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 Mechanical ~ Requires medium for propagation
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 RAdio Detection And Ranging
Radar is an electromagnetic wave that 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) Plane Wave (Far 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 is measured in either degrees or radians.
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 degrees degrees = (360o/2p) x radians
57.3o per radian
Positive phase shift wave is advanced Negative phase shift wave is retarded

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. No internal reflection when starting in a lower n because sin  1
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
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 .
Destructive
Constructive 0o
240o
120o

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

23. Short Range (Tactical)
Frequency
Band
Range (nm)
Power
Rate
Space Waves
Short Range (Tactical)
GHz
EHF
Attenuation susceptible
100 Mbps
3-30 GHz
SHF
40 (G/ LOS)
(Tropo)
P/G limit (Satellite)
250 kbps
MHz
UHF
(LOS)
300 (LOS Air)
1000s (Satellite) W W
56 kbps
MHz
VHF
25-50 (G)
LOS (D) W
75 baud
9600 bps
3-30 MHz HF
(G)
Span Globe (S)
2-100 kW
2400 bps
Sky Wave
Long Range
kHz MF
(G)
(S)
Ground Waves
Very Long Range (Strategic)
kHz LF kW
3-30 kHz
VLF
5000+ kW
50 baud Hz
ELF
100 MW
1-2 baud

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

32. Attenuation susceptible
Frequency
Band
Range (nm)
Power
Rate
Space Waves
Short Range (Tactical)
GHz
EHF
Attenuation susceptible
100 Mbps
3-30 GHz
SHF
40 (G/ LOS)
(Tropo)
P/G limit (Satellite)
250 kbps
MHz
UHF
(LOS)
300 (LOS Air)
1000s (Satellite) W W
56 kbps
MHz
VHF
25-50 (G)
LOS (D) W
75 baud
9600 bps
3-30 MHz HF
(G)
Span Globe (S)
2-100 kW
2400 bps
Sky Wave
Long Range
kHz MF
(G)
(S)
Ground Waves
Very Long Range (Strategic)
kHz LF kW
3-30 kHz
VLF
5000+ kW
50 baud Hz
ELF
100 MW
1-2 baud