1. Learning Objectives
By the end of this study guide, the student should be able to:
- Define the ground wave (surface wave) and distinguish it from space waves and sky waves; state where each dominates as a function of frequency and distance.
- Explain the physical mechanism of ground-wave propagation: induced ground currents, the tilt of the wavefront, and the role of ground conductivity and permittivity in attenuation.
- Describe the Sommerfeld/Norton ground-wave formulation in practical terms, including the surface-wave factor F and its dependence on numerical distance.
- Compute ground-wave field strength using the flat-earth and spherical-earth (FCC/ITU) curves, and account for land/sea, frequency, and antenna height effects.
- Specify antennas for ground-wave systems (vertical monopoles, top loading, ground screens) and explain their interaction with the ground (image theory, ground loss).
- Design a ground-wave link budget including atmospheric noise at LF/MF and typical receiver noise figures.
- Solve numerical problems on field strength, service range, and required transmitter power for ground-wave systems (AM broadcast, maritime NAVTEX, Loran/eLoran, VLF time signals).
2. Introduction
The ground wave (more precisely the surface wave) is the component of a radio wave that propagates along the interface between air and ground, guided by the Earth's surface. It is the dominant mode at VLF (3–30 kHz), LF (30–300 kHz) and MF (300 kHz – 3 MHz) — exactly the bands where sky-wave is unreliable (D-layer absorbed by day) and line-of-sight is impossible.
- Key applications: MF AM sound broadcasting (540–1700 kHz, e.g. Kenya Broadcasting Corporation services), maritime radiotelephony/coast stations (2182 kHz distress), NAVTEX (518 kHz) and DSC (MF/HF), Loran-C / eLoran navigation (100 kHz), VLF time-and-frequency stations (WWVB 60 kHz, DCF77 77.5 kHz), submarine VLF (3–30 kHz) and geological/telemetry links.
- Range: tens of km at MF over land to ~1 000 km+ at VLF; over sea water (excellent conductor) ground waves hug the surface much further — which is why maritime HF at 2 MHz still reaches hundreds of km at night.
- No skip zone, no fading structure: ground-wave field strength is stable and predictable day and night — a huge operational advantage.
Why this is core ECE 523 material: the ground wave is the purest example of antenna–ground interaction. The Earth is half of the antenna system: its conductivity sets launch efficiency, its curvature sets the horizon, and its dielectric loss sets the attenuation per kilometre. Nothing in propagation teaches ground-plane design better than a ground-wave link.
3. Ground-Wave Theory
3.1 Components Near the Surface
At radio frequencies below ~3 MHz, any antenna close to the ground excites three field components: the direct (space) wave, the ground-reflected wave, and the surface (ground) wave — a lateral wave bound to the interface. Within a few wavelengths of the antenna the first two largely cancel (the reflection coefficient at grazing incidence is ≈ −1 for vertical polarization over earth), leaving the surface wave to do the long-distance work. That is why ground-wave services are engineered with vertical polarization and low antennas: a horizontal antenna's surface wave is shorted out by the ground.
3.2 The Tilted Wavefront
As the surface wave advances, it continuously induces currents in the (lossy) ground. Those currents:
- slow the wave near the surface → the wavefront tilts forward, continuously converting some energy into the forward-guided surface wave.
The stronger the ground conductivity, the smaller the induced currents and the smaller the attenuation. Sea water (σ ≈ 5 S/m) is nearly a perfect conductor at MF; dry ground (σ ≈ 0.001 S/m) is very lossy.
3.3 Sommerfeld–Norton Surface Wave
The classical result (Sommerfeld 1909; Norton's practical form) gives the vertical-electric field of a short vertical dipole over a flat, homogeneous earth:
Free-space reference E0 = (η 2π he I) / (λ d) (short vertical monopole, he effective height)
Numerical distance p = (π d / λ) × (x) , x = √( (εr+1)² + (60 λ σ)² ) − (εr+1) ... for vertical polarization
Flat-earth range behaviour E ∝ 1/d² once surface-wave attenuation dominates (d beyond "fading zone")
Because both path spreading and ground absorption act, ground-wave field falls faster than free space: 1/d² at moderate distances (versus 1/d in free space). The practical engineering tool is the family of ITU-R/FCC ground-wave field-strength curves (flat earth for d < ~100 km at MF; spherical-earth corrections beyond).
3.4 Spherical Earth and Diffraction
Beyond ~50–100 km the Earth's curvature matters: the wave must diffract around the bulge. Ground-wave coverage then follows diffraction theory (Fresnel–Kirchhoff over a smooth sphere); at VLF the long wavelength makes diffraction loss tiny, giving trans-horizon ranges of thousands of km. Standard curves (ITU-R P.368, FCC 73.184) integrate all of this; use them rather than the flat-earth formula beyond the "radio horizon".
4. The Ground as a Circuit Element
| Ground type | σ (S/m) | εr | Ground-wave effect |
|---|---|---|---|
| Sea water | ≈ 5 | ≈ 70 | Excellent: minimal attenuation; MF maritime ranges 300–1000+ km |
| Wet/loamy soil | 0.01 – 0.03 | 10 – 30 | Moderate; typical farmland coverage ~50–100 km at MF |
| Dry/sandy soil | 0.001 – 0.005 | 4 – 10 | Poor; high attenuation, range tens of km |
| Rock/mountains | ≪ 0.001 | 5 – 10 | Very poor; ground wave quickly lost |
Skin depth δ = √(2 / (ω μ0 σ)) (how deep ground currents flow)
- Launch efficiency: a vertical monopole's radiation resistance (~37 Ω for λ/4 over perfect ground) is fed against ground-loss resistance; over average soil the system may lose 3–10 dB unless a ground screen (radials ≥ 0.25λ, or a counterpoise) is installed.
- Image theory: the ground acts as an electrical mirror: a λ/4 monopole over perfect ground behaves like a λ/2 dipole, with ~3 dB gain and zero elevation along the surface — the ideal ground-wave launcher.
- Effect of elevated antennas: raising a ground-wave antenna above ~0.1λ reduces surface-wave coupling and adds a space-wave lobe; ground-wave stations keep antennas LOW.
5. Field Strength Prediction
5.1 Flat-Earth Short-Distance Formula (d ≲ 80–100 km at MF)
E (mV/m) ≈ 300 √(PkW) × F / dkm (P radiated, in kW; F = ground/height factor ≤ 1)
The constant hides unit conversions; for precise work use ITU-R P.368 curves with the appropriate ground constants, polarization, and antenna heights.
5.2 Practical Coverage Numbers (rule-of-thumb, 1 kW radiated, vertical monopole)
| Band | Over sea water | Over average land |
|---|---|---|
| VLF (20 kHz) | several 1 000 km | 1 000+ km |
| LF (100 kHz) | ~1 000 km | ~300–500 km |
| MF (1 MHz) | ~300–500 km | ~50–100 km |
| HF (10 MHz) | ~100 km (night more) | ~30–50 km |
5.3 Beyond the Horizon
At ranges beyond the smooth-horizon distance, field strength is set by diffraction over the spherical earth; terrain roughness (hills, buildings) adds empirical clutter loss. Standard curves (P.368; FCC 73.184 for AM broadcast) already fold these in — always use curves for regulatory coverage proofs.
6. Frequency Dependence and Representative Services
| Service | Frequency | Ground-wave role |
|---|---|---|
| VLF submarine / time signals (WWVB, DCF77) | 16 – 60 kHz | Primary mode; global or continental coverage; extremely low data rates, stable phase |
| Loran-C / eLoran | 100 kHz | Primary; 1 000+ km over sea; navigation accuracy from ground-wave stability |
| NAVTEX maritime warnings | 518 kHz (490 kHz national) | Primary; ~400 km at sea by day/night |
| MF AM broadcasting | 531 – 1611 kHz (9 kHz steps) | Primary daytime coverage ~50–100 km land; sky wave extends night coverage (causes interference — see box) |
| Maritime MF (DSC 2187.5 kHz, radiotelephony 2182 kHz legacy) | 1.6 – 4 MHz | Coastal coverage ~100–200 km over sea |
Sky-wave contamination at MF: at night the D layer disappears and MF sky waves return over 1 000+ km — why distant AM stations "come in" after sunset. Broadcasters exploit it (cleared-channel stations), but it also creates co-channel interference; regulators plan AM networks assuming day = ground-wave-only, night = ground + sky-wave.
7. Antennas for Ground Wave
- Quarter-wave vertical monopole over a ground plane: the canonical ground-wave antenna — strong surface-wave launch, omnidirectional azimuth, needs a radial system (≥ 16–120 radials of ≥ 0.25λ, or buried ground screen).
- Top-loaded short verticals (T, inverted-L): when λ/4 is impractical (LF/VLF, masts < 60 m at 200 kHz): top loading raises radiation resistance and current distribution; used for Loran and beacon transmitters.
- Height vs take-off angle: keep h ≤ 0.1–0.2λ for pure surface-wave launch; higher antennas add space-wave lobes (useful only if a sky-wave service is also wanted at MF).
- Horizontal antennas are ineffective for ground wave: their image cancels the surface wave (Beverages and loops are receiving special cases, not launchers).
- Receiving antennas: small active whip, loop (for direction finding), or a low Beverage along the path; atmospheric noise is high at LF/MF, so again antenna directivity buys "noise figure".
Radial system rule ≥ 0.25λ long, ≥ 16 radials; loss Rg ≈ small vs 36 Ω on good ground
8. Ground-Wave Link Budget
Practical form E(dBµV/m) = 20log E(µV/m) ; receiver input V(dBµV) = E + G(dBd) − Lcable + 107 (for 50 Ω) ≈ E + G − Lcable + 6 (dipole ref)
Noise Fam at LF/MF: 30–60 dB above kTB (day) — dominates; sky-wave noise pickup on elevated antennas must be managed
- Because the ground wave is stable (slow quasi-static fading, ≈ 1–3 dB), required margins are modest (≈ 8–10 dB) compared with mobile VHF (location variability) — a planning advantage.
- Power requirements scale steeply: doubling range (in the 1/d² regime) costs ≈ 6–12 dB more ERP; MF broadcasters use 1–50 kW for this reason.
9. Worked Examples
Example 1 — Free-space vs ground-wave fall-off
A 1 kW MF station produces 100 mV/m at 1 km (reference). Estimate the field at 10 km (a) free space, (b) ground wave over average land (1/d²).
Example 2 — Skin depth of ground currents
Find the skin depth in sea water (σ = 5 S/m) and dry soil (σ = 0.001 S/m) at 1 MHz.
Example 3 — Field from a short monopole
A 10 kW MF transmitter feeds a λ/4 monopole (assume 90% efficiency, ground system OK). Estimate field at 20 km using E = 300√P·F/d with F ≈ 0.5 (average land).
Example 4 — Range scaling for a service
A NAVTEX coast station gives 25 µV/m (28 dBµV/m above 1 µV/m baseline) at 100 km over sea (F≈0.9). Receiver needs 2 µV/m. Estimate maximum range (1/d²).
Example 5 — ERP and monopole gain
A 5 kW transmitter feeds a λ/4 monopole over perfect ground (D = 3, η = 0.95). Find ERP and EIRP.
Example 6 — Compare sea vs land at MF
Same 1 kW, 1 MHz, 100 km: compare approximate fields over sea (F = 0.95) and average land (F = 0.2) using E = 300√P·F/d.
Example 7 — Power for a target field
Desired: 1 mV/m at 30 km over average land (F = 0.5). Required radiated power?
10. Interactive Calculators
10.1 Flat-Earth Ground-Wave Field (E = 300√P·F/d)
10.2 Range for Target Field (1/d²)
10.3 Skin Depth in Ground
10.4 Power for Target Field
10.5 ERP from Monopole
11. Summary of Key Points
- The ground (surface) wave is the dominant LF/MF mode: stable, day-and-night, no skip zone — ideal for broadcast, maritime and navigation services.
- It exists because ground currents tilt the wavefront forward; lossy ground makes E fall ≈ 1/d² — much faster than free space.
- Ground conductivity rules: sea water ≈ 5 S/m gives hundreds of km at MF; dry land ≈ 0.001 S/m gives tens of km. Skin depth shows where the currents flow.
- Practical design uses ITU-R P.368 / FCC curves (flat earth short-range; spherical earth + diffraction beyond the horizon).
- Antennas: LOW vertical monopoles with radial ground systems; horizontal antennas cancel their own surface wave; keep h ≤ 0.1–0.2λ.
- At night, MF sky-wave returns and extends/interferes — AM network planning is a day (ground wave) / night (ground + sky) problem.
- Link budgets: atmospheric noise dominates at LF/MF; stable signal means small margins (~8–10 dB); range doubling costs ~6–12 dB in the 1/d² region.
12. Self-Test Quiz (12 Questions)
Attempt each question, then click "Check Answers".
1. The ground (surface) wave is the dominant propagation mode at:
2. Ground-wave antennas must be:
3. Beyond the near field, ground-wave field strength over average land falls approximately as:
4. The best ground for ground-wave propagation is:
5. Horizontal antennas perform poorly for ground wave because:
6. At night, distant MF AM stations become receivable because:
7. The skin depth in ground determines:
8. NAVTEX at 518 kHz relies on ground wave because:
9. Doubling ground-wave range in the 1/d² region requires approximately:
10. A quarter-wave vertical over perfect ground has radiation resistance ≈ 37 Ω and gain:
11. Loran-C at 100 kHz achieves 1000+ km ground-wave range primarily because:
12. The fading experienced on ground-wave links is:
13. References & Further Reading
- ITU-R P.368 — Ground-wave propagation curves for frequencies between 10 kHz and 30 MHz.
- Jordan, E. C. & Balmain, K. G. — Electromagnetic Waves and Radiating Systems (surface-wave theory).
- Burrows, M. L. — ELF Communications Antennas / Wait, J. R. — Electromagnetic Waves in Stratified Media (Sommerfeld/Norton formulations).
- FCC Rules §73.184 — Ground-wave field strength curves (AM broadcast).
- Stutzman, W. L. & Thiele, G. A. — Antenna Theory and Design (monopoles, ground systems, radials).
- IEC/ITU maritime documents: NAVTEX (IMO MSC.306(87)), MF DSC (ITU-R M.541).
Prepared for ECE 523E — Antenna & Radio Wave Propagation, Department of Electrical & Communication Engineering, Masinde Muliro University of Science and Technology.