1. Learning Objectives
By the end of this study guide, the student should be able to:
- Describe the structure of the ionosphere (D, E, F1, F2 layers) and explain how ionization by solar radiation supports long-range HF radio communication.
- Explain the principal HF propagation modes — ground wave, sky wave (E/F-layer reflections, multi-hop), NVIS — and their frequency-dependent behaviour.
- Define and compute MUF, LUF, OWF, skip distance, virtual height and maximum single-hop range using the secant law and simple geometry.
- Perform an HF link budget: account for free-space loss, ionospheric absorption (D-layer), ground reflection loss per hop, antenna gains, and compare with the system noise floor.
- Describe suitable HF antennas (half-wave dipole, vertical, Yagi, log-periodic, rhombic), their gain, radiation patterns, polarization, and matching at HF.
- Describe modern HF systems: SSB, ALE, channel sounding, and digital modems; and the effect of the solar cycle on link planning.
- Solve numerical problems on sky-wave geometry, MUF determination, absorption, and SNR at the HF receiver.
2. Introduction to HF Communication
The High Frequency (HF) band spans 3 – 30 MHz (wavelengths 100 – 10 m). It occupies a special place in radio engineering: it is the lowest band in which ionospheric sky-wave propagation routinely enables beyond-line-of-sight communication of thousands of kilometres without any infrastructure — no towers, no satellites, no repeaters.
- Frequency allocations (ITU): 3.5–4.0 MHz (80 m amateur), 5.3–5.4 MHz (60 m), 7.0–7.3 MHz (40 m), 10.1–10.15 MHz (30 m), 14.0–14.35 MHz (20 m), 18 MHz (17 m), 21 MHz (15 m), 24 MHz (12 m), 26.5–28 MHz (11 m/CB, 27 MHz ISM); aeronautical mobile (3–22 MHz) and maritime (4–27.5 MHz) are heavy users, as are international broadcasters.
- Applications: long-distance aviation and maritime comms, diplomatic and military links, amateur radio, remote-area telemetry, international broadcasting, backup when satellite/VHF fails, and NVIS regional networks.
- Data rates: legacy SSB voice ~3 kHz channels; modern digital modems (STANAG 5066, MIL-STD-188-110) achieve 75–9600 bit/s and beyond on 3 kHz channels, up to ~120 kbit/s on wideband HF.
Why HF is core ECE 523 material: the entire discipline of antenna & propagation engineering is on display at HF — ionospheric refraction (a "variable mirror"), antenna height/gain trading against noise, ground conductivity in wave velocity, and link budgets dominated by absorption and atmospheric noise rather than free-space loss. Master HF and every other band's behaviour becomes easier to reason about.
3. The Ionosphere
3.1 Structure and Formation
Solar EUV and X-ray radiation ionizes the upper atmosphere, creating free electrons and ions. Electron density varies with height in layers, each with a characteristic critical frequency fo (the highest frequency that reflects vertically):
| Layer | Height (km) | Day fo | Night behaviour | Role |
|---|---|---|---|---|
| D | 60 – 90 | — (absorbs; fo ~0.3–0.6 MHz) | Practically vanishes | Heavy absorption of LF/MF; weakens above ~4–5 MHz |
| E | 90 – 130 | ≈ 3 – 4 MHz | fo ≈ 0.5–1 MHz | Sporadic-E (Es) supports 50–150 MHz DX at times; single-hop ~2000 km |
| F1 | 150 – 220 | ≈ 4 – 6 MHz | Merges into F2 at night | Daytime secondary reflector |
| F2 | 220 – 400+ | ≈ 8 – 14 MHz | fo ≈ 3 – 6 MHz (persists) | Main long-haul reflector; highest MUFs |
Electron density peaks near midday, falls at night; F2 additionally responds to geomagnetic latitude and solar cycle with a ~24 h lag.
3.2 Refraction, not Reflection
A radio wave in an ionized medium experiences a refractive index n = √(1 − (fp/f)²), where fp = 8.98√Ne is the plasma frequency (Ne in electrons/m³). As the wave ascends into denser ionization, n decreases, the wave bends, and — if f < MUF — it returns to Earth. If f exceeds the layer's capability at the required angle, the wave penetrates into space.
Secant law MUF = fo × sec(i) = fo / cos(i) (i = angle of incidence at the layer)
3.3 Solar Control
- Sunspot number (SSN / R12): the 11-year solar cycle modulates foF2 and absorption roughly linearly; R12 10 → foF2 ~5 MHz, R12 150 → foF2 ~12 MHz.
- Diurnal variation: MUF highest near noon, lowest just before dawn — hence frequency plans change through the day.
- Disturbances: solar flares cause Sudden Ionospheric Disturbances (SID — D-layer absorption spike, HF blackout on sunlit side); geomagnetic storms spread the auroral absorption zone equatorward.
4. HF Propagation Modes
4.1 Ground Wave
Follows the Earth's curvature, hugging the surface; strongly attenuated by conductivity and frequency — useful to ~50–100 km by day at the low end of HF, and negligible above ~5 MHz over land. Over sea water (σ ≈ 5 S/m) ranges extend several hundred km at 2–4 MHz — why maritime HF works.
4.2 Sky Wave (E and F Layer)
- Single hop: E-layer hop ≈ 1 800–2 000 km; F-layer hop ≈ 3 000–4 000 km (virtual heights 100 km and 250–400 km).
- Multi-hop: successive ionosphere↔ground reflections extend global range (e.g., 10 000 km = 3 F hops). Each ground reflection loses 2–8 dB depending on terrain and grazing angle.
- Skip zone (skip distance): the annular dead zone between the ground-wave limit and the first sky-wave return. Only frequencies near the LUF have no skip zone.
- Sporadic E (Es): thin dense patches at ~100 km supporting single-hop to ~2 500 km at up to 50–150 MHz — a bonus mode in equatorial regions (relevant to East Africa).
4.3 NVIS (Near-Vertical-Incidence Skywave)
Radiating energy nearly straight up (elevation > 70°) from a horizontal antenna, so the wave reflects nearly vertically and rains down within 100–500 km — no skip zone. NVIS is the regional-network mode: it fills the gap ground wave cannot reach and sky wave skips over. Frequency choice is strict: too high penetrates the layer (no return); too low is absorbed. NVIS circuits operate between LUF and the vertical-incidence critical frequency foF2 — typically 3–8 MHz by day, 1.5–4 MHz at night.
Mode selection summary: ground wave (short range, low band), NVIS (100–500 km regional), low-angle sky wave (500–4 000 km single hop, >4 000 km multi-hop). Day: higher frequencies (10–20 MHz); night: lower (3–10 MHz) as D-layer absorption vanishes and foF2 falls.
5. MUF, LUF, OWF and Skip Distance
Single-hop range d = 2 hv tan(θi) , with θi = arcsin( [R/(R+hv)] cos(Δ/2) )-style spherical correction for accuracy
Flat-earth approx d ≈ 2 hv √((MUF/fo)² − 1) for the range at which frequency MUF just returns
OWF (optimum working frequency) ≈ 0.85 × MUF — best trade of availability vs absorption
- LUF (lowest usable frequency): set by D-layer absorption + atmospheric noise + required SNR. Absorption ∝ 1/f², so the LUF rises with path length, solar activity and daytime.
- Usable window: LUF < f < MUF. The OWF (85 % of MUF) is the classical choice for ~90 % circuit availability.
- Prediction services (ITU-R P.533, VOACAP online) compute MUF/LUF/SNR by hour, month, SSN and path.
6. The HF Link Budget
HF budgeting differs from VHF/UHF: the dominant terms are ionospheric absorption and external (atmospheric) noise, not free-space loss.
Free space Lfs = 32.44 + 20log f(MHz) + 20log d(km)
System noise Fam = atmospheric/ionospheric noise figure above kTB (CCIR/ITU-R curves, 0.5–30 dB typical)
- Ionospheric absorption Liono: mostly D-layer; ~1/f² behaviour; daytime 3–15 dB (multi-hop paths accumulate per transit); night: ≈ 0–3 dB.
- Ground reflection loss Lgnd (per intermediate ground point): 2–8 dB; use low grazing angles and good ground conductivity (sea best).
- Atmospheric noise (thunderstorms, tropical): can reach 40–50 dB above kTB at 3 MHz, falling to ~0 dB by 20 MHz — this, not the receiver, often sets the noise floor. HF receivers are intentionally deaf (NF 10–15 dB is fine).
- Fading: multipath within the ionosphere (multi-path spreads of 0.5–3 ms) and layer movements cause Rayleigh-type fading, 10–20 dB deep; countered by interleaving + FEC in digital modems, and by space/frequency diversity.
7. Antennas for HF
| Antenna | Gain | Pattern | Best use |
|---|---|---|---|
| Half-wave dipole at ½–1 λ height | 0 – 6 dBi | Figure-8, low-angle lobes when high; near-vertical when low | General purpose; NVIS when < 0.25 λ high |
| Quarter-wave vertical with radials | 0 – 4 dBi | Omnidirectional, high angle (NVIS) if top-loaded short | Mobile/maritime; regional nets |
| 2–4 element Yagi (rotatable) | 8 – 13 dBi | Directional, low angle | DX (long-haul) circuits, one azimuth |
| Log-periodic | 7 – 12 dBi | Directional, broad bandwidth | Frequency-agile / ALE stations |
| Rhombic / travelling wave | 10 – 17 dBi | Highly directional, terminated | Fixed point-to-point links |
| Long wire / beverage (receiving) | −2 – 3 dBi (rx) | Low-angle directive | Receive-side directivity to cut noise |
- Polarization: ionospheric propagation scrambles polarization (Faraday rotation, multi-path) — antenna polarization is largely irrelevant at HF; choose for pattern, not polarization.
- Height vs NVIS/DX: antenna < 0.25 λ above ground concentrates energy at high angles (NVIS); ≥ 0.5 λ suppresses high angles for low-angle DX.
- Matching: HF beams present 50 Ω; wire antennas often need antenna tuners (L-networks). Small losses matter: 3 dB of tuner loss halves your SNR at the noise-limited margin.
- Ground: for verticals and NVIS, radial systems or ground screens of ¼ λ radius dramatically improve efficiency.
8. Modern HF Systems
- SSB (J3E): single-sideband suppressed carrier; 3 kHz channel, ~2.7 kHz occupied; the universal voice mode; power quoted as PEP.
- ALE (Automatic Link Establishment, MIL-STD-188-141): radios sound each channel and build a link-quality matrix, automatically selecting the best frequency — the practical answer to the MUF's hourly drift.
- Digital modems (STANAG 5066, MIL-STD-188-110): serial-tone PSK with adaptive equalization and interleaving against multi-path; 75–9600 bit/s in 3 kHz, up to 120 kbit/s wideband; robust waveforms operate at negative SNR.
- Channel sounding: chirp/pseudo-noise probes (e.g., WSPR, Ionosonde) map the channel in real time.
- Operational practice: daytime high band (10–18 MHz), night low band (3–8 MHz); plan with VOACAP/ITU-R P.533; keep OWF discipline; diversity (space, frequency, time) against fading.
Kenya & regional relevance: equatorial ionosphere features strong sporadic-E and equatorial anomaly effects (±15° latitude), supporting short-hop VHF openings; NVIS serves humanitarian/ disaster-relief networks (e.g., amateur EmComms on 80/40 m) and aviation over the Indian Ocean uses HF sky wave as primary beyond-LOS medium.
9. Worked Examples
Example 1 — MUF by the secant law
foF2 = 9 MHz. What is the MUF for a single hop with incidence angle 60° at the layer?
Example 2 — Maximum single-hop range (flat-earth)
For a layer virtual height hv = 300 km and fo = 6 MHz, find the range at which a 12 MHz signal just returns.
Example 3 — Skip distance
Ground-wave range 40 km; first sky-wave return at 1 000 km. Describe the skip zone and what happens as frequency decreases toward the LUF.
Example 4 — Free-space loss at HF
Find FSPL for a 3 000 km path at 10 MHz. Comment on its magnitude.
Example 5 — HF link budget
Transmitter 400 W PEP (+56 dBm), TX antenna gain 10 dBi, RX antenna 6 dBi, single F hop 3 000 km at 12 MHz, ionospheric absorption 8 dB, ground reflection loss 5 dB (one intermediate hop), feeder losses 2 dB total. Atmospheric noise Fam = 25 dB, bandwidth 3 kHz. Find the SNR.
Example 6 — Antenna height for NVIS
At what maximum height above ground should a 40 m (7.2 MHz) dipole be mounted to favour NVIS?
Example 7 — OWF selection
At noon foF2 = 11 MHz; ground-reflection geometry for the required 2 500 km path demands incidence 65°. Choose the working frequency and estimate the hop type.
10. Interactive Calculators
10.1 MUF / OWF (Secant Law)
10.2 Single-Hop Range (flat-earth)
10.3 HF Link Budget
10.4 NVIS / Dipole Height & Wavelength
11. Summary of Key Points
- HF (3–30 MHz) enables infrastructure-free beyond-LOS communication via ionospheric refraction; range from 100 km (NVIS) to global (multi-hop).
- The ionosphere's D/E/F1/F2 layers have diurnal, seasonal and solar-cycle (SSN) controlled critical frequencies; F2 dominates long-haul paths.
- MUF = fo·sec θ (secant law); OWF ≈ 0.85 MUF; LUF set by D-layer absorption (∝1/f²) and atmospheric noise; usable window LUF–MUF drifts hourly.
- Sky-wave hops: E ≈ 2 000 km, F ≈ 3 000–4 000 km; ground losses 2–8 dB per hop; skip zones exist between ground-wave limit and first return — cured by NVIS (near-vertical radiation).
- HF link budgets: FSPL is modest; absorption and external noise dominate; receivers can be high-NF because atmospheric noise sets the floor.
- Antennas: dipole height trades NVIS (low, <0.25λ) against DX (high, low-angle lobes); Yagi/log-periodic/rhombic for gain; polarization is unimportant after the ionosphere.
- Modern systems: SSB voice, ALE for automatic frequency selection, PSK modems with interleaving/equalization for robust data down to negative SNR.
12. Self-Test Quiz (12 Questions)
Attempt each question, then click "Check Answers".
1. The HF band is:
2. The MUF is related to the critical frequency by:
3. The D layer primarily:
4. NVIS is achieved by:
5. The OWF is conventionally chosen as:
6. The LUF is mainly determined by:
7. A single F2-layer hop typically covers:
8. In HF link budgets, the quantity that usually sets the receiver noise floor is:
9. Ionospheric absorption varies approximately as:
10. For NVIS at 7 MHz (λ ≈ 43 m), the dipole should be mounted below approximately:
11. Antenna polarization at HF is generally unimportant because:
12. ALE (Automatic Link Establishment) primarily:
13. References & Further Reading
- ITU-R P.533 — Method for the prediction of the performance of HF circuits.
- ITU-R P.372 — Radio noise (atmospheric noise figure curves).
- Davies, K. — Ionospheric Radio, IEE Electromagnetic Waves Series.
- Maral, G. & Bousquet, M. — Satellite Communications Systems (for link-budget methodology).
- ARRL — Antenna Book and Radio Amateur's Handbook (HF antenna practice).
- MIL-STD-188-141B (ALE), MIL-STD-188-110 (HF modems), STANAG 5066.
- Voluntary outage/online tools: VOACAP (voice of America coverage analysis program).
Prepared for ECE 523E — Antenna & Radio Wave Propagation, Department of Electrical & Communication Engineering, Masinde Muliro University of Science and Technology.