Math Bridge: Fixed-Site Panel Gain

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Math BridgeCellular IoTStruggle-friendly runway

Why can a fixed basement cabinet spend link budget on antenna gain?

Connect panel gain to EIRP, beamwidth, and the one-time aiming evidence a fixed site can preserve.

Radio Remi, the guideRadio Remi guides
The one targetQuantify the gain-versus-beamwidth trade for a fixed cabinet.
The chapter case23 dBm module; −2 dBi internal antenna; 5 dBi external panel.
What it buys youTurn “use an external antenna” into an aiming and release record.

A technician must decide whether external on-axis eirp is safe before changing external panel gain on the real device. The result is unresolved until the rule and units are checked. Predict the direction first.

See the relationship before changing it

Set the input, apply the rule, then read the result with its unit.

The retained audit below checks several chapter fixtures. This model keeps those stated values fixed and changes only external panel gain, so the numeric fixture does not switch without explanation.

The page derives EIRP as transmit power plus antenna gain, then converts the 7 dB recovery into a 5.01× on-axis power ratio and a 114° symmetric Kraus beam. The left panel plots EIRP against external panel gain with the internal baseline as a reference. The right panel plots the symmetric beamwidth against the same gain, showing the trade-off that a fixed cabinet can preserve.
Panel gain, EIRP and symmetric beamwidth

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline is 5 dBi.

  2. 2

    Name the relationship. EIRP = 23 dBm transmit power + panel gain

  3. 3

    Substitute with units. 23 + 5 = 28.0 dBm

  4. 4

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

Predict, then change external panel gain

Try Predict the direction of EIRP = 23 dBm transmit power + panel gain. Test another external panel gain, then compare external on-axis eirp.

5 dBi
Chapter baseline
External on-axis EIRP

Observe More panel gain raises on-axis EIRP while shrinking the ideal beam. Reset external panel gain to 5 and compare external on-axis eirp.

Explain The panel focuses the transmitter's fixed power toward its axis, so each extra gain decibel raises on-axis effective isotropic radiated power by one decibel.

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 external panel gain moves here. Field effects named in the technical boundary stay fixed.

Honesty note. This teaching model changes only external panel gain. It is not a field prediction.

1. Use the fixed orientation

A moving device cannot keep a panel aimed. A bolted-down cabinet can. A technician can find an azimuth once, fasten the antenna, and preserve that orientation in the site record.

Radio Remi: Directional gain is useful only when the installation can keep the direction.

2. Name the algebra moves

1

Find both EIRPsEIRPint=Pt+Gint; EIRPext=Pt+Gpanel.

2

Subtract budgetsΔ=EIRPext−EIRPint.

3

Convert to power ratioR=10^(Δ/10).

4

Estimate the beamθ=√(41253/10^(Gpanel/10)).

3. Reproduce the cabinet comparison

Internal: 23−2=21 dBm; external: 23+5=28 dBm; Δ=7 dB=5.01×

The 5 dBi symmetric Kraus estimate gives a 114° beam. Half the beam is about 57.1°. That is a starting tolerance for an install survey, not a pass limit.

4. Try one controlled change

EIRPext=Pt+Gpanel; θ=√(41253/10^(Gpanel/10))

TryChange only panel gain. The 23 dBm module, −2 dBi internal installed gain, and symmetric-beam estimate stay fixed.

Internal EIRP
External EIRP
Recovered budget
On-axis power ratio
Symmetric beamwidth
Half-beam angle

ObserveAt 5.00 dBi, external EIRP is 28.0 dBm versus 21.0 dBm internal. The recovery is 7.00 dB or 5.01× on-axis. The estimated beam is 114.2° with a 57.1° half-beam.

ExplainMore gain raises the on-axis budget but narrows the beam. A fixed site can accept that trade only after the installer proves and records a stable orientation.

Technical boundaries.

The gain slider is not a product or compliance selector.

Beam
Kraus gives a rough symmetric estimate; the real E- and H-plane patterns differ
Feed
Cable, connector, mismatch, polarization, enclosure, and mounting losses subtract from gain
Cell
Serving direction, downtilt, clutter, band, interference, and network policy remain

Use approved hardware and an installed site survey.

5. Read the 57.1° as a test cue

The half-beam comes from an ideal symmetric estimate. It says that aim matters. It does not prove useful service throughout that angle or failure outside it.

6. Carry the evidence forward

Record cabinet material, antenna model, approval, cable route and loss, mounting height, azimuth, tilt, fastening, serving cell, band, RSRP, SINR, attach time, retries, and before/after current traces.

7. Check yourself

Why is a panel safer here than on a tracker?
Answer: The fixed installation can preserve one verified orientation.
Does 7 dB mean 7× power density?
Answer: No. The ratio is 10^(7/10)=5.01×.
Is 57.1° an acceptance threshold?
Answer: No. It is half of an approximate symmetric beamwidth.
Honesty boundary.

The page makes the geometric trade explicit but does not predict an installed cellular link.

−2 dBi
Illustrative internal installed gain
5 dBi
Illustrative panel gain before feed losses
114°
Symmetric Kraus estimate

Approve the site from installed RF, current, and configuration evidence.

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