Wave propagation is key to understanding signal transmission in EMC studies. It impacts how electromagnetic energy travels through space and interacts with objects, affecting interference and compatibility between devices.

Engineers use wave propagation principles to design systems that minimize interference. This topic covers different types of waves, their characteristics, propagation mechanisms, and models used to predict signal behavior in various environments.

Fundamentals of wave propagation

• Electromagnetic wave propagation forms the foundation for understanding signal transmission in Electromagnetic Interference and Compatibility studies
• Comprehending wave propagation principles enables engineers to design systems that minimize interference and maximize compatibility between electronic devices
• Wave propagation concepts directly impact the analysis of electromagnetic emissions, susceptibility, and shielding effectiveness in EMC applications

Types of electromagnetic waves

• Radio waves span frequencies from 3 kHz to 300 GHz, used in communication systems and radar
• Microwaves range from 300 MHz to 300 GHz, utilized in satellite communications and microwave ovens
• Infrared waves occupy 300 GHz to 430 THz, found in thermal imaging and remote controls
• Visible light covers 430 THz to 750 THz, essential for human vision and optical communications
• Ultraviolet radiation extends from 750 THz to 30 PHz, applied in sterilization and photolithography
  • UV-A (315-400 nm) used in black lights and phototherapy
  • UV-B (280-315 nm) responsible for vitamin D synthesis in skin
  • UV-C (100-280 nm) employed in germicidal lamps

Wave characteristics

• Amplitude measures the maximum displacement of a wave from its equilibrium position
• Phase describes the position of a wave relative to a reference point, measured in degrees or radians
• Polarization indicates the orientation of the electric field vector in electromagnetic waves
  • Linear polarization occurs when the electric field oscillates in a single plane
  • Circular polarization results from two perpendicular linear waves 90° out of phase
  • Elliptical polarization arises from unequal amplitudes or phase differences other than 90°
• Wavefront represents the surface of constant phase in a propagating wave
  • Plane waves have flat wavefronts, common in far-field regions
  • Spherical waves exhibit curved wavefronts, typical near point sources

Frequency vs wavelength

• Frequency denotes the number of wave cycles passing a fixed point per second, measured in Hertz (Hz)
• Wavelength represents the distance between two consecutive wave crests or troughs
• Inverse relationship between frequency and wavelength expressed by the equation $\lambda = \frac{c}{f}$
  • $\lambda$ wavelength in meters
  • $c$ speed of light in vacuum (approximately 3 x 10^8 m/s)
  • $f$ frequency in Hertz
• Higher frequencies correspond to shorter wavelengths, impacting propagation characteristics
  • Microwaves (high frequency) exhibit more line-of-sight behavior
  • AM radio waves (low frequency) can follow the Earth's curvature

Propagation mechanisms

• Understanding propagation mechanisms aids in predicting signal coverage and potential interference sources in EMC studies
• Different propagation mechanisms dominate at various frequencies, influencing the design of EMC mitigation strategies
• Propagation mechanisms play a crucial role in determining the effective range and reliability of wireless communication systems

Free space propagation

• Occurs in an ideal, unobstructed environment without atmospheric effects or reflections
• Signal strength decreases with the square of the distance according to the inverse square law
• Friis transmission equation models free space path loss $P_r = P_t G_t G_r (\frac{\lambda}{4\pi R})^2$
  • $P_r$ received power
  • $P_t$ transmitted power
  • $G_t$ transmitting antenna gain
  • $G_r$ receiving antenna gain
  • $\lambda$ wavelength
  • $R$ distance between antennas
• Applicable to satellite communications and line-of-sight microwave links

Ground wave propagation

• Electromagnetic waves travel along the Earth's surface, following its curvature
• Predominant mode for low-frequency signals (below 2 MHz)
• Attenuation increases with frequency and distance due to ground absorption
• Vertically polarized waves propagate more efficiently than horizontally polarized waves
• Used in AM radio broadcasting and maritime communication systems
  • Allows communication beyond the horizon for coastal areas

Sky wave propagation

• Involves reflection and refraction of radio waves by the ionosphere
• Enables long-distance communication in the HF band (3-30 MHz)
• Exhibits time-of-day and seasonal variations due to changes in ionospheric conditions
• Multiple hops between the Earth and ionosphere can extend communication range
• Affected by solar activity and geomagnetic disturbances
  • Solar flares can cause sudden ionospheric disturbances, disrupting HF communications

Line-of-sight propagation

• Direct path between transmitter and receiver without obstructions
• Dominant mode for VHF, UHF, and microwave frequencies
• Limited by Earth's curvature and terrain features
• Fresnel zones concept crucial for determining clearance requirements
  • First Fresnel zone radius $r = \sqrt{\frac{\lambda d_1 d_2}{d_1 + d_2}}$
  • $r$ radius of the first Fresnel zone
  • $\lambda$ wavelength
  • $d_1$ and $d_2$ distances from obstruction to transmitter and receiver
• Used in terrestrial microwave links and satellite communications

Propagation models

• Propagation models serve as essential tools for predicting signal behavior in EMC analysis and system design
• These models help engineers estimate potential interference levels and coverage areas for wireless systems
• Accurate propagation modeling contributes to optimizing antenna placement and power levels in EMC-compliant designs

Free space path loss

• Describes signal attenuation in an ideal, obstruction-free environment
• Path loss increases with frequency and distance
• Free space path loss equation $FSPL = 20 \log_{10}(d) + 20 \log_{10}(f) + 32.44$
  • $FSPL$ free space path loss in dB
  • $d$ distance in kilometers
  • $f$ frequency in MHz
• Serves as a baseline for more complex propagation models
• Applicable in satellite communications and short-range, line-of-sight links

Two-ray ground reflection

• Accounts for both direct and ground-reflected paths between transmitter and receiver
• Applicable in scenarios with a strong ground reflection (flat terrain)
• Path loss equation $PL = 40 \log_{10}(d) - 20 \log_{10}(h_t h_r)$
  • $PL$ path loss in dB
  • $d$ distance between transmitter and receiver
  • $h_t$ transmitter antenna height
  • $h_r$ receiver antenna height
• Predicts faster signal decay (fourth power of distance) compared to free space model
• Used in cellular network planning and mobile radio systems

Log-distance path loss

• Empirical model that accounts for signal attenuation in various environments
• Path loss equation $PL(d) = PL(d_0) + 10n \log_{10}(\frac{d}{d_0})$
  • $PL(d)$ path loss at distance d
  • $PL(d_0)$ path loss at reference distance d_0
  • $n$ path loss exponent (varies with environment)
  • $d$ distance between transmitter and receiver
• Path loss exponent n depends on the propagation environment
  • n = 2 for free space
  • n = 3-5 for urban areas
  • n = 1.6-1.8 for indoor line-of-sight
• Widely used in wireless network planning and interference analysis

Atmospheric effects

• Atmospheric effects significantly impact wave propagation in EMC studies, particularly for outdoor and long-range systems
• Understanding these effects helps engineers design more robust and interference-resistant communication systems
• Atmospheric phenomena can both enhance and degrade signal propagation, influencing EMC performance

Refraction and ducting

• Refraction occurs when electromagnetic waves change direction due to variations in atmospheric refractive index
• Atmospheric ducting traps radio waves within a layer of the atmosphere, enabling extended propagation
• Types of atmospheric ducts
  • Surface ducts form near the Earth's surface, common in coastal areas
  • Elevated ducts occur at higher altitudes, often associated with temperature inversions
• Ducting can cause interference between widely separated systems operating on the same frequency
• Refractive index variations modeled using the modified refractivity $M = N + 0.157h$
  • $N$ refractivity
  • $h$ height above sea level in meters

Absorption and scattering

• Atmospheric gases and particles absorb and scatter electromagnetic waves, causing signal attenuation
• Absorption peaks occur at specific frequencies due to molecular resonances
  • Water vapor absorption peak at 22.2 GHz
  • Oxygen absorption peak at 60 GHz
• Rayleigh scattering affects waves with wavelengths much larger than particle size
  • Proportional to $\frac{1}{\lambda^4}$, more significant at higher frequencies
• Mie scattering occurs when wavelengths are comparable to particle size
  • Affects microwave and millimeter-wave propagation in rain and fog
• Rain attenuation modeled using specific attenuation $\gamma_R = kR^\alpha$
  • $\gamma_R$ specific attenuation in dB/km
  • $R$ rainfall rate in mm/h
  • $k$ and $\alpha$ frequency-dependent coefficients

Multipath fading

• Results from constructive and destructive interference of signals arriving via multiple paths
• Types of multipath fading
  • Flat fading affects all frequencies in the signal bandwidth equally
  • Frequency-selective fading distorts different frequency components differently
• Characterized by statistical distributions
  • Rayleigh fading for non-line-of-sight scenarios
  • Rician fading when a dominant line-of-sight path exists
• Causes signal strength variations and intersymbol interference in digital communications
• Mitigation techniques
  • Diversity reception (spatial, frequency, or polarization diversity)
  • Adaptive equalization to compensate for channel distortions

Ionospheric propagation

• Ionospheric propagation plays a crucial role in long-distance HF communications and impacts EMC considerations for systems operating in this frequency range
• Understanding ionospheric effects aids in predicting potential interference sources and designing EMC-compliant systems for HF applications
• Ionospheric propagation characteristics vary with time of day, season, and solar activity, requiring adaptive EMC strategies

Structure of ionosphere

• Ionosphere consists of multiple layers of ionized gas in the upper atmosphere
• D layer (60-90 km) forms during daylight hours, absorbs low-frequency signals
• E layer (90-150 km) reflects signals in the 3-5 MHz range
• F1 layer (150-220 km) merges with F2 layer at night
• F2 layer (220-800 km) primary layer for long-distance HF propagation
  • Highest electron density, reflects frequencies up to 30 MHz
• Electron density varies with altitude, time of day, and solar activity
  • Maximum electron density occurs in the F2 layer
  • Density profiles modeled using Chapman function

Critical frequency

• Highest frequency that can be reflected by an ionospheric layer at vertical incidence
• Determined by the maximum electron density in the layer
• Critical frequency equation $f_c = 9 \sqrt{N_m}$
  • $f_c$ critical frequency in MHz
  • $N_m$ maximum electron density in electrons per cubic meter
• Varies with time of day, season, and solar activity
  • Typically higher during daytime and solar maximum periods
• Crucial for determining usable frequency range for ionospheric communication

Maximum usable frequency

• Highest frequency that can be used for communication between two points via ionospheric reflection
• Related to critical frequency by the secant law $MUF = \frac{f_c}{\cos \theta}$
  • $MUF$ maximum usable frequency
  • $f_c$ critical frequency
  • $\theta$ angle of incidence at the ionosphere
• Depends on distance between transmitter and receiver
  • Longer paths allow higher MUF due to larger angles of incidence
• Varies with time of day, season, and solar activity
  • Typically peaks in the afternoon and during equinoxes
• Used in frequency selection for HF communication systems to optimize propagation

Tropospheric propagation

• Tropospheric propagation mechanisms significantly impact EMC in the VHF, UHF, and microwave frequency ranges
• Understanding these effects helps engineers design more reliable communication systems and predict potential interference sources
• Tropospheric propagation can extend the range of signals beyond the horizon, affecting EMC considerations for widely separated systems

Tropospheric scatter

• Involves scattering of radio waves by irregularities in the troposphere
• Enables communication beyond the horizon for frequencies above 300 MHz
• Signal strength decreases rapidly with distance, following an inverse power law
• Path loss equation $L = 30 \log f + 30 \log d + F(θ) - G_t - G_r + 190$
  • $L$ path loss in dB
  • $f$ frequency in MHz
  • $d$ path length in km
  • $F(θ)$ angular distance function
  • $G_t$ and $G_r$ transmit and receive antenna gains
• Used in long-distance communication systems (300-1000 km)
  • Military communication networks
  • Backup links for submarine cable systems

Tropospheric ducting

• Occurs when a layer of warm air traps radio waves, creating a waveguide effect
• Enables long-distance propagation of VHF and UHF signals
• Types of tropospheric ducts
  • Surface-based ducts form near the ground, common in coastal areas
  • Elevated ducts occur at higher altitudes, often associated with temperature inversions
• Duct strength characterized by modified refractivity gradient
  • Strong ducts form when $\frac{dM}{dh} < -157$ M-units/km
• Can cause interference between widely separated systems operating on the same frequency
• Ducting events predicted using meteorological data and refractivity models
  • Parabolic equation method used for accurate duct propagation modeling

Terrain effects

• Terrain effects significantly impact wave propagation in EMC studies, particularly for terrestrial communication systems
• Understanding these effects helps engineers design more effective EMC mitigation strategies and predict potential interference sources
• Terrain-induced propagation phenomena can both enhance and degrade signal strength, influencing EMC performance

Diffraction over obstacles

• Occurs when radio waves bend around obstacles in the propagation path
• Huygens-Fresnel principle explains the formation of secondary wavelets at obstacle edges
• Fresnel diffraction parameter $v = h \sqrt{\frac{2(d_1 + d_2)}{\lambda d_1 d_2}}$
  • $v$ Fresnel diffraction parameter
  • $h$ height of obstacle above the line-of-sight path
  • $d_1$ and $d_2$ distances from obstacle to transmitter and receiver
  • $\lambda$ wavelength
• Diffraction loss calculated using Fresnel integrals or approximations (Bullington model)
• Significant for frequencies below 3 GHz, less effective at higher frequencies

Reflection from surfaces

• Occurs when radio waves encounter smooth surfaces larger than the wavelength
• Reflection coefficient depends on surface material properties and angle of incidence
• Fresnel reflection coefficients for horizontal and vertical polarizations
  • $R_h = \frac{\sin θ - \sqrt{ε_r - \cos^2 θ}}{\sin θ + \sqrt{ε_r - \cos^2 θ}}$
  • $R_v = \frac{ε_r \sin θ - \sqrt{ε_r - \cos^2 θ}}{ε_r \sin θ + \sqrt{ε_r - \cos^2 θ}}$
  • $ε_r$ relative permittivity of the reflecting surface
  • $θ$ angle of incidence
• Specular reflection occurs on smooth surfaces, following Snell's law
• Diffuse reflection occurs on rough surfaces, scattering energy in multiple directions
• Reflection from the ground and buildings can create multipath effects

Knife-edge diffraction model

• Simplified model for calculating diffraction loss over a thin obstacle
• Assumes obstacle can be represented as an infinitely thin, absorbing half-plane
• Diffraction loss calculated using Fresnel integrals or approximations
  • Lee's approximation $L_{dB} = 20 \log_{10}(\sqrt{(1-C(v))^2 + (S(v))^2})$
  • $C(v)$ and $S(v)$ are cosine and sine Fresnel integrals
• Fresnel diffraction parameter $v$ calculated as in the general diffraction case
• Multiple knife-edge diffraction models available for scenarios with multiple obstacles
  • Deygout method for dominant edge
  • Epstein-Peterson method for successive edges
• Widely used in radio planning tools for quick estimation of diffraction losses

Antenna considerations

• Antenna characteristics play a crucial role in EMC studies, affecting both the emission and susceptibility of electronic systems
• Understanding antenna properties helps engineers design more effective EMC mitigation strategies and predict potential interference sources
• Proper antenna selection and placement can significantly improve system performance and reduce electromagnetic compatibility issues

Radiation patterns

• Describe the spatial distribution of radiated energy from an antenna
• Represented by 2D cuts (E-plane and H-plane) or 3D patterns
• Key parameters derived from radiation patterns
  • Beamwidth measures the angular width of the main lobe
  • Front-to-back ratio indicates the difference between forward and backward radiation
  • Side lobe levels quantify undesired radiation in non-main beam directions
• Isotropic antenna serves as a theoretical reference (uniform radiation in all directions)
• Dipole antennas exhibit figure-eight patterns in the E-plane and omnidirectional patterns in the H-plane
• Directional antennas (Yagi, parabolic dish) concentrate energy in specific directions

Polarization effects

• Describes the orientation of the electric field vector in the radiated wave
• Types of polarization
  • Linear polarization (vertical, horizontal, or slant)
  • Circular polarization (right-hand or left-hand)
  • Elliptical polarization (general case)
• Polarization mismatch loss occurs when transmit and receive antennas have different polarizations
  • Loss calculated as $L_{pol} = -20 \log_{10}(|\cos \psi|)$
  • $\psi$ angle between the polarization vectors
• Cross-polarization discrimination (XPD) measures an antenna's ability to reject orthogonally polarized signals
• Polarization diversity used to mitigate multipath fading in wireless systems

Antenna gain

• Measures the antenna's ability to concentrate energy in a particular direction
• Expressed relative to an isotropic antenna (dBi) or a dipole antenna (dBd)
• Relationship between gain and effective aperture $G = \frac{4\pi A_e}{\lambda^2}$
  • $G$ antenna gain
  • $A_e$ effective aperture area
  • $\lambda$ wavelength
• Gain related to directivity and efficiency $G = ηD$
  • $η$ antenna efficiency
  • $D$ directivity
• High-gain antennas increase signal strength in desired directions but may increase interference potential
• Low-gain antennas provide wider coverage but require higher transmit power for the same range

Propagation in different media

• Understanding wave propagation in various media aids in analyzing EMC issues in complex environments
• Different propagation characteristics in conductors, dielectrics, and lossy media impact shielding effectiveness and interference coupling mechanisms
• Proper modeling of wave behavior in different materials helps in designing effective EMC solutions

Propagation in conductors

• Characterized by high conductivity and rapid attenuation of electromagnetic waves
• Skin effect concentrates current flow near the conductor surface at high frequencies
• Skin depth $δ = \sqrt{\frac{2}{ωμσ}}$
  • $δ$ skin depth
  • $ω$ angular frequency
  • $μ$ permeability
  • $σ$ conductivity
• Wave impedance in good conductors $Z_c = \sqrt{\frac{jωμ}{σ}}$
• Attenuation constant $α = \sqrt{\frac{ωμσ}{2}}$ nepers/meter
• Applications in shielding and transmission line design

Propagation in dielectrics

• Characterized by low conductivity and minimal attenuation
• Wave propagation speed $v = \frac{c}{\sqrt{ε_r μ_r}}$
  • $c$ speed of light in vacuum
  • $ε_r$ relative permittivity
  • $μ_r$ relative permeability
• Wave impedance in lossless dielectrics $Z_d = \sqrt{\frac{μ}{ε}}$
• Dielectric constant affects wavelength and impedance matching
• Loss tangent $\tan δ = \frac{σ}{ωε}$ quantifies dielectric losses
• Applications in antenna design and substrate selection for PCBs

Propagation in lossy media

• Combines characteristics of both conductors and dielectrics
• Complex permittivity $ε_c = ε' - jε''$
  • $ε'$ real part (energy storage)
  • $ε''$ imaginary part (energy dissipation)
• Complex propagation constant $γ = α + jβ$
  • $α$ attenuation constant
  • $β$ phase constant
• Wave impedance in lossy media $Z_l = \sqrt{\frac{jωμ}{σ + jωε}}$
• Penetration depth depends on frequency and material properties
• Applications in biological tissue modeling and ground penetrating radar

Wave propagation measurements

• Wave propagation measurements are essential for validating EMC models and assessing system performance in real-world environments
• Accurate measurement techniques help engineers identify potential interference sources and evaluate the effectiveness of EMC mitigation strategies
• Propagation measurements provide valuable data for refining prediction tools and improving EMC design practices

Field strength measurements

• Measure electric or magnetic field intensity at specific locations
• Equipment used
  • Field strength meters with calibrated antennas
  • Spectrum analyzers with appropriate probes
• Measurement procedures
  • Calibrate equipment and account for cable losses
  • Consider antenna factors for accurate field strength conversion
  • Perform spatial averaging to account for small-scale variations
• Near-field vs far-field measurements
  • Near-field complex field structure, separate E and H-field measurements
  • Far-field simpler relationship between E and H fields
• Applications
  • EMC compliance testing
  • RF exposure assessment
  • Coverage verification for wireless systems

Path loss calculations

• Determine signal attenuation between transmitter and receiver
• Path loss equation $PL = P_t + G_t + G_r - P_r$
  • $PL$ path loss in dB
  • $P_t$ transmit power in dBm
  • $G_t$ and $G_r$ transmit and receive antenna gains in dBi
  • $P_r$ received power in dBm
• Measurement techniques
  • CW (Continuous Wave) method for narrowband systems
  • Wideband channel sounders for frequency-selective channels
• Factors affecting path loss
  • Distance between transmitter and receiver
  • Frequency of operation
  • Antenna heights and surrounding environment
• Statistical analysis of path loss data
  • Log-normal shadowing model
  • Determination of path loss exponent and shadowing standard deviation

Propagation prediction tools

• Software applications for estimating signal coverage and interference potential
• Types of propagation models used
  • Empirical models (Okumura-Hata, COST-231)
  • Semi-empirical models (ITU-R P.1546)
  • Deterministic models (Ray tracing, FDTD)
• Input data requirements
  • Terrain elevation data
  • Land use/land cover information
  • Building footprints for urban areas
  • Transmitter and receiver parameters
• Output capabilities
  • Coverage plots and contours
  • Point-to-point path profiles
  • Interference analysis and frequency planning
• Validation and calibration of prediction tools
  • Comparison with field measurements
  • Model tuning based on local propagation characteristics
• Applications in wireless network planning and EMC analysis