Math Bridge: Antenna Gain and NB-IoT Repetitions

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Math BridgeCellular IoTStruggle-friendly runway

How does antenna gain trade against ideal NB-IoT repetitions?

Use one 900 MHz basement-meter case to connect wavelength, collecting aperture, EIRP, and repetition pressure.

Radio Remi, the guideRadio Remi guides
The one targetTranslate installed antenna gain into four auditable link-budget quantities.
The chapter case900 MHz; 23 dBm; 0 to 5 dBi; 16 illustrative repeats.
What it buys youSeparate a physics bound from a modem setting and a field claim.

A field team faces an unresolved physical question: How does antenna gain trade against ideal NB-IoT repetitions? 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 linear gain. 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 linear gain An input card leads through the page relationship to the linear gain result. SET INPUT ONE CONTROL APPLY RULE predict calculate check units READ RESULT
Walk the arrows. The gain factor multiplies aperture and divides the ideal repetition pressure. It says nothing by itself about which repetition values the modem or network supports.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline for installed antenna gain is 5.

  2. 2

    Name the relationship. λ=c/f; G=10^(g/10); Ae=Gλ²/(4π); EIRP=Pt+g; Nideal=N0/G

  3. 3

    Substitute the chapter fixture. Set installed antenna gain to 5. The page ledger gives linear gain as 3.16 times.

  4. 4

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

Predict, then change installed antenna gain

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

5
Chapter baseline
Linear gain

Observe The gain factor multiplies aperture and divides the ideal repetition pressure. It says nothing by itself about which repetition values the modem or network supports. Reset the control to 5 and compare linear gain.

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. Start with the wave

Frequency tells us how long one radio wave is. Gain then tells us how strongly the installed antenna concentrates and collects energy relative to an ideal equal-direction radiator.

Radio Remi: Gain redirects energy. It does not create transmitter power.

2. Name the algebra moves

1

Divide speed by frequencyλ=c/f.

2

Undo decibelsGlinear=10^(GdBi/10).

3

Find effective apertureAe=Glinearλ²/(4π).

4

Add the link budgetEIRP=Pt+GdBi.

5

Form an ideal boundNideal=N0/10^(GdBi/10).

3. Reproduce the chapter values

λ=3.00×10⁸/(900×10⁶)=0.333 m; Glinear=10^(5/10)=3.16

At 5 dBi, effective aperture is 0.0280 m², EIRP is 28.0 dBm, and 16/3.16=5.06 is the ideal repetition count. Five is not automatically a supported network step.

4. Try one controlled change

λ=c/f; G=10^(g/10); Ae=Gλ²/(4π); EIRP=Pt+g; Nideal=N0/G

TryChange only installed antenna gain. Frequency, conducted power, and the illustrative baseline repeat count stay fixed.

Wavelength
Linear gain
Effective aperture
Installed EIRP
Ideal repetitions
Ideal airtime ratio

ObserveAt 5.00 dBi the wavelength remains 0.333 m, while gain is 3.16×, aperture is 0.02796 m², EIRP is 28.0 dBm, and the ideal count is 5.06.

ExplainThe gain factor multiplies aperture and divides the ideal repetition pressure. It says nothing by itself about which repetition values the modem or network supports.

Technical boundaries.

This compact engine follows one ideal on-axis link-budget thread.

Aperture
Effective aperture is not the antenna's physical panel area
Gain
Installed pattern, polarization, cable, mismatch, and orientation still matter
Repeats
Ideal energy combining is not a scheduler or battery model

Use installed RF measurements and modem traces before choosing hardware or settings.

5. Keep the units visible

Linear gain has no unit. Aperture is in square metres. EIRP is in dBm. Repetition count is a count. Mixing those labels is how a useful comparison turns into a false claim.

6. Carry the field evidence

Record band, conducted power, antenna part and orientation, installed S11 or VSWR, efficiency, pattern, RSRP, SINR, granted repetitions, retries, radio-on time, payload delivery, and current trace.

7. Check yourself

Why does 5 dBi become 3.16 in the aperture formula?
Answer: Aperture needs linear gain, so use 10^(5/10)=3.16.
Does 5.06 mean the modem will use five repeats?
Answer: No. It is an ideal bound; supported settings and network grants need evidence.
Does 28 dBm prove better basement coverage?
Answer: No. Direction, polarization, losses, interference, receiver behavior, and regulation remain.
Honesty boundary.

The page makes a gain-to-repetition comparison inspectable without calling it a field result.

900 MHz
Illustrative chapter band
5 dBi
Installed-gain input, not a measured guarantee
5.06
Ideal repetition count only

Go deeper in the chapter's Practitioner and Under the Hood layers, then validate the complete installed device.

Return to NB-IoT Fundamentals with the maths unpacked →