Engineering Reference
RF Propagation, Path Loss and Link Terms Reference
Reference free-space path loss, isotropic assumptions, EIRP, received power, receiver sensitivity, link margin, distance and frequency scaling, and excluded real-world losses.
The equations on this page assume free-space propagation, far-field antenna separation, an unobstructed line of sight, clearly defined reference planes, and consistent units. They are not a site-specific channel model or a regulatory allocation table.
Propagation and Link Terms
| Term | Engineering meaning | Boundary |
|---|---|---|
| Free-space path loss (FSPL) | Geometric spreading term between isotropic reference points in ideal free space | It is not a complete measured path-loss model. |
| Isotropic radiator | Ideal point reference that radiates equally in every direction | dBi antenna gain is referenced to this ideal, not to a lossless practical antenna. |
| EIRP | Transmit power minus feed loss plus transmit antenna gain, expressed relative to isotropic | Regulatory limits and averaging conventions are jurisdiction- and service-specific and are outside this Reference. |
| Received power | Power available at the receiver reference plane after gains and losses | State whether cable, connector, mismatch, polarization, and other losses are included. |
| Receiver sensitivity | Input power associated with a specified performance criterion | It depends on bandwidth, modulation, coding, data rate, BER/PER target, temperature, and implementation. |
| Link margin | Calculated received power minus required receiver threshold and design reserve | Positive arithmetic margin does not guarantee availability in an unmodeled fading environment. |
| Fade margin | Budget reserve allocated to propagation variability | Required value depends on reliability target, environment, diversity, mobility, and statistical model. |
| Far field | Region where the radiated field has the assumptions needed by the Friis relation | The boundary depends on antenna dimensions and wavelength; distance alone is not enough. |
Free-Space Assumptions
| Assumption | Required interpretation |
|---|---|
| Free-space medium | No absorbing, reflecting, refracting, or scattering objects alter the direct path. |
| Unobstructed line of sight | The direct path and relevant Fresnel region are not blocked. |
| Far-field operation | Antenna separation is sufficient for the Friis far-field approximation for both antennas. |
| Known reference planes | Transmit power, antenna gain, and received power are referred to clearly defined electrical planes. |
| Matched polarization and impedance | Any mismatch or polarization loss is either negligible or entered separately. |
| Consistent units | The logarithmic constant must match the chosen distance and frequency units. |
Core Relationships
λ = c / f
FSPL(dB) = 20 log10(4πdf / c)
Pr(dBm) = Pt(dBm) + Gt(dBi) + Gr(dBi) - FSPL(dB)
EIRP(dBm) = Pt(dBm) - Ltx(dB) + Gt(dBi)
Link margin(dB) = Pr(dBm) - sensitivity(dBm) - required reserve(dB)
c = 299,792,458 m/s
Scaling Rules
| Change | Ideal result | Reason or boundary |
|---|---|---|
| Distance ×2 | +6.0206 dB | FSPL changes by 20 log10(2) |
| Distance ×10 | +20 dB | One decade greater distance |
| Frequency ×2 | +6.0206 dB | For the same physical distance and isotropic-reference formulation |
| Frequency ×10 | +20 dB | One decade greater frequency |
| Tx antenna gain +3 dB | Received power +3 dB | If all loss terms and reference planes remain unchanged |
| Path loss +10 dB | Received power -10 dB | Equivalent to one tenth of the previous power ratio |
FSPL Is Not Every Loss
| Term | What it represents | How to obtain it |
|---|---|---|
| FSPL | Distance and frequency in ideal free space | 20 log10(4πdf/c) |
| Cable and connector loss | Dissipation between radio and antenna reference plane | Use measured or manufacturer insertion-loss data at frequency. |
| Mismatch loss | Power not accepted because impedances are not conjugately matched | Derive from reflection coefficient or measured S-parameters. |
| Polarization loss | Tx and Rx polarization mismatch | Depends on orientation and polarization state. |
| Atmospheric and rain loss | Frequency-, path-, weather-, and elevation-dependent absorption/scattering | Requires an appropriate propagation recommendation or measured model. |
| Obstruction and diffraction | Terrain, buildings, foliage, Fresnel blockage, and edge diffraction | Not included in the free-space equation. |
| Multipath and fading | Constructive and destructive combination of propagation paths | Use statistical, ray-based, or measured channel models. |
| Implementation margin | Reserve for tolerances, aging, installation, and model uncertainty | Keep distinct from physical losses so assumptions remain auditable. |
Canonical Calculation Anchors
| Case | Calculated result | Interpretation |
|---|---|---|
| 2.4 GHz over 1 km | 100.052 dB FSPL | Ideal free-space spreading only |
| Friis received power | -76.052 dBm | 20 dBm Tx, 2 dBi at each antenna, same ideal path |
| Example complete budget | -77.000 dBm received; 3.000 dB available margin | Includes explicit feed, other-loss, sensitivity, and reserve terms |
| Double distance check | 6.0206 dB | Confirms 20 log10(2) scaling |
Engineering Review Checklist
- Define every RF power reference plane.
- Verify both antennas are in each other's far field.
- Check line of sight and Fresnel-zone obstruction.
- Keep cable and connector loss separate from FSPL.
- Include mismatch and polarization loss where relevant.
- Choose a propagation and fading model appropriate to the environment.
- Tie receiver sensitivity to bandwidth, waveform, and error criterion.
- Allocate fade and implementation margin explicitly.
- Confirm antenna gain for frequency, installation, and polarization.
- Validate critical links with simulation, site survey, and measurement.
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FAQ
What is free-space path loss?
FSPL is the ideal geometric spreading term between isotropic reference points in unobstructed free space. It does not include cable, mismatch, fading, terrain, obstruction, atmospheric, or receiver losses.
How is FSPL calculated?
Use FSPL = 20 log10(4πdf/c) with distance d and frequency f in units consistent with the speed of light c.
Why does FSPL increase with frequency?
At a fixed physical separation and isotropic-reference antenna gains, the Friis aperture relationship produces a 20 log10(f) term. Practical antennas of fixed physical aperture require more careful comparison.
How much does FSPL change when distance doubles?
It increases by 20 log10(2), approximately 6.0206 dB, if all other assumptions remain unchanged.
Is FSPL the same as measured path loss?
No. Measured path loss can include obstruction, reflection, diffraction, scattering, absorption, polarization, antenna installation, and other environmental effects.
What is EIRP?
EIRP is transmit power minus transmit-side feed losses plus antenna gain referenced to an isotropic radiator. State the reference plane and units.
What is link margin?
It is the calculated received level above a defined receiver threshold after required reserve is considered. A positive number is only as reliable as the model and assumptions.
When is the Friis equation valid?
It requires free-space, line-of-sight, far-field conditions with defined antenna gains, polarization, impedance, and reference planes.
Does FSPL include antenna gain?
No. FSPL is the path spreading term. Transmit and receive antenna gains are separate terms in Friis or a link budget.
Does this Reference define legal RF frequencies or power limits?
No. Frequency allocations, licensing, EIRP limits, duty cycle, bandwidth, and equipment authorization depend on current rules in each jurisdiction and service.