Warehouse sensor relocation
A 2.4 GHz sensor moves from 10 m clear line of sight to 100 m with a documented 6 dB obstruction allowance. The comparison isolates the distance penalty from the obstruction penalty.
Physics and electromagnetism
Electromagnetic Wave Scenario Calculator
Compare received power for two far-field line-of-sight free-space radio scenarios using frequency, distance, antenna gains, and explicit additional losses.
Two-scenario electromagnetic link budget
Compare two free-space links without hiding distance or loss assumptions
This page compares two ideal far-field, matched-polarization line-of-sight links with the Friis relation expressed as a dB budget. Scenario means a concrete distance and added-loss case, not a generic score or probability.
Scenario A received power-
Scenario B received power-
B minus A-
B/A power ratio-
Current model evidence
Two-link budget comparison
Keep free-space spreading and user-specified additional losses visible for both links.
| Scenario | Distance or ratio | FSPL or delta (dB) | Extra loss or delta (dB) | Received power or delta (dBm/dB) | Linear power or ratio |
|---|
DETAILED CALCULATION PROCESS
Formula, units, default substitution, and reconciliation
1. Governing relation
lambda = c/f; FSPL = 20 log10(4 pi r/lambda); P_r(dBm) = P_t(dBm) + G_t + G_r - FSPL - L_extra
The Friis free-space relation is evaluated in logarithmic form. Distance and wavelength determine FSPL, while antenna gains and explicitly entered non-free-space losses complete each link budget.
2. Symbols and default basis
| Symbol | Meaning | Unit | Default basis |
|---|---|---|---|
| P_t | Power at transmit antenna input | W or dBm | 1 W = 30 dBm |
| f, lambda | Carrier frequency and vacuum wavelength | Hz; m | 2400 MHz |
| G_t, G_r | Directional antenna gains | dBi | 2 dBi each |
| r_A, r_B | Far-field path lengths | m | 10 m; 100 m |
| FSPL | Free-space path loss | dB | calculated separately |
| L_extra | Loss beyond free-space spreading | dB | 0 dB; 6 dB |
| P_r | Power at receive antenna output reference | dBm | calculated |
3. Unit and sign normalization
- Megahertz are multiplied by 1e6 before lambda = c/f.
- Watts convert to dBm with 10 log10(1000 P_W).
- dB gains and losses add algebraically; convert a dB difference to a power ratio with 10^(Delta/10).
4. Current numerical substitution
5. Independent reconciliation
HOW TO USE THIS CALCULATOR
Five steps from physical inputs to a defensible result
- Use transmitter power at the antenna reference plane after upstream feeder loss unless that loss is entered explicitly.
- Enter the shared carrier frequency and gains in the actual link directions.
- Set Scenario A as the reference distance and document any losses beyond free-space spreading.
- Enter Scenario B distance and its own obstruction, cable, polarization, or radome loss allowance.
- Compare dBm and linear ratio, then test receiver sensitivity and fade margin outside this calculator.
PHYSICS FOUNDATIONS FOR THIS MODEL
Concepts that control this specific calculation
- Free-space loss is geometric spreading
- It increases with both distance and frequency for antennas specified by gain.
- dBi is directional gain
- Antenna gain redistributes radiated power; it is not added watts.
- dBm is absolute power
- Unlike dB, dBm has a one-milliwatt reference and can be converted to milliwatts.
- Additional loss needs provenance
- Cable, polarization, rain, walls, foliage, and mismatch should not be silently folded into FSPL.
- Friis has a domain
- The classical form assumes far-field line of sight, matched polarization, and compatible reference planes.
DEEP ANALYSIS 1
A tenfold distance increase costs 20 dB
With frequency and other terms fixed, received power follows 1/r^2, so a distance ratio of ten produces a 100-fold power reduction.
DEEP ANALYSIS 2
Frequency comparisons depend on antenna description
At fixed dBi gains, higher frequency increases FSPL. At fixed physical apertures, gain may rise with frequency, changing the comparison.
DEEP ANALYSIS 3
Received power is not reliability
Sensitivity, required SNR, noise bandwidth, modulation, interference, fading, availability target, and regulatory power limits remain separate decisions.
RESULT INTERPRETATION
What the current output does and does not decide
A negative B-minus-A value means Scenario B receives less power. The ratio is always positive and is the linear counterpart of that dB change.
If both scenarios are identical, zero dB and a ratio of one are the correct boundary. Very short distances may violate far-field assumptions even though the formula returns a number.
REAL USE CASES
Two decisions with different boundary conditions
Point-to-point antenna choice
Two proposed sites use the same radios and directional gains but different path lengths. The resulting received-power difference becomes one input to a separate fade-margin analysis.
EVIDENCE AND DATA QUALITY
What to retain with the exported result
Retain transmitter reference-plane power, cable-loss accounting, frequency, antenna models and orientations, gain patterns, polarization, path geometry, far-field justification, and the measurement or engineering basis for each additional loss.
LIMITS AND EXCLUSIONS
Where this physical model stops
- Both paths are ideal far-field line-of-sight free-space links before entered extra loss.
- Antenna gains are aligned, polarization matched, and stated at the carrier frequency.
- Multipath, diffraction, Fresnel obstruction, atmospheric variability, fading, interference, and receiver noise are not solved.
- Extra losses are deterministic user inputs rather than predictions.
- The result is not a regulatory EIRP check, coverage guarantee, or safety assessment.
TERMS USED HERE
Six terms that keep the calculation unambiguous
- Friis equation
- Relation between transmit and receive power for an ideal free-space link.
- Free-space path loss
- Apparent link loss caused by spherical spreading and wavelength.
- dBi
- Antenna gain in decibels relative to an isotropic radiator.
- dBm
- Power level in decibels relative to one milliwatt.
- Far field
- Region where angular field pattern and wave impedance have settled.
- Link margin
- Received power above the receiver requirement after all allowances.
RELIABLE SOURCES
References supporting the equation and units
FREQUENTLY ASKED QUESTIONS
Questions specific to this calculation
Why does higher frequency increase FSPL here?
The equation holds antenna gains in dBi fixed; wavelength becomes shorter while geometric capture relative to isotropic changes.
Can I use a distance of zero?
No. Friis contains 1/r^2 and has no valid zero-distance link.
Where do cable losses go?
Include them in the appropriate extra-loss entry unless transmit power and received reference planes already exclude them.
Does this account for walls or trees?
Only through a defensible user-entered extra loss; the page does not predict obstruction loss.
Is received dBm enough to decide whether a link works?
No. Compare it with sensitivity and required SNR, then include fading, interference, and availability margin.
What does a B/A ratio of one mean?
The calculated received powers are equal; this occurs for identical budgets or offsetting distance, gain, and loss changes.
IMPORTANT BOUNDARY
Use the result as analysis, not certification
This ideal link comparison is not a coverage prediction, licensed-system design, interference study, compliance filing, or operational availability guarantee.