Math Bridge: Enclosure loss and antenna power

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Math BridgeUX DesignStruggle-friendly runway

What does a metal cabinet cost in dB and battery current?

Keep antenna focus, enclosure loss, conducted power, and EIRP in one ledger.

UX Uma, the guideUX Uma guides
The one targetCalculate whether antenna placement can reach an EIRP target.
The chapter case14 dBm target; 1.5 dBi chip antenna; 10 dB cabinet loss.
What it buys youA form-factor decision tied to link and power evidence.

A field team faces an unresolved physical question: What does a metal cabinet cost in dB and battery current? They must answer it before changing enclosure loss 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 enclosure loss. The middle card applies this page's relationship. The green card is effective 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.

Enclosure loss changes effective gain An input card leads through the page relationship to the effective gain result. SET INPUT ONE CONTROL APPLY RULE predict calculate check units READ RESULT
Walk the arrows. dB terms add linearly, but the power and battery-current cost grows exponentially.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline for enclosure loss is 10.

  2. 2

    Name the relationship. Geff=1.5-10.0=-8.5 dBi Pt,needed=14-(-8.5)=22.5 dBm=178 mW 20 dBm maximum gives only 11.5 dBm EIRP: 2.50 dB short external 3.0 dBi antenna: Pt=11.0 dBm=12.6 mW; current≈12.7 mA

  3. 3

    Substitute the chapter fixture. Set enclosure loss to 10. The page ledger gives effective gain as -8.50 dBi.

  4. 4

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

Predict, then change enclosure loss

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

10
Chapter baseline
Effective gain

Observe dB terms add linearly, but the power and battery-current cost grows exponentially. Reset the control to 10 and compare effective gain.

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

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

1. Read dB as additions and subtractions

Antenna gain in dBi focuses radiated energy; it does not create energy. Enclosure absorption and detuning subtract from that gain. Conducted radio power plus effective gain gives EIRP.

UX Uma: A cabinet cannot remove the regulatory ceiling; it only spends link margin beneath it.

2. Name every algebra move

1

Subtract enclosure lossGeff=Gantenna−Lenclosure.

2

Rearrange the EIRP sumPt,needed=EIRPtarget−Geff.

3

Convert dBm to milliwattsPmW=10^(PdBm/10).

4

Convert PA power to currentI=P/(ηV).

3. Reproduce the cabinet comparison

Geff=1.5−10.0=−8.5 dBi
Pt,needed=14−(−8.5)=22.5 dBm=178 mW
20 dBm maximum gives only 11.5 dBm EIRP: 2.50 dB short
external 3.0 dBi antenna: Pt=11.0 dBm=12.6 mW; current≈12.7 mA

The capped internal PA draws about 101 mA at 30% efficiency and 3.3 V, roughly 7.94 times the external case.

4. Try the enclosure loss

TryIncrease cabinet loss while keeping the antenna and target fixed.

Enclosure loss
Effective gain
Free-air need
Cabinet need
Needed RF power
Maximum EIRP
Target shortfall
External conducted
External RF power
Capped internal current
External current
Current ratio

ObserveEvery extra enclosure dB demands one extra conducted dB until the radio reaches its limit.

ExplaindB terms add linearly, but the power and battery-current cost grows exponentially.

Technical boundaries.

This is one EIRP ledger, not a complete installed link budget.

Antenna
Pattern, cable, connector, ground plane, and orientation still matter
Radio
PA efficiency and current vary by output setting and temperature
Law
Band, region, duty cycle, and certification set the real limits

Measure total radiated performance and receiver margin in the final enclosure.

5. Test the installed antenna

Compare free-air and installed return loss, radiated power, receiver margin, and burst current across orientations, doors, cables, batteries, and representative sites.

6. Record the form-factor state

Store enclosure, material, antenna, cable, connector, band, firmware power setting, measured loss, EIRP, current, site, and retest triggers.

7. Check yourself

Why is 1.5 dBi not extra electrical power?
Answer: It describes directional focus relative to an isotropic radiator.
Why is the cabinet case 2.50 dB short?
Answer: A 20 dBm PA plus -8.5 dBi effective gain reaches only 11.5 dBm EIRP.
Does an external antenna automatically qualify the link?
Answer: No. Cable loss, pattern, site propagation, receiver margin, and regulation still need evidence.
Honesty boundary.

The cabinet scenario reproduces the chapter's stated catalog-typical teaching assumptions.

14 dBm
Illustrative sub-GHz target, not a universal legal ceiling
10 dB
Severe illustrative enclosure loss
30%
Simplified PA efficiency for current comparison

Correct, not complete: an EIRP ledger does not qualify an installed radio link.

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