Wave Optics: Diffraction Concepts

Diffraction

• Diffraction occurs when waves hit the edge of an obstacle.
• Secondary waves propagate into the shadowed region.
• Diffraction results from the propagation of secondary wavelets into a shadowed region.
• Excess path length leads to a phase shift.
• The field strength of a diffracted wave in the shadowed region is the vector sum of the electric field components of all the secondary wavelets around the obstacle.
• Huygens’ principle states that all points on a wavefront can be considered as point sources for the production of secondary wavelets, which combine to produce a new wavefront in the direction of propagation.

Diffraction Geometry

• Equations 4.54-4.57 can be derived from the diffraction geometry.

Fresnel-Kirchoff Diffraction Parameters

• Equation 4.56 defines Fresnel-Kirchoff diffraction parameters.

Fresnel Screens

• Fresnel zones relate phase shifts to the positions of obstacles.
• Equation 4.58 defines the Fresnel zone.
• A rule of thumb for line-of-sight microwave links is to keep 55% of the first Fresnel zone clear.

Fresnel Zones

• Bounded by elliptical loci of constant delay.
• Zones alternate in phase by 180 degrees.
• Line of sight (LOS) corresponds to the 1st zone.
• If the LOS is partially blocked, the 2nd zone can destructively interfere, resulting in diffraction loss.
• The amount of power propagated through the Fresnel zone can be estimated, with the 1st zone typically having 5 to 25 dB below free space propagation.

Knife-edge Diffraction

• Equation 4.59 defines Fresnel integral.

Knife-edge Diffraction Loss

• Diffraction loss is a measure of the attenuation of a signal due to the presence of an obstacle, such as a building or a hill.
• It can be calculated using the Fresnel integral.
• Exam 4.7 and 4.8 involve calculating diffraction loss.

Multiple Knife-edge Diffraction

• Multiple knife-edge diffraction occurs when there are multiple obstacles in the path of a signal.
• The diffraction loss in this case is the sum of the diffraction losses from each individual obstacle.

Scattering

• Rough surfaces, such as lamp posts and trees, scatter waves in all directions.
• The critical height for bumps is a function of the wavelength and incident angle, as defined by Equation 4.62.
• A surface is considered smooth if its minimum to maximum protuberance is less than the critical height.
• Scattering loss factor can be modeled using a Gaussian distribution (Equations 4.63 and 4.64).
• Nearby metal objects (street signs, etc.) can scatter waves, usually modeled statistically.
• Large distant objects can also scatter waves, and can be modeled using the Radar Cross Section (RCS).
• Equation 4.66 defines the bistatic radar equation.

Measured Results

• Measurements of radio wave propagation show that the signal strength can vary significantly, even over short distances. This variation is due to multipath propagation, which is the phenomenon of radio waves reflecting off objects and traveling along multiple paths.
• The amount of variation in the signal strength is dependent on the environment, the frequency of the radio waves, and the distance between the transmitter and receiver.

Propagation Models

• Large-scale models, which predict average behavior over distances much larger than the wavelength of the signal, are used to model the general trend of signal loss over distance.
• These models are frequency-independent and useful for range calculations and capacity planning.
• They are based on experimental data and often use path loss models, which include outdoor and indoor models.
• Small-scale models focus on signal variability over short distances or time, known as fading. They model the rapid change in signal strength due to multipath effects.
• Small-scale models are frequency and bandwidth-dependent.

Free Space Path Loss

• Path loss is a measure of signal attenuation based on distance to the transmitter.
• The free space model is only valid in the far field, which is defined by a distance greater than a certain threshold "d0".
• Path loss models typically use a reference point d0 and define path loss relative to this point.
• The log-distance model generalizes path loss to account for other environmental factors by introducing a distance-dependent exponent "beta".
• The free space path loss can be measured or calculated for a reference point, and by taking measurements and deriving beta empirically, the path loss at other distances can be determined.