Ground-Wave and Terrestrial PropagationIntroduction and ContextRadio communication does not occur in free space alone. In practical terrestrial systems, the transmitting antenna, receiving antenna, and the intervening medium are strongly influenced by the Earth’s surface, terrain, vegetation, buildings, atmospheric conditions, and the electrical properties of soil and water. These influences determine whether a signal reaches a receiver by following the Earth’s surface, by direct visibility, by diffraction around obstacles, or by reflection and scattering from terrain and atmospheric layers. Ground-wave propagation is especially important at low and medium frequencies, where the wavelength is sufficiently large for the wave to couple to the Earth and bend around its curvature. Terrestrial propagation is a broader engineering concept that includes ground-wave propagation, line-of-sight propagation, diffraction, reflection, scattering, and the effects of the lower atmosphere. It is fundamental to the design of broadcasting, maritime communication, navigation, land-mobile radio, radar, wireless sensor networks, and emergency communication systems. At postgraduate level, the subject should not be treated as a collection of empirical range charts. Propagation is a boundary-value problem involving Maxwell’s equations, the electrical characteristics of the ground, antenna geometry, frequency, polarization, atmospheric refractivity, and environmental variability. A useful design therefore combines analytical models with measurement, numerical prediction, and statistical margins. Learning ObjectivesAfter studying this chapter, the reader should be able to: - Distinguish ground-wave, surface-wave, space-wave, diffraction, reflection, and tropospheric-scatter propagation.
- Explain how ground conductivity, permittivity, frequency, polarization, and antenna height affect propagation.
- Apply the Sommerfeld–Norton concept and engineering approximations to estimate field strength.
- Calculate radio-horizon distances and interpret Fresnel-zone clearance.
- Analyse diffraction and two-ray interference in terrestrial links.
- Select suitable propagation mechanisms for broadcasting, mobile, maritime, and microwave systems.
- Evaluate uncertainty, fading, interference, and regulatory constraints in practical link design.
1. Propagation Mechanisms in the Terrestrial EnvironmentA radio signal may arrive at a receiver through several paths. The dominant mechanism depends mainly on frequency, distance, antenna heights, terrain, atmospheric conditions, and surface properties. 1.1 Ground wave and surface waveA ground wave is a wave whose field remains influenced by the Earth’s surface and can reach beyond the geometric horizon. The term is often used broadly for the combination of a space-wave component and a surface-wave component. Strictly, a surface wave is bound to the interface and experiences attenuation because real ground is lossy. At low frequencies, the wave induces currents in the ground. These currents dissipate energy as heat, causing attenuation. The wave also bends gradually around the Earth because the field is constrained by the conducting surface. This mechanism supports long-range medium-wave broadcasting and very-long-range low-frequency communication. 1.2 Space wave and line-of-sight propagationAt VHF and higher frequencies, terrestrial links are commonly dominated by the direct ray and reflected rays. The direct ray is possible when the antennas have a sufficiently unobstructed path. Earth curvature limits the geometrical range, although atmospheric refraction often extends it beyond the optical horizon. 1.3 DiffractionDiffraction is the redistribution of electromagnetic energy when a wave encounters an edge or obstacle. It permits reception in a shadow region, but with a field reduction that depends on obstacle height relative to the direct path, wavelength, and geometry. Knife-edge diffraction is a useful first-order model; real terrain requires multiple-edge or terrain-profile methods. 1.4 Reflection and scatteringReflection from the ground, water, buildings, or mountains creates multiple paths. Their phase differences may produce constructive or destructive interference. Rough surfaces scatter energy in many directions, while smooth surfaces produce more specular reflection. Foliage and urban structures create absorption, diffraction, and diffuse scattering simultaneously. 1.5 Tropospheric propagationThe troposphere is electrically nonuniform. Variations in temperature, pressure, and humidity produce changes in refractive index. Under normal conditions, radio rays bend slightly toward the Earth. Temperature inversions can produce ducting, in which energy is trapped between atmospheric layers or between a layer and the surface. Ducting may extend range but can also create unexpected interference. 2. Electromagnetic Basis of Ground-Wave PropagationThe ground is characterised, to first order, by conductivity σ and relative permittivity εᵣ. Conductivity σ is measured in siemens per metre (S/m), while permittivity is ε = ε₀εᵣ, where ε₀ is the permittivity of free space. The intrinsic impedance of a homogeneous conducting medium is η = √[jωμ /(σ + jωε)] where η is intrinsic impedance in ohms, ω = 2πf is angular frequency in rad/s, μ is permeability in H/m, σ is conductivity in S/m, and ε is permittivity in F/m. The expression assumes a linear, isotropic, homogeneous medium and sinusoidal steady state. The propagation constant is γ = α + jβ = √[(jωμ)(σ + jωε)] where α is attenuation constant in Np/m and β is phase constant in rad/m. For a good conductor, σ ≫ ωε, and the approximations become α ≈ β ≈ √(ωμσ/2) The skin depth is δ = 1/α ≈ √[2/(ωμσ)] A good-conductor approximation is not automatically valid for ordinary soil at every frequency. The ratio σ/(ωε) must be examined. Dry ground, wet ground, sea water, and ice can differ by orders of magnitude in conductivity and permittivity. The wave impedance of a plane wave in free space is approximately 377 Ω. At a lossy ground boundary, the reflection coefficient and the tangential electric and magnetic fields depend on the complex impedance of the ground. Consequently, a simple perfect-conductor reflection model may be seriously inaccurate for low-frequency surface-wave prediction or for grazing-incidence terrestrial links. 3. Sommerfeld and Norton DescriptionsThe rigorous solution for a vertical electric dipole above a planar conducting half-space was developed through Sommerfeld’s theory. It separates the received field conceptually into a direct or space-wave contribution, a reflected contribution, and a surface-wave contribution. The exact integral solution is mathematically demanding because it contains complex wave-number integrals and branch-point contributions. For engineering work, the Norton surface-wave formulation is widely used. It expresses the ground-wave field as a free-space field multiplied by a complex attenuation or surface-wave factor. A representative form is Eg(d) = E0(d) A(p, q) where E_g is the ground-wave field, E₀(d) is the corresponding reference field, and A(p,q) is a dimensionless attenuation factor. The parameters p and q are dimensionless combinations of frequency, distance, antenna height, and the complex electrical properties of the ground. Their exact definitions depend on the selected Norton or numerical formulation. This formulation is important because it prevents a common error: applying inverse-distance free-space spreading alone to a surface wave. The ground-wave field is influenced by both geometric spreading and ohmic loss. At sufficiently large distance, the additional ground attenuation can dominate. A practical low-frequency field-strength model is often written in decibels as E(dBμV/m) = Eref(dBμV/m) − Ag(dB) where E_ref is a reference field, often based on a specified transmitter power and antenna system, and A_g is ground attenuation obtained from validated curves, software, or a propagation recommendation. The model is valid only when the reference definition and ground parameters are consistent. PolarizationVertical polarization is normally preferred for ground-wave service. For a vertically polarized wave, the electric field has a component normal to the ground and the boundary conditions permit useful surface-wave coupling. A horizontally polarized wave generally suffers stronger attenuation near a conducting surface, particularly at low elevation angles. This is why long-wave and medium-wave broadcasting commonly use vertical monopoles or electrically short vertical radiators with effective ground systems. Ground electrical propertiesTypical qualitative trends are as follows: | Surface | Conductivity | Ground-wave performance |
|---|
| Sea water | Very high | Lowest attenuation; long range | | Wet, flat soil | Moderate to high | Good propagation | | Moist farmland | Moderate | Usually favourable | | Dry sandy soil | Low | Greater attenuation | | Rock or urban concrete | Low or irregular | Often poor and variable | | Frozen or snow-covered ground | Variable, often low | Seasonal degradation possible |
Conductivity generally has a stronger influence on low-frequency ground-wave attenuation than relative permittivity, although both enter the boundary problem. Surface roughness, slope, layered soil, and finite ground planes can make the homogeneous half-space approximation inadequate. 4. Frequency Dependence and Practical Service RegionsAs frequency increases, the wavelength decreases and the relative importance of the surface-wave mechanism changes. At very low frequencies, ground-wave propagation can cover large distances, while ionospheric propagation may also become important. In the MF broadcasting band, the daytime service area is often determined by ground-wave attenuation, whereas nighttime sky-wave signals can return from the ionosphere and create interference and fading. At HF, ground waves normally provide only local coverage compared with ionospheric sky waves. At VHF and UHF, ground-wave terminology is less useful for most links; direct, reflected, diffracted, and scattered space-wave components dominate. At microwave frequencies, surface roughness and atmospheric effects become increasingly significant. Frequency alone does not determine range. A low-frequency transmitter with an inefficient antenna and poor ground system may perform worse locally than a higher-frequency system with favourable antenna gain and terrain. The complete link budget must include transmitted power, antenna gain, feeder loss, polarization mismatch, propagation loss, receiver sensitivity, and required reliability. 5. Terrestrial Line-of-Sight GeometryFor two antennas of heights h₁ and h₂ above a smooth spherical Earth of radius Rₑ, the approximate radio-horizon distance is dh ≈ √(2kRₑh₁) + √(2kRₑh₂) where d_h is in the same distance unit as Rₑ and h₁, h₂, kRₑ is the effective Earth radius, and k is the effective-Earth-radius factor. Under standard atmospheric refractivity, k is often approximated as 4/3. Without atmospheric correction, k = 1. Using Rₑ ≈ 6.371 × 10⁶ m and heights in metres, the geometric horizon for one antenna is approximately d ≈ 3.57√h where d is in kilometres and h is in metres. With the 4/3 effective-Earth approximation, d ≈ 4.12√h in kilometres. These formulas assume a smooth spherical Earth, unobstructed terrain, and a representative atmosphere. They do not guarantee an adequate received signal because diffraction, Fresnel clearance, multipath, and system link budget remain relevant. Worked Example 1: Radio horizonTwo antennas are mounted at 25 m and 100 m above local terrain. Estimate the standard-atmosphere radio horizon. Using k = 4/3, dh = 4.12(√25 + √100) = 4.12(5 + 10) = 61.8 km Thus the approximate radio horizon is 61.8 km. A practical service range may be smaller because of clutter, terrain blockage, rainfall at higher frequencies, multipath fading, and receiver requirements. 6. Fresnel-Zone ClearanceA direct line of sight is not sufficient for a reliable terrestrial link. The first Fresnel zone is an ellipsoidal region around the direct path in which obstructions can cause significant phase cancellation. At a point whose distances from the two antennas are d₁ and d₂, with total path length d = d₁ + d₂, the radius of the nth Fresnel zone is rn = √[nλd₁d₂/d] where r_n is in metres when λ, d₁, d₂, and d use metres, and n is a positive integer. The first-zone radius is obtained by setting n = 1. A common engineering objective is to clear at least 60% of the first Fresnel-zone radius, although the required clearance depends on terrain, frequency, link margin, and the nature of the obstacle. Worked Example 2: First Fresnel-zone radiusA 6 GHz link has a path length of 20 km, with an obstruction at the midpoint. The wavelength is λ = c/f = (3 × 10⁸)/(6 × 10⁹) = 0.05 m At the midpoint d₁ = d₂ = 10,000 m. Therefore, r₁ = √[0.05 × 10,000 × 10,000 / 20,000] = √25 = 5 m A 60% clearance criterion requires approximately 3 m of clearance from the direct path at the obstruction. This is a geometric screening value, not a complete propagation guarantee. 7. Reflection and the Two-Ray ModelFor a flat ground plane, the received field may be approximated as the sum of a direct ray and a ground-reflected ray. The complex received field is Etotal = Edirect + ΓEreflected e^(−jΔφ) where Γ is the complex ground reflection coefficient and Δφ is the phase difference caused by path-length difference and reflection phase. The received power is proportional to |E_total|², not to the sum of the individual powers. This distinction explains deep fading in terrestrial links. For sufficiently large separation and antenna heights, the idealised two-ray power relation is often approximated by Pr ≈ Pt Gt Gr (ht hr/d²)² where P_t is transmitted power, G_t and G_r are antenna gains in the relevant directions, h_t and h_r are antenna heights, and d is separation. This asymptotic form assumes a flat, smooth, conducting ground, far-field operation, dominant direct and reflected rays, and appropriate polarization. It must not be used close to the transmitter, near a terrain obstruction, or where diffuse scattering dominates. The transition from free-space-like behaviour to the two-ray asymptotic region can be estimated by the break distance db ≈ 4hthr/λ where d_b and heights use the same units and λ is wavelength. This is an order-of-magnitude criterion rather than a universal boundary. 8. Diffraction Over ObstaclesFor a single knife edge, the diffraction parameter is ν = h√[2(d₁ + d₂)/(λd₁d₂)] where h is the obstacle height above the straight line joining the antennas; h is positive when the obstacle penetrates the direct path. The distances d₁ and d₂ are measured from the obstacle to the transmitting and receiving antennas. The knife-edge diffraction loss is commonly evaluated using a Fresnel integral. A widely used engineering approximation, valid over the usual practical range, is Ld ≈ 6.9 + 20log₁₀[√((ν − 0.1)² + 1) + ν − 0.1] dB for ν > −0.7. For sufficiently negative ν, the loss approaches zero in this approximation. The formula assumes a sharp, isolated edge and does not model rounded hills, forests, buildings, or multiple obstacles accurately. For multiple terrain edges, methods such as Deygout, Epstein–Peterson, Bullington, and numerical terrain diffraction models may be used. Their predictions can differ significantly when secondary edges are close together or when terrain is smooth rather than sharply segmented. A high-quality design should compare model predictions with measured or statistically calibrated data. 9. Atmospheric Refraction and Terrestrial AnomaliesThe radio refractive index is expressed as n = c/v, where c is the speed of light in vacuum and v is phase velocity in the medium. Since n is close to unity, radio engineers often use refractivity N = (n − 1) × 10⁶ A commonly used approximation for standard atmospheric refractivity is N ≈ 77.6(P/T) + 3.73 × 10⁵(e/T²) where P is total pressure in hPa, e is water-vapour partial pressure in hPa, and T is absolute temperature in kelvins. The formula is empirical and intended for ordinary atmospheric conditions in radio propagation studies. A decrease of refractivity with height causes normal downward bending. The effective-Earth-radius method incorporates this average bending by replacing Rₑ with kRₑ. Standard k ≈ 4/3 is useful for preliminary planning, but actual k varies with weather and location. Important anomalous modes include: - Super-refraction: stronger-than-normal downward bending, increasing apparent range.
- Ducting: trapping of energy in a layer, potentially producing very long range and strong interference.
- Sub-refraction: reduced downward bending, shortening the radio horizon and increasing blockage.
- Troposcatter: forward scattering from irregularities in the troposphere, enabling beyond-horizon links with high antenna gains and substantial link margins.
10. Link-Budget and Reliability AnalysisA terrestrial link budget begins with the received power Pr(dBm) = Pt(dBm) + Gt(dBi) + Gr(dBi) − Lp(dB) − Ls(dB) − Lm(dB) where L_p is propagation loss, L_s represents feeder, connector, and implementation losses, and L_m represents additional margins or losses. If gains and losses are specified in dB, all terms are dimensionally consistent in logarithmic power units. For free space, Lfs = 20log₁₀(4πd/λ) dB where d and λ use the same units. This equation is derived from spherical spreading and assumes far-field propagation in unobstructed free space. It is not a ground-wave attenuation model. The link margin is M = Pr − Pmin where P_min is the minimum receiver input power required for the specified modulation, coding, bandwidth, and target error performance. A positive nominal margin does not guarantee reliability because shadowing, multipath fading, rain, ducting, and equipment variation are random or time-varying. For a specified availability, the designer may add a fade margin based on measured distributions or a validated statistical model. In mobile and urban systems, median path loss and shadowing standard deviation are often used. In fixed microwave systems, rain attenuation, multipath outage, and terrain clearance are evaluated with regional propagation recommendations. 11. Practical ApplicationsBroadcastingLF and MF broadcasting use vertically polarised antennas and carefully designed ground systems. Radials, buried conductors, soil moisture, and transmitter grounding influence efficiency and service area. Daytime ground-wave coverage may be estimated using conductivity-dependent curves. Nighttime sky-wave interference requires frequency planning and field-strength protection. Maritime and coastal communicationSea water has high conductivity, so surface-wave propagation over the sea can be much better than over dry land. However, coastal paths may cross several surface types. A prediction should therefore segment the path and account for transitions between sea, wet soil, and dry land. Land-mobile and public-safety networksVHF and UHF systems use elevated base stations, strategically placed repeaters, and terrain-aware planning. Ground-wave effects near the surface combine with diffraction, building penetration, vehicle blockage, and fast multipath fading. Diversity, adaptive modulation, coding, and carefully selected antenna heights improve reliability. Microwave terrestrial backhaulMicrowave links require Fresnel-zone clearance, high-gain antennas, accurate alignment, rain and multipath analysis, and regulatory coordination. The path profile should include terrain, vegetation growth, buildings, and the effective Earth radius. A nominal line of sight without adequate clearance is not a robust design. Navigation and emergency systemsPropagation anomalies can produce misleading signal levels and coverage holes. Safety-critical systems should use conservative propagation margins, monitoring, redundancy, and procedures for degraded conditions rather than relying solely on a deterministic prediction. 12. Illustrative Case Study: Coastal Emergency Communication LinkBackgroundConsider an illustrative 150 MHz emergency network connecting a coastal command centre to mobile response units. The proposed base station is 30 m above ground, and vehicles operate over a route that alternately crosses sea-facing terrain, wet farmland, and a compact urban area. ProblemA free-space calculation predicts satisfactory coverage, but field trials show intermittent dead zones near a low ridge and strong signal fluctuations in the urban section. During humid coastal weather, coverage occasionally extends farther than expected, while at other times the service boundary contracts. AnalysisAt 150 MHz, the wavelength is approximately 2 m. The system is not primarily a long-distance MF surface-wave service; direct, reflected, diffracted, and scattered components are more relevant. The ridge penetrates the first Fresnel zone, so diffraction loss is expected. The coastal section offers a relatively conductive surface and may support stronger low-angle propagation than the dry upland section. In the urban area, building reflections create multipath, producing rapid phase changes as vehicles move. Weather-dependent extension is consistent with changes in tropospheric refractivity. A single k = 4/3 prediction cannot represent all conditions. The route also contains different clutter classes, so a homogeneous-ground model is inappropriate. Approach and solutionThe engineering team: - Generated a terrain profile and evaluated Fresnel clearance along the route.
- Used a terrain-diffraction model for the ridge.
- Divided the path into sea, farmland, and urban segments.
- Performed drive testing under dry, humid, and wet conditions.
- Added a fade margin based on the lower percentile of measured received power.
- Improved base-station antenna height and installed a relay near the ridge.
- Used antenna diversity and coding in mobile terminals.
- Established monitoring thresholds and a backup communication channel.
OutcomeThe relay removed the deterministic ridge shadow, while diversity reduced urban outage caused by multipath. The final design accepted occasional anomalous propagation rather than treating it as guaranteed coverage. Coverage maps were reported with confidence levels and environmental assumptions. Learning pointsThe case demonstrates that terrestrial propagation is path-specific and statistical. Free-space loss alone is inadequate; terrain, surface transitions, Fresnel clearance, multipath, atmospheric variability, and system reliability targets must be evaluated together. 13. Limitations, Governance, and Best PracticePropagation models are approximations. Their uncertainty arises from inaccurate terrain databases, unknown soil parameters, vegetation changes, atmospheric variability, antenna pattern errors, installation differences, and receiver implementation effects. Predictions should therefore report assumptions, frequency, polarization, antenna heights, ground model, clutter data, confidence level, and expected uncertainty. Regulatory agencies allocate frequency bands, limit radiated power, specify antenna characteristics, and protect neighbouring services. Ground-wave broadcasting additionally involves field-strength contours and interference constraints. Engineers must comply with national regulations, electromagnetic-exposure requirements, aviation and maritime rules, and site permissions. Best practice includes: - use the simplest model that captures the dominant mechanism;
- verify whether the ground is electrically homogeneous;
- inspect terrain and Fresnel clearance, not merely optical visibility;
- model polarization and antenna radiation patterns correctly;
- separate median coverage from fade and outage probability;
- calibrate models with representative measurements;
- document weather, season, and surface conditions;
- use conservative margins for safety-critical services;
- avoid presenting a single coverage contour as a certainty;
- repeat measurements after construction, vegetation growth, or major environmental change.
Artificial intelligence can assist with terrain classification, path-loss calibration, anomaly detection, and prediction from large measurement databases. However, machine-learning outputs remain dependent on training data and may fail under unseen weather, terrain, or deployment conditions. Physics-based constraints, uncertainty estimates, validation data, and human engineering review remain essential. Chapter SummaryGround-wave propagation is the interaction of electromagnetic fields with the Earth’s lossy surface. Its behaviour depends on frequency, conductivity, permittivity, polarization, antenna configuration, and distance. Sommerfeld theory provides the rigorous foundation, while Norton-type surface-wave factors and engineering curves make prediction practical. Terrestrial propagation also includes line-of-sight transmission, reflection, two-ray interference, diffraction, scattering, tropospheric refraction, ducting, and troposcatter. Radio-horizon equations provide first-order geometric limits, while Fresnel-zone analysis determines whether an apparently visible path is sufficiently clear. Ground reflection can produce constructive or destructive interference, and knife-edge models provide a useful but limited estimate of obstacle loss. Practical link design requires a complete budget, realistic antenna and terrain data, propagation margins, statistical reliability analysis, measurement validation, and regulatory compliance. No single model is universally reliable; the correct model is selected according to the dominant physical mechanism and the required engineering confidence. Key TermsGround wave: A radio wave whose propagation remains significantly influenced by the Earth’s surface. Surface wave: A wave bound to and travelling along a material interface, with attenuation caused by loss. Space wave: A direct or reflected wave travelling primarily through the atmosphere. Ground conductivity: The ability of soil or water to conduct electric current, measured in S/m. Relative permittivity: Material permittivity divided by free-space permittivity. Sommerfeld theory: Rigorous electromagnetic treatment of a dipole above a conducting half-space. Norton attenuation factor: A factor representing additional ground-wave attenuation relative to a reference field. Polarization: Orientation of the electric-field vector of a radio wave. Radio horizon: Maximum geometrical range for a line-of-sight path over a spherical Earth under a specified atmospheric model. Effective Earth radius: Earth radius modified to represent average atmospheric refraction. Fresnel zone: Ellipsoidal region around a propagation path where phase differences affect interference. Diffraction: Bending and spreading of waves around edges or obstacles. Knife-edge model: First-order diffraction model for a sharp isolated obstacle. Two-ray model: Model combining direct and ground-reflected propagation paths. Multipath: Reception of multiple copies of a signal through different paths. Troposcatter: Beyond-horizon propagation produced by forward scattering in the troposphere. Ducting: Trapping of radio energy in an atmospheric layer or surface-atmosphere channel. Fade margin: Additional received-power margin allocated to overcome signal variability. Path loss: Reduction in signal power between transmitting and receiving antennas due to propagation and related effects. Refractivity: A scaled measure of atmospheric refractive index used in radio propagation analysis. Review QuestionsShort Answer Questions- Why is vertical polarization generally preferred for low-frequency ground-wave transmission?
- Define the effective Earth-radius factor k and explain its significance.
- What physical effects are represented by the first Fresnel zone?
- State two limitations of the knife-edge diffraction model.
- Distinguish between troposcatter and tropospheric ducting.
Long Answer Questions- Explain the electromagnetic basis of ground-wave propagation and discuss the roles of soil conductivity, permittivity, frequency, and polarization.
- Describe the Sommerfeld–Norton approach and explain why a free-space model is insufficient for surface-wave prediction.
- Derive and interpret the radio-horizon relation for two antennas over an effective spherical Earth.
- Explain the two-ray model, including reflection coefficient, phase difference, interference, and its asymptotic power relation.
- Discuss a complete engineering methodology for designing a reliable terrestrial microwave link.
Analytical / Application Questions- A 900 MHz link has antennas of heights 20 m and 45 m. Estimate its standard-atmosphere radio horizon using the 4/3 Earth-radius approximation. Discuss why the actual reliable range may be smaller.
- A 3 GHz path has total length 12 km and an obstruction at the midpoint. Calculate the first Fresnel-zone radius and state the approximate 60% clearance requirement.
- Compare two proposed emergency-network routes: one over conductive sea water with a clear path, and one over dry irregular terrain with a ridge penetrating the Fresnel zone. Recommend suitable propagation models, measurements, and reliability margins for each route.
Multiple Choice Questions with AnswersQuestion 1Which ground property most directly reduces low-frequency surface-wave attenuation? A. Higher ground conductivity B. Lower antenna height C. Greater polarization mismatch D. Higher connector loss Correct Answer: A. Higher ground conductivity Question 2For standard atmospheric planning, the commonly used effective-Earth-radius factor is approximately: A. 1/3 B. 1 C. 4/3 D. 3 Correct Answer: C. 4/3 Question 3The first Fresnel-zone radius at a path point is proportional to: A. The square root of wavelength and distance-product ratio B. The inverse square of wavelength C. Only the transmitter power D. Only the antenna gain Correct Answer: A. The square root of wavelength and distance-product ratio Question 4In the two-ray model, received power is determined by: A. Only the direct-ray power B. The sum of field amplitudes including phase C. Only the reflected-ray power D. The arithmetic mean of antenna heights Correct Answer: B. The sum of field amplitudes including phase Question 5A positive knife-edge diffraction parameter ν normally indicates that the obstacle: A. Is below the direct path B. Penetrates above the direct path C. Has zero electrical conductivity D. Is located at the transmitter Correct Answer: B. Penetrates above the direct path Question 6For a 6 GHz signal, the approximate free-space wavelength is: A. 0.005 m B. 0.05 m C. 0.5 m D. 5 m Correct Answer: B. 0.05 m Question 7Which propagation phenomenon can trap radio energy in an atmospheric layer? A. Normal reflection B. Ducting C. Polarization rotation only D. Free-space spreading Correct Answer: B. Ducting Question 8The free-space path-loss formula assumes: A. A homogeneous lossy ground half-space B. Far-field unobstructed propagation C. A knife-edge obstacle D. Tropospheric ducting Correct Answer: B. Far-field unobstructed propagation Question 9Why can a terrestrial receiver experience a deep fade even when the direct path is unobstructed? A. Multiple paths can combine destructively B. The wavelength becomes zero C. Ground conductivity becomes infinite D. The receiver stops obeying Maxwell’s equations Correct Answer: A. Multiple paths can combine destructively Question 10Which system most strongly benefits from a conductive sea surface for ground-wave propagation? A. Long-wave or medium-wave coastal broadcasting B. A short indoor infrared link C. A fibre-optic cable D. A vacuum microwave bench Correct Answer: A. Long-wave or medium-wave coastal broadcasting
|