Math Bridge: Tracker Gain under an EIRP Cap

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Does more tracker antenna gain help under a fixed EIRP cap?

Hold an illustrative EIRP budget fixed while antenna gain changes conducted power and heading coverage.

Radio Remi, the guideRadio Remi guides
The one targetSee why antenna gain is not free EIRP for a rotating tracker.
The chapter case14 dBm plus 2.15 dBi baseline; illustrative cap 16.15 dBm.
What it buys youKeep regional limits, antenna pattern, and current evidence separate.

A field team has a real problem to settle: Does more tracker antenna gain help under a fixed EIRP cap? They must decide what happens before they change tracker antenna gain on the device. Predict the direction first.

See the relationship first

The figure reads from left to right. The blue card is tracker antenna gain. The middle card uses this page's rule. The green card is conducted rf power. Follow the arrows: set the input, use the rule, then read the result and its unit.

The audit later on checks more than one number. Here, the added model uses the baseline named below and holds every other chapter value fixed. That sentence bridges the fixtures, so the numbers do not change without a reason.

Tracker antenna gain changes conducted rf power An input card leads through the page rule to the conducted rf power result. SET INPUT ONE CONTROL USE RULE predict calculate check units READ RESULT
Follow the arrows. Higher gain does not lift the capped on-axis budget. It narrows the pattern and reduces the configured RF output. A rotating tracker may spend much of its route outside that favourable direction.

Derive the baseline in four moves

  1. 1

    Name the input. The chapter baseline for tracker antenna gain is 8.

  2. 2

    Name the rule. Pt=EIRPcap-G; θ=√(41253/10^(G/10))

  3. 3

    Put in the chapter value. Set tracker antenna gain to 8. The page rule gives conducted rf power as 6.531 mW.

  4. 4

    Read the result. Keep mW next to the value. Use it only within the limits on this page.

Predict, then change tracker antenna gain

Try Predict what happens to conducted rf power. Move one control, calculate, then check your idea.

8
Chapter baseline
Conducted RF power

Observe Higher gain does not lift the capped on-axis budget. It narrows the pattern and reduces the configured RF output. A rotating tracker may spend much of its route outside that favourable direction. Reset to 8 and compare conducted rf power.

Explain Only tracker antenna gain moves here. The other chapter values stay fixed.

Check yourself

What should you do before you trust the result?
Answer: Predict its direction, use the shown rule, keep the units, and reset to the worked baseline.
What does this small model leave out?
Answer: Only tracker antenna gain moves. Field effects named in the page limits stay fixed.

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

1. Hold the cap fixed

If the applicable rule and product configuration cap EIRP, extra antenna gain must be matched by less conducted power. The on-axis EIRP stays fixed while the pattern narrows.

Radio Remi: A gain figure changes both the power setting and where the energy goes.

2. Name the algebra moves

1

Rearrange the budgetPt=EIRPcap−G.

2

Convert dBm to mWPt,mW=10^(Pt,dBm/10).

3

Find linear gainGlin=10^(GdBi/10).

4

Estimate the beamθ=√(41253/Glin); heading share=θ/360.

3. Reproduce the two antennas

Baseline: 14+2.15=16.15 dBm; 8 dBi panel: Pt=16.15−8=8.15 dBm

The conducted power changes from 25.1 mW to 6.53 mW. That is an RF output ratio. It is not a radio current ratio because amplifier efficiency and modem states also matter.

4. Try one controlled change

Pt=EIRPcap−G; θ=√(41253/10^(G/10))

TryChange only antenna gain. The illustrative 16.15 dBm cap and symmetric Kraus estimate stay fixed.

Conducted power
Conducted RF power
On-axis EIRP
Symmetric beamwidth
Half-beam angle
Heading coverage proxy

ObserveAt 8.00 dBi, conducted power is 8.15 dBm or 6.53 mW while on-axis EIRP remains 16.15 dBm. The symmetric beam estimate is 80.9°, a 40.4° half-beam and 22.5% heading proxy.

ExplainHigher gain does not lift the capped on-axis budget. It narrows the pattern and reduces the configured RF output. A rotating tracker may spend much of its route outside that favourable direction.

Technical boundaries.

This is an illustrative capped budget, not regulatory or device configuration advice.

Rules
Region, band, duty cycle, antenna, certification, and network policy determine the real limit
Current
RF output power is not proportional to supply current across amplifier settings and modem states
Pattern
Real mobile antennas have orientation, enclosure, polarization, body, and vehicle effects

Use approved configuration, applicable rules, installed patterns, and current traces.

5. Correct the tempting shortcut

A 5.85 dB reduction gives 0.260× RF output power. It does not prove 0.260× transmit current. The modem supply includes bias, conversion loss, digital work, and time in other states.

6. Carry the evidence forward

Record region and radio configuration, approved antenna, cable loss, conducted setting, measured EIRP, orientation distribution, installed pattern, packet success, retries, airtime, supply current, temperature, and route states.

7. Check yourself

Why does on-axis EIRP stay at 16.15 dBm?
Answer: The model reduces conducted power by exactly the increase in antenna gain.
Does 6.53 mW imply one-quarter supply current?
Answer: No. It is RF output power, not a supply-current model.
Can the 80.9° estimate predict nulls?
Answer: No. A real measured pattern is needed.
Honesty boundary.

The page corrects the algebra while keeping regulation, hardware, and network decisions outside the toy model.

16.15 dBm
Illustrative held cap
6.53 mW
Calculated RF output at 8.15 dBm
22.5%
Symmetric heading proxy, not availability

A deployment decision needs the applicable rules and measured installed behaviour.

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