Math Bridge: Private 5G Frequency Trade

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What does 28 GHz trade away against 3.5 GHz?

Follow frequency through wavelength, fixed-range free-space loss, equal-gain aperture, and a directive-gain target.

Radio Remi, the guideRadio Remi guides
The one targetQuantify one frequency-only comparison without turning it into a site plan.
The chapter case3.5 GHz n78 reference versus illustrative 28.0 GHz n257.
What it buys youA link-budget question for the RF planner and array vendor.

A field team faces an unresolved physical question: What does 28 GHz trade away against 3.5 GHz? They must answer it before changing private 5g comparison frequency in gigahertz 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 private 5g comparison frequency in gigahertz. The middle card applies this page's relationship. The green card is frequency ratio. 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.

Private 5G comparison frequency in gigahertz changes frequency ratio An input card leads through the page relationship to the frequency ratio result. SET INPUT ONE CONTROL APPLY RULE predict calculate check units READ RESULT
Walk the arrows. An ideal 18.06 dB directive-gain increase can balance the frequency-only free-space term. It does not repay wall loss, blockage, tracking error, polarization, or hardware loss.

Derive the baseline in four named moves

  1. 1

    Name the input. The chapter baseline for private 5g comparison frequency in gigahertz is 28.

  2. 2

    Name the relationship. λ=c/f; r=f/f0; ΔFSPL=20log10(r); A/A0=1/r²

  3. 3

    Substitute the chapter fixture. Set private 5g comparison frequency in gigahertz to 28. The page ledger gives frequency ratio as 8.00 times.

  4. 4

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

Predict, then change private 5g comparison frequency in gigahertz

Try Predict the direction of frequency ratio. Move one control, calculate, then check your prediction.

28
Chapter baseline
Frequency ratio

Observe An ideal 18.06 dB directive-gain increase can balance the frequency-only free-space term. It does not repay wall loss, blockage, tracking error, polarization, or hardware loss. Reset the control to 28 and compare frequency ratio.

Explain Only private 5g comparison frequency in gigahertz 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 private 5g comparison frequency in gigahertz moves. Field effects named in the page's technical boundary stay fixed.

Honesty note. This teaching model changes only private 5g comparison frequency in gigahertz. It replays the chapter fixture; it is not a field prediction.

1. Start with the frequency ratio

At a fixed propagation speed, higher frequency means shorter wavelength. At the same distance, that ratio also sets the free-space path-loss difference.

Radio Remi: Frequency creates a starting budget, not the final warehouse coverage map.

2. Name the algebra moves

1

Convert gigahertzfHz=fGHz×10⁹.

2

Divide speed by frequencyλ=c/f.

3

Form the ratior=f/f0.

4

Find the loss differenceΔFSPL=20log10(r).

5

Square the wavelength ratioA/A0=(λ/λ0)²=1/r².

3. Reproduce n78 versus n257

r=28.0/3.50=8.00; λ28=3.00×10⁸/(28×10⁹)=1.07 cm

The fixed-range free-space difference is 20log10(8)=18.1 dB. At equal gain, aperture is 1/8²=1.56% of the 3.5 GHz reference, a 64.0× ratio.

4. Try one controlled change

λ=c/f; r=f/f0; ΔFSPL=20log10(r); A/A0=1/r²

TryChange only the comparison frequency. The 3.5 GHz reference, distance, and equal-gain assumption stay fixed.

Wavelength
Frequency ratio
FSPL difference
Equal-gain aperture
Collection ratio
Equalizing gain target

ObserveAt 28.0 GHz, wavelength is 1.07 cm, the ratio is 8.00×, fixed-range free-space loss is 18.06 dB higher, and equal-gain aperture is 1.56%.

ExplainAn ideal 18.06 dB directive-gain increase can balance the frequency-only free-space term. It does not repay wall loss, blockage, tracking error, polarization, or hardware loss.

Technical boundaries.

This is a same-distance, free-space, equal-gain comparison.

Path
Walls, machinery, diffraction, reflection, foliage, rain, and clutter are omitted
Aperture
Equal gain is not equal physical antenna area or equal array design
Array
Element count, scan loss, sidelobes, efficiency, EIRP limits, and beam tracking remain

Use a site survey, link budget, array pattern, legal limits, and failure tests before selecting a band.

5. Do not count the penalty twice

The 18.1 dB FSPL difference and 64× equal-gain aperture ratio are two views of the same frequency scaling. They are not separate losses to add together.

6. Carry the site evidence

Record band and bandwidth, range and geometry, wall and machinery paths, legal EIRP, array gain and scan loss, polarization, blockage, handover or beam recovery, SINR, capacity, latency, and outage cases.

7. Check yourself

Why is the 28 GHz wavelength one eighth of the 3.5 GHz wavelength?
Answer: Wavelength is inversely proportional to frequency, and 28/3.5=8.
Should 18.1 dB and 64× be added as two losses?
Answer: No. They express the same frequency ratio in decibel and aperture forms.
Does 18.1 dB array gain make the two bands equivalent?
Answer: No. It balances only the ideal fixed-range free-space frequency term.
Honesty boundary.

The page makes the frequency scaling auditable without claiming a propagation or array design.

3.5 GHz
Reference mid-band frequency
28.0 GHz
Illustrative mmWave comparison
18.1 dB
Frequency-only free-space difference

Go deeper into the chapter's private-network choices, then validate the actual site and radio design.

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