antenna loss as measured truth.

0.500 dB
Illustrative cable and connector loss
−3.00 dBi
Illustrative installed gain
1.78×
Bench-to-EIRP power ratio only

Go deeper into the chapter's lab gates and approve only the integrated field result.

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