// RF Theory
RF Link Budget Theory
How to systematically account for every gain and loss in an RF communication link — from the transmitter power amplifier through space to the receiver's detection threshold. Covers EIRP, path loss, system noise figure, sensitivity, fade margin and link margin with four fully worked examples.
// Foundation
What Is an RF Link Budget?
A link budget is a complete accounting of all the gains and losses experienced by a signal as it travels from a transmitter to a receiver. Every element in the signal chain — antennas, cables, connectors, the propagation medium, the receiver's noise — either adds to or subtracts from the received signal level. The link budget adds them all up and answers the fundamental question: does the receiver have enough signal to work?
Link budgets are written in dB because all the gains and losses simply add and subtract — a cascade of multiplications and divisions in the linear domain becomes simple addition in the logarithmic domain. This is why RF engineers think almost exclusively in dBm, dBW and dB.
The fundamental link budget equation:
P_RX (dBm) = P_TX (dBm) + G_TX (dBi) − L_TX_cable (dB) − FSPL (dB) − L_other (dB) + G_RX (dBi) − L_RX_cable (dB)
Link passes if: P_RX > Sensitivity + Required_fade_margin
P_RX (dBm) = P_TX (dBm) + G_TX (dBi) − L_TX_cable (dB) − FSPL (dB) − L_other (dB) + G_RX (dBi) − L_RX_cable (dB)
Link passes if: P_RX > Sensitivity + Required_fade_margin
// System View
The Complete Signal Chain
// Transmit Side
EIRP — Equivalent Isotropically Radiated Power
EIRP is the total effective power radiated from the TX antenna in the direction of maximum gain. It combines TX power, cable losses, and antenna gain into a single number that fully characterises the transmit side of the link budget.
EIRP Formula
EIRP (dBm) = P_TX (dBm) − L_TX_feed (dB) + G_TX (dBi)P_TX = transmitter output power at the PA output connector
L_TX_feed = cable + connector + duplexer + filter losses between PA and antenna
G_TX = antenna gain in the direction of the receiver (dBi = dB relative to isotropic)
ERP (dBd): Same as EIRP but referenced to a half-wave dipole (0 dBd = 2.15 dBi)
ERP = EIRP − 2.15 dB always
Example: P_TX = +33 dBm, L_feed = 2 dB, G_TX = 15 dBi → EIRP = 46 dBm = 40 W
Regulatory context: FCC Part 15 limits EIRP to +36 dBm (4 W) for 5.8 GHz ISM band point-to-point
EIRP vs transmit power: A 100 mW (20 dBm) transmitter with a 20 dBi directional antenna has EIRP = 40 dBm = 10 W. A 10 W transmitter with a 0 dBi omnidirectional antenna also has EIRP = 40 dBm. In terms of link performance, they are equivalent — the receiver cannot tell the difference. This is why regulators specify EIRP limits rather than transmit power limits.
// Propagation
Path Loss — Every dB Between TX and RX
Free-Space Path Loss (FSPL)
FSPL Formula (Most Important in Link Budget)
FSPL (dB) = 20·log₁₀(4πd/λ) = 20·log₁₀(d) + 20·log₁₀(f) + 20·log₁₀(4π/c)Practical form: FSPL = 20·log₁₀(d_km) + 20·log₁₀(f_MHz) + 32.44
Rules of thumb:
Every doubling of distance → +6 dB path loss
Every decade of distance → +20 dB path loss
Every doubling of frequency → +6 dB path loss
Key reference values:
WiFi 2.4 GHz at 100 m: 80 dB | WiFi 5 GHz at 100 m: 86 dB
LTE 900 MHz at 1 km: 91 dB | 5G 28 GHz at 200 m: 107 dB
GPS L1 at 20,200 km: 182 dB | Ku-band GEO sat at 36,000 km: 205 dB
Other Propagation Losses
Free-space path loss assumes a clear, unobstructed path through vacuum. Real links have additional losses:
| Loss Type | Typical Value | When It Applies |
|---|---|---|
| Atmospheric absorption | 0.01–20 dB/km | Above 10 GHz (O₂ at 60 GHz: 15 dB/km; H₂O at 22 GHz: 0.2 dB/km) |
| Rain attenuation | 0.01–10 dB/km | Above 6 GHz, heavy rain. 28 GHz in 50 mm/hr rain: ~10 dB/km |
| Multipath fading | 0–40 dB | Terrestrial links — standing waves from reflections |
| Shadowing | 5–20 dB | Obstructions (buildings, terrain, trees) |
| Pointing loss | 0.5–3 dB | Directional antennas not perfectly aimed |
| Polarisation loss | 0–∞ dB | TX and RX polarisation mismatch: crossed = total loss |
| Ionospheric loss | 0.1–2 dB | Below 1 GHz, satellite links through ionosphere |
| Connector and cable | 0.5–5 dB total | Every connector (~0.1 dB), every metre of coax (freq-dependent) |
// Receive Side
Receiver Sensitivity — The Minimum Detectable Signal
The receiver sensitivity is the minimum received signal power that allows the receiver to demodulate the signal with acceptable error rate. It is determined entirely by the receiver's noise floor and the modulation scheme's SNR requirement.
Thermal Noise Floor
Thermal Noise Power
N_floor = k_B × T × Bk_B = 1.38×10⁻²³ J/K (Boltzmann constant)
T = system noise temperature (290 K = room temperature standard)
B = receiver noise bandwidth (Hz)
In dBm: N_floor = −174 dBm/Hz + 10·log₁₀(B_Hz)
At standard room temp: −174 dBm/Hz (Johnson noise spectral density)
Examples:
B = 200 kHz (GSM): N_floor = −174 + 53 = −121 dBm
B = 20 MHz (WiFi 802.11n): N_floor = −174 + 73 = −101 dBm
B = 100 MHz (5G NR): N_floor = −174 + 80 = −94 dBm
B = 500 MHz (UWB): N_floor = −174 + 87 = −87 dBm
Required SNR
Different modulation schemes and error rates require different SNR at the receiver decision point. This directly sets the sensitivity:
| Modulation | Required Eb/N₀ | Required SNR (BER 10⁻⁶) | Use |
|---|---|---|---|
| BPSK / QPSK | 10.5 dB | 10.5 dB | Satellite, GPS, CDMA |
| 16-QAM | 17 dB | 20 dB | WiFi 802.11g, LTE |
| 64-QAM | 23 dB | 26 dB | Cable TV, WiFi 802.11n/ac |
| 256-QAM | 29 dB | 32 dB | WiFi 802.11ac/ax, 5G NR |
| 1024-QAM | 35 dB | 38 dB | WiFi 802.11ax, 5G NR mmWave |
| FSK / FM | 6–12 dB | 6–12 dB | Land mobile radio, IoT |
Cascaded Noise Figure
Complete Receiver Sensitivity
Sensitivity (dBm) = N_floor (dBm) + NF_system (dB) + SNR_required (dB)= −174 + 10·log₁₀(B) + NF_system + SNR_req
System NF (Friis cascade):
F_system = F₁ + (F₂−1)/G₁ + (F₃−1)/(G₁G₂) + ...
where F = noise factor (linear), G = gain (linear)
Key insight: The first element in the receive chain dominates system NF.
A 2 dB NF LNA with 20 dB gain: F_system ≈ F_LNA = 1.58 (2 dB)
Without the LNA, cable with 3 dB loss: F_system = 3 dB loss as noise figure contribution
LTE example (B = 10 MHz, 64-QAM, NF = 7 dB):
Sensitivity = −174 + 70 + 7 + 26 = −71 dBm
// Design Headroom
Link Margin & Fade Margin
Link Margin
Link Margin Definition
Link Margin (dB) = P_RX (dBm) − Sensitivity (dBm)Link margin > 0 dB: link works
Link margin < 0 dB: link fails — increase EIRP, reduce distance, or improve sensitivity
Typical required margins:
Fixed point-to-point (indoor): 10 dB minimum
Cellular (outdoor mobile): 20–30 dB (accounts for fading and user movement)
Satellite: 3–10 dB (plus rain margin)
Safety-critical: 30+ dB
Fade Margin
The fade margin is the additional link margin reserved to overcome fading — temporary reductions in received signal level due to multipath interference, atmospheric ducting, or physical obstructions. The required fade margin depends on the link availability requirement (what percentage of time must the link work?).
Fade Margin for Terrestrial Links (Multipath)
FM = 30·log₁₀(d_km) + 10·log₁₀(6·a·b·f_GHz) − 10·log₁₀(1−A) − 70a = terrain factor (0.25 for smooth, 1.0 for rough, 4.0 for water)
b = climate factor (0.125 for arid, 0.5 for temperate, 1.0 for humid)
A = required availability (0.9999 = four nines = 99.99%)
Typical values:
99% availability: FM ≈ 20 dB
99.9% availability: FM ≈ 30 dB
99.99% availability: FM ≈ 40 dB
99.999% (five nines): FM ≈ 50 dB
Rain Attenuation
Above 6 GHz, rain drops become comparable in size to the wavelength and absorb and scatter the signal. Rain attenuation dominates system margin for satellite and terrestrial point-to-point links above 10 GHz.
ITU-R P.838 Rain Attenuation Model
A_rain = γ_R × L_eff (dB)γ_R = specific attenuation (dB/km) = k × R^α
R = rain rate (mm/hr); k and α depend on frequency and polarisation
L_eff = effective path length through rain
Approximate values (horizontal polarisation):
6 GHz, R=50 mm/hr: γ_R ≈ 0.3 dB/km
12 GHz, R=50 mm/hr: γ_R ≈ 2.5 dB/km
28 GHz, R=50 mm/hr: γ_R ≈ 10 dB/km
60 GHz, R=50 mm/hr: γ_R ≈ 25 dB/km
This is why 5G mmWave (28 GHz) links need significant rain margin for outdoor use in tropical climates.
// Visualisation
The Link Budget Waterfall
A link budget waterfall diagram shows each gain and loss as a horizontal bar, with a running total. Green bars are gains (add to the received level), red bars are losses (subtract). The final level is compared to the sensitivity. The gap between the final level and sensitivity is the link margin.
WiFi 2.4 GHz example: 20 dBm TX · 2 dBi antennas · 100 m distance · 7 dB system NF · 10 dB SNR required
// Worked Examples
Four Complete Link Budgets
Example 1 — WiFi 802.11n, 2.4 GHz, 100 m Indoor
WiFi Link Budget
Transmit side:
P_TX = +20 dBm (100 mW, regulatory limit)
Cable/connector loss = 0.5 dB (short pigtail)
TX antenna gain = 2 dBi (dipole)
EIRP = 20 − 0.5 + 2 = 21.5 dBm
Propagation (100 m, 2.4 GHz):
FSPL = 20·log(0.1) + 20·log(2400) + 32.44 = −20 + 67.6 + 32.44 = 80 dB
Indoor wall losses (3 walls × 5 dB/wall) = 15 dB
Multipath fading margin = 10 dB
Total path loss = 105 dB
Receive side:
RX antenna gain = 2 dBi
RX cable loss = 0.3 dB
System NF = 8 dB (WLAN RFIC)
Bandwidth = 20 MHz → N_floor = −174 + 73 = −101 dBm
Required SNR (64-QAM, 802.11n) = 25 dB
Sensitivity = −101 + 8 + 25 = −68 dBm
Result:
P_RX = 21.5 − 105 + 2 − 0.3 = −81.8 dBm
Link margin = −81.8 − (−68) = −13.8 dB
Link fails for 64-QAM at 100 m with walls!
At lower rate (BPSK, SNR=10 dB): Sensitivity = −101+8+10 = −83 dBm → Link margin = +1.2 dB ✓
→ WiFi adapts by falling back to BPSK at range, maintaining connection but at lower throughput.
P_TX = +20 dBm (100 mW, regulatory limit)
Cable/connector loss = 0.5 dB (short pigtail)
TX antenna gain = 2 dBi (dipole)
EIRP = 20 − 0.5 + 2 = 21.5 dBm
Propagation (100 m, 2.4 GHz):
FSPL = 20·log(0.1) + 20·log(2400) + 32.44 = −20 + 67.6 + 32.44 = 80 dB
Indoor wall losses (3 walls × 5 dB/wall) = 15 dB
Multipath fading margin = 10 dB
Total path loss = 105 dB
Receive side:
RX antenna gain = 2 dBi
RX cable loss = 0.3 dB
System NF = 8 dB (WLAN RFIC)
Bandwidth = 20 MHz → N_floor = −174 + 73 = −101 dBm
Required SNR (64-QAM, 802.11n) = 25 dB
Sensitivity = −101 + 8 + 25 = −68 dBm
Result:
P_RX = 21.5 − 105 + 2 − 0.3 = −81.8 dBm
Link margin = −81.8 − (−68) = −13.8 dB
Link fails for 64-QAM at 100 m with walls!
At lower rate (BPSK, SNR=10 dB): Sensitivity = −101+8+10 = −83 dBm → Link margin = +1.2 dB ✓
→ WiFi adapts by falling back to BPSK at range, maintaining connection but at lower throughput.
Example 2 — LTE Uplink, 900 MHz, 3 km Rural
LTE Uplink Link Budget
Transmit side (handset):
P_TX = +23 dBm (200 mW, 3GPP max)
Body loss = 3 dB (phone against head/body)
Antenna gain = 0 dBi (built-in handset antenna)
EIRP = 23 − 3 + 0 = 20 dBm
Propagation (3 km, 900 MHz, rural Okumura-Hata):
FSPL = 20·log(3) + 20·log(900) + 32.44 = 9.5 + 59.1 + 32.44 = 101 dB
Shadowing margin = 8 dB (rural, σ=6 dB, 90% coverage)
Total path loss = 109 dB
Receive side (base station):
RX antenna gain = 18 dBi (sector antenna, 3-sector cell)
Cable/feeder loss = 3 dB (tower-top to BTS)
System NF = 5 dB (tower-mounted LNA + BTS)
Bandwidth = 5 MHz → N_floor = −174 + 67 = −107 dBm
Required SNR (QPSK, SINR target) = 1 dB (with HARQ retransmissions)
Sensitivity = −107 + 5 + 1 = −101 dBm
Result:
P_RX = 20 − 109 + 18 − 3 = −74 dBm
Link margin = −74 − (−101) = +27 dB
Strong uplink — 27 dB margin. QPSK coding supports this range.
P_TX = +23 dBm (200 mW, 3GPP max)
Body loss = 3 dB (phone against head/body)
Antenna gain = 0 dBi (built-in handset antenna)
EIRP = 23 − 3 + 0 = 20 dBm
Propagation (3 km, 900 MHz, rural Okumura-Hata):
FSPL = 20·log(3) + 20·log(900) + 32.44 = 9.5 + 59.1 + 32.44 = 101 dB
Shadowing margin = 8 dB (rural, σ=6 dB, 90% coverage)
Total path loss = 109 dB
Receive side (base station):
RX antenna gain = 18 dBi (sector antenna, 3-sector cell)
Cable/feeder loss = 3 dB (tower-top to BTS)
System NF = 5 dB (tower-mounted LNA + BTS)
Bandwidth = 5 MHz → N_floor = −174 + 67 = −107 dBm
Required SNR (QPSK, SINR target) = 1 dB (with HARQ retransmissions)
Sensitivity = −107 + 5 + 1 = −101 dBm
Result:
P_RX = 20 − 109 + 18 − 3 = −74 dBm
Link margin = −74 − (−101) = +27 dB
Strong uplink — 27 dB margin. QPSK coding supports this range.
Example 3 — Ku-band Satellite Downlink, 12 GHz
Satellite Link Budget (GEO, 36,000 km)
Transmit side (satellite):
P_TX = +47 dBm (50 W TWTA transponder)
Waveguide loss = 1 dB
TX antenna gain = 33 dBi (1.5 m reflector at 12 GHz)
EIRP = 47 − 1 + 33 = 79 dBm
Propagation (GEO, 12 GHz):
FSPL = 20·log(36000) + 20·log(12000) + 32.44 = 91.1 + 81.6 + 32.44 = 205 dB
Atmospheric absorption = 0.3 dB
Pointing loss = 0.5 dB
Rain margin (0.01% unavailability, tropical) = 5 dB
Total path loss = 210.8 dB
Receive side (VSAT terminal):
RX antenna gain = 41 dBi (0.9 m dish at 12 GHz)
LNB noise figure = 0.7 dB (LNB system NF)
Bandwidth = 36 MHz → N_floor = −174 + 75.6 = −98.4 dBm
Required SNR (DVB-S2, 8PSK 2/3 FEC) = 6 dB
Sensitivity = −98.4 + 0.7 + 6 = −91.7 dBm
Result:
P_RX = 79 − 210.8 + 41 = −90.8 dBm
Link margin = −90.8 − (−91.7) = +0.9 dB
Marginal — meets spec but rain margin is tight. Standard for broadcast satellite design at edge of beam.
P_TX = +47 dBm (50 W TWTA transponder)
Waveguide loss = 1 dB
TX antenna gain = 33 dBi (1.5 m reflector at 12 GHz)
EIRP = 47 − 1 + 33 = 79 dBm
Propagation (GEO, 12 GHz):
FSPL = 20·log(36000) + 20·log(12000) + 32.44 = 91.1 + 81.6 + 32.44 = 205 dB
Atmospheric absorption = 0.3 dB
Pointing loss = 0.5 dB
Rain margin (0.01% unavailability, tropical) = 5 dB
Total path loss = 210.8 dB
Receive side (VSAT terminal):
RX antenna gain = 41 dBi (0.9 m dish at 12 GHz)
LNB noise figure = 0.7 dB (LNB system NF)
Bandwidth = 36 MHz → N_floor = −174 + 75.6 = −98.4 dBm
Required SNR (DVB-S2, 8PSK 2/3 FEC) = 6 dB
Sensitivity = −98.4 + 0.7 + 6 = −91.7 dBm
Result:
P_RX = 79 − 210.8 + 41 = −90.8 dBm
Link margin = −90.8 − (−91.7) = +0.9 dB
Marginal — meets spec but rain margin is tight. Standard for broadcast satellite design at edge of beam.
Example 4 — X-band Radar (10 GHz, 10 km range)
Radar Link Budget (Monostatic, Round-Trip)
Radar uses the same antenna for TX and RX. The signal travels from the radar to the target AND back, so path loss applies twice. The target's radar cross-section (RCS, σ) determines how much power is reflected toward the radar.
Radar Range Equation (in dB):
P_RX = P_TX + G_TX + G_RX − 2·FSPL(d) − L_system + 10·log₁₀(σ/4πd²·λ²)
Parameters (surveillance radar):
P_TX = +60 dBm (1 kW peak)
G_TX = G_RX = 35 dBi (parabolic dish)
FSPL(10 km, 10 GHz) = 20·log(10) + 20·log(10000) + 32.44 = 132.4 dB
Two-way path loss = 2 × 132.4 = 264.8 dB
System losses (duplexer, cable, rotary joint) = 5 dB
Target RCS σ = 1 m² (small aircraft) → 10·log₁₀(σ) = 0 dBsm
λ = 0.03 m → 10·log₁₀(λ²/(4π)²) = −52 dB
Result:
P_RX = 60 + 35 + 35 − 264.8 − 5 + 0 − 52 = −191.8 dBW = −161.8 dBm
Noise floor (1 MHz pulse-compressed BW, NF=4 dB):
Sensitivity = −174 + 60 + 4 + 13 (SNR for Pd=0.9, Pfa=10⁻⁶) = −97 dBm
Link margin = −161.8 − (−97) = −64.8 dB !
Link fails — too far for 1 m² target at 10 km without integration gain.
With pulse compression (1000:1 ratio = 30 dB gain): Effective SNR improves by 30 dB.
With coherent integration (100 pulses = 20 dB gain): Further +20 dB.
Net margin = −64.8 + 30 + 20 = +15.2 dB ✓ — viable with modern signal processing.
Radar Range Equation (in dB):
P_RX = P_TX + G_TX + G_RX − 2·FSPL(d) − L_system + 10·log₁₀(σ/4πd²·λ²)
Parameters (surveillance radar):
P_TX = +60 dBm (1 kW peak)
G_TX = G_RX = 35 dBi (parabolic dish)
FSPL(10 km, 10 GHz) = 20·log(10) + 20·log(10000) + 32.44 = 132.4 dB
Two-way path loss = 2 × 132.4 = 264.8 dB
System losses (duplexer, cable, rotary joint) = 5 dB
Target RCS σ = 1 m² (small aircraft) → 10·log₁₀(σ) = 0 dBsm
λ = 0.03 m → 10·log₁₀(λ²/(4π)²) = −52 dB
Result:
P_RX = 60 + 35 + 35 − 264.8 − 5 + 0 − 52 = −191.8 dBW = −161.8 dBm
Noise floor (1 MHz pulse-compressed BW, NF=4 dB):
Sensitivity = −174 + 60 + 4 + 13 (SNR for Pd=0.9, Pfa=10⁻⁶) = −97 dBm
Link margin = −161.8 − (−97) = −64.8 dB !
Link fails — too far for 1 m² target at 10 km without integration gain.
With pulse compression (1000:1 ratio = 30 dB gain): Effective SNR improves by 30 dB.
With coherent integration (100 pulses = 20 dB gain): Further +20 dB.
Net margin = −64.8 + 30 + 20 = +15.2 dB ✓ — viable with modern signal processing.
// Practical Summary
Link Budget Design Rules
| Rule | Guideline | Why |
|---|---|---|
| Noise figure first | Minimise NF of first RX element — prioritise LNA over anything else | First element dominates system NF (Friis). 1 dB saved here = 1 dB more sensitivity |
| Antenna gain is free dB | +1 dBi TX = +1 dBi RX in terms of link margin impact | Unlike PA power, antenna gain doesn't cost DC power or add noise |
| Cable losses kill | Minimise cable between LNA and antenna — every 1 dB cable loss = 1 dB higher system NF | Cable loss before the LNA is directly added to NF. Mount LNA at the antenna (tower-top) |
| Budget 30 dB fade margin for mobile | Mobile cellular links need 20–30 dB beyond the FSPL calculation for coverage reliability | Multipath fading, shadowing, and body loss can temporarily reduce signal by 20+ dB |
| Double-check FSPL at both frequencies | For FDD: compute link budget at both TX and RX frequencies (they differ) | Uplink and downlink have different path losses, antenna gains, and noise figures |
| Sensitivity = margin bank | Better sensitivity directly buys range or allows lower TX power | 3 dB better sensitivity = 41% range increase (6 dB = double the range) |
| Rain margin above 10 GHz | Add 5–20 dB rain attenuation margin for links above 10 GHz in areas with heavy rain | 28 GHz sees 10 dB/km in 50 mm/hr rain — can completely fade a 1 km link |