Wave Propagation

1. Wave Propagation

3. Objectives • Apply the relationship between Frequency, Wavelength and the Speed of Propagation • Distinguish between Reflection, Refraction, and Diffraction • Solve refraction angles using Snell’s Law • Explain the relationship between an electric field and it’s magnetic field and how because of this relationship, electromagnetic waves propagate • Explain Constructive and Destructive Interference and calculate the amount of Interference and Phase Angle • Identify the range of frequencies associated with each EM band designation • List the various wave propagation paths and the band designations associated with the propagation • Solve for the radar horizon using the height relationship between the target and sensor

4. Particles vs. Waves • Two great concepts in physics • Particles suggest a tiny concentration of matter capable of transmitting energy • Waves suggest just the opposite – a broad distribution of energy filling the space through which it passes.

5. Wave Characteristics • Two Types (for our purposes). • Mechanical~ Requires medium for propagation • Sound (Sonar) (Air or Water) • Electromagnetic ~ Doesn’t require medium for propagation • Light (Air or Water) • Radio (Air or Water) • Radar (Air) • Mechanical Waves Propagate as Longitudinal Waves • Disturbance in line with direction of propagation • Electromagnetic Waves Propagate as Transverse Waves • Disturbance right angles to direction of propagation

6. Energy Fundamentals • RAdioDetectionAndRanging • Radar is an electromagnetic wavethat acts like any other electromagnetic wave (radio, light, etc.) • Characteristics of a radio wave assuming a frequency of 50 Hertz: 1 Cycle / .02 Sec 50 Cycles / 1 Sec

7. Wave Propagation • Spherical Wave (Near Field) • Undisturbed wave • Omni directional from source • Ripples on a pond. • Plane Wave (Far Field) • Far from origin • Spreads out to appear to have same amplitude everywhere on plane perpendicular to direction of travel • Think of entire wave traveling in one direction

8. Wave Terms • Frequency (f) – Rate at which source disturbance oscillates through one complete cycle (Hertz – Hz sec –1) • Wavelength (l) – Distance between two identical points on adjacent waves or distance traveled by wave in one cycle. (Length cm, mm, m) λ = c/f • Velocity (c) – EM waves travel at speed of light, (c = 3 x 108 m/s) • Amplitude (A) – Maximum displacement of wave from constant reference value. • Period (T) – Time to complete one cycle (time, sec)

9. Phase Positive phase shift wave is advancedNegative phase shift wave is retarded • Identical Waves shifted either ahead or behind due to distance separations or time delay. • Pick one as a reference and determine phase difference or phase shift between the two. Phase is measured in either degrees or radians. radians = (2p/360o) x degreesdegrees = (360o/2p) x radians 57.3o per radian

10. Fourier Analysis • French mathematician Jean Baptist Fourier explained how the principles of interference can be used to analyze non-sinusoidal wave forms. • Specifying amount and frequency of each component (cosine and sine waves) is representative of frequency domain. 8 Hz easily recognizable, other freqs. questionable.

11. Propagation Paths of Electromagnetic Waves • Reflection • Refraction • Diffraction • Absorption

12. Reflection • Medium boundaries with dissimilar propagation result in reflection Diffuse reflection results from waves striking an irregular surface and reflecting over a broad range Specular reflection is reflected at equal but opposite angle from smooth surface

13. Reflection • When we examine at the ‘particle’ level…

14. Refraction • Incident wave passes through two transparent media in which the velocity of light differs • Incident wave divides into a reflected wave and a refracted wave. • As the angle of incidence increases, angle of refraction increases • When the angle of refraction = 90o then critical angle • For a range of incidence greater than 90o, no refraction, only internal reflection No internal reflection when starting in a lower n because sin  1

15. Refraction • Electromagnetic waves propagate at speed of light (c) = 3 x 108 m/s (in vacuum) • Speed of light varies in different medium (Cm) • Light refracts at medium boundary layer. • Index of refraction, n, defined as; • n = c/cm We can determine either indices of refraction or angle of refraction by applying Snell’s Law n1sinq1 = n2sinq2

16. Diffraction • Spreading of wave along edge of an object • Amount of diffraction is wavelength and size related • Wave ‘bends’ when wavelength is larger than object or opening • Can hear around corner, but can’t see around a corner. • Radar can detect around an object under the right conditions

17. Interference 0o Constructive Constructive 240o 120o Destructive • Interference – when two or more waves collide, superposition of amplitudes add to produce a resulting wave. • Described as either constructive or destructive interference, depending on phase shift between waves. • Constructive – phase difference between 0o and 120o or between 240o and 360o . • Destructive – phase difference between 120o and 240o .

18. Electromagnetic Signal Loss • Spreading - energy distributed over an increasingly larger area. Energy per unit area proportional to 1/R2. • Absorption - energy dissipated into medium. Molecules of medium absorb some of the energy as it passes through. • Scattering - energy bouncing off suspended particles within a medium. Scattering is going to be particulate size/radar frequency dependent.

19. Spreading

20. Absorption

21. Absorption

22. Wave Propagation • There is a relationship between distance and frequency • Propagation Modes • Ground Wave • Sky Wave • Space Wave

24. Ground Wave • Very low frequencies (5-10Khz) • Vertical polarization • Waves travel along earth’s surface. • Very long wavelengths - unsuitable for ships & aircraft, but used for sub comms • Shore-based installations (HF-DF)

25. Sky Wave • E-M energy refracts in upper ionosphere and is directed back to Earth. May occur multiple times • Frequencies used up to 550 KHz effectively • Wavelengths still too long for anything but comms by aircraft and ships. (Antenna Length)

26. Space Wave • Higher frequency signals that penetrate the ionosphere and travel through space. • Above 30 MHz, ionosphere will not refract E-M waves back toward earth. • Energy tends to travel in straight line.

27. Atmospheric effects on Space Waves • Ionospheric Scatter • Scattered reflection of VHF and up signals • 600 – 1000 miles • Tropospheric Scatter • Scattering signal off of troposphere. • Air turbulence, irregularities in refractive index, homogeneous discontinuities. • Boundary layers between stratified pockets of air. • Strong function of weather. • 400 miles. • Tropospheric ducting • Present in inversion conditions (as is all ducting). • Refraction curve matches curvature of the earth. • Improves ranges greatly.

29. Radar Line of Sight • Due to refraction, certain electromagnetic waves can transmit farther than the “visual” Line of Sight (LOS).

30. Radar Horizon (LOS) • To compute the maximum detection range between a target and electromagnetic transmitting antenna, the following equation can be employed: • HT = Target Height in METERS • HR = Radar Antenna Height in METERS • Resultant Range is in Kilometers!

31. Objectives • Apply the relationship between Frequency, Wavelength and the Speed of Wave Propagation • Distinguish between Reflection, Refraction, and Diffraction • Solve refraction angles using Snell’s Law • Explain the relationship between an electric field and it’s magnetic field and how because of this relationship, electromagnetic waves propagate • Explain Constructive or Destructive EM wave Interference waves and calculate the amount of Interference and Phase Angle • Identify the range of frequencies associated with each EM band designation • List the various wave propagation paths and the band designations associated with the propagation • Solve for the radar horizon using the height relationship between the target and sensor