2. UPenn NROTC Unit, dtd Fall 2004 Naval Weapons Systems Energy Fundamentals

3. Learning Objectives 2.1 Define the terms frequency, wavelength, velocity, amplitude and period as applied to wave propagation. 2.2 Describe two types of interference. 2.3 Describe the three propagation paths of EM waves. 2.4 Discuss the difference between ground waves, sky waves and space waves. 2.5 Discuss the EM spectrum and calculate maximum range (LOS).

4. Lets Get Started…

5. Waves Defn: Disturbance in a parameter that varies over spacial dimensions. Defn: Disturbance in a parameter that varies over spacial dimensions. Propagation: Movement of that disturbance (while maintaining that shape) Propagation: Movement of that disturbance (while maintaining that shape) INFORMATION to be exchanged can be carried on waves!! INFORMATION to be exchanged can be carried on waves!!

6. Wave Propagation Spherical Wave Spherical Wave Undisturbed wave Undisturbed wave Omni directional from source Omni directional from source Ripples on a pond. Ripples on a pond. Plane Wave Far from origin Spreads out to appear to have same amplitude everywhere on plane  direction of travel Think of entire wave traveling in one direction

7. Wave Propagation Localized disturbance in medium which effects neighboring portion of medium, and so on, and so on… Localized disturbance in medium which effects neighboring portion of medium, and so on, and so on… Sinusoidal in nature Sinusoidal in nature Localized disturbance in medium which effects neighboring portion of medium, and so on, and so on… Localized disturbance in medium which effects neighboring portion of medium, and so on, and so on… Sinusoidal in nature Sinusoidal in nature Two major types Two major types Longitudinal… disturbance in line with direction of propagation (Sound) Transverse… Disturbance at right angle to direction of propagation (Electromagnetic) Two major types Two major types Longitudinal… disturbance in line with direction of propagation (Sound) Transverse… Disturbance at right angle to direction of propagation (Electromagnetic)

8. Wave Terms Frequency (f) – Rate at which source disturbance oscillates through one complete cycle (Hertz – Hz sec –1 ) 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) Wavelength (l) – Distance between two identical points on adjacent waves or distance traveled by wave in one cycle. (Length cm, mm, m) Velocity (c) – EM waves travel at speed of light, (c = 3 x 10 8 m/s) Velocity (c) – EM waves travel at speed of light, (c = 3 x 10 8 m/s) λ = c/f

9. Wave Terms, Continued... Amplitude (a) – Maximum displacement of wave from constant reference value. Amplitude (a) – Maximum displacement of wave from constant reference value. Period (T) – Time to complete one cycle (time, sec) Period (T) – Time to complete one cycle (time, sec) T = 1/f

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

11. Interference… When two or more waves meet, amplitudes add to produce a new wave. Can be described as either constructive or destructive interference, depending on phase shift between waves Constructive… Phase difference between 0 o and 120 o or between 240 o and 360 o Destructive…Phase difference between 120 o and 240 o Interference… When two or more waves meet, amplitudes add to produce a new wave. Can be described as either constructive or destructive interference, depending on phase shift between waves Constructive… Phase difference between 0 o and 120 o or between 240 o and 360 o Destructive…Phase difference between 120 o and 240 o Interference

12. Interference E P = electric field at point (P) P = point (r) distance from two sources Φ= Phase angle between two sources IN DEG If the phase angle difference is caused by a difference in path length (  x), it can be calculated by the following: Φ = 360  x/ (in deg) = 2  x/ (in radians) = 2  x/ (in radians) 120 Deg 240 Deg CC DD

13. Example Two antennas are operating at 7 MHz with a separation of 10 m. Is there constructive or destructive interference? Two antennas are operating at 7 MHz with a separation of 10 m. Is there constructive or destructive interference?

14. Energy Fundamentals RAdio Detection And Ranging RAdio Detection And Ranging Radar is an electromagnetic wave that acts like any other electromagnetic wave (i.e. - radio, light, etc.) Radar is an electromagnetic wave that acts like any other electromagnetic wave (i.e. - radio, light, etc.) Characteristics of a radio wave assuming a frequency of 2 Hertz: Characteristics of a radio wave assuming a frequency of 2 Hertz: Cycle Amplitude 1 second

15. Maxwell’s Theory An accelerating electric field will generate a time-varying magnetic field. An accelerating electric field will generate a time-varying magnetic field. A time-varying magnetic field will generate a time-varying electric field. A time-varying magnetic field will generate a time-varying electric field....and so on...and so on...and so on......and so on...and so on...and so on...

16. Generation of Electromagnetic Radiation + - + - - + abc d = Alternating Current Source

17. Formation of Electric and Magnetic Fields around an Antenna e- E-line Mag field Electric field | Magnetic Field | Direction of Propagation.

18. What is Polarization? The direction of polarization of an antenna is defined as the electric field vector. The direction of polarization of an antenna is defined as the electric field vector. 3 Kinds: 3 Kinds: Horizontal Horizontal Vertical Vertical Circular Circular

19. Propagation Paths of E-M Waves Reflection Reflection Refraction Refraction Diffraction Diffraction

20. Reflection Incident Wave Reflected Wave Phase shift = 180 degrees. Angle of incidence = Angle of reflected wave.

21. Refraction 1. Incident wave passes through two transparent media in which the velocity of light differs... 2.Incident wave divides into a reflected wave and a refracted wave. 3. The result is that the energy ray will bend toward the area of higher density.

22. Refraction Not all wave is reflected. Some is transmitted into medium interface at some angle. This angle can be determined using Snell’s Law. Snell’s Law n 1 sin   = n 2 sin   v Electromagnetic waves propagate at speed of light (c) = 3 x 10 8 m/s (in vacuum) –Speed of light varies in different medium (C 0 ) –Light refracts at medium boundary layer. –Index of refraction, n, defined as; n = C/C 0

23. Snell’s Law n1*Sin θ1=n2*Sin θ2 θ1θ1 θ2θ2 Medium 1 Medium 2

24. Example An electromagnetic wave strikes a boundary between two media with an angle of incidence of 45 deg. The index of refraction for the incident medium is 1.2 and the index of refraction for the second medium is 1.15. What is the angle of refraction? An electromagnetic wave strikes a boundary between two media with an angle of incidence of 45 deg. The index of refraction for the incident medium is 1.2 and the index of refraction for the second medium is 1.15. What is the angle of refraction?

25. Diffraction island not detected detected...plane waves traveling in a straight path bend around a boundary or obstruction.

26. Wave Propagation Distance and Frequency Ground Waves Ground Waves Sky Waves Sky Waves Space Waves Space Waves

27. Ground Wave Very low frequencies, 5- 10Khz Very low frequencies, 5- 10Khz Vertical polarization Vertical polarization Waves travel along earth’s surface. Waves travel along earth’s surface. Very long wavelengths - unsuitable for ships & aircraft, except comms Very long wavelengths - unsuitable for ships & aircraft, except comms Shore-based installations Shore-based installations Cutler, Maine & Aguada, Puerto Rico Cutler, Maine & Aguada, Puerto Rico

28. Sky Wave EM energy refracts back towards the earth’s surface in upper ionosphere layer. EM energy refracts back towards the earth’s surface in upper ionosphere layer. EM energy then reflects back toward upper layer again. EM energy then reflects back toward upper layer again. Frequencies used up to 550 KHz effectively Frequencies used up to 550 KHz effectively Wavelengths still too long for anything but comms by aircraft and ships. Wavelengths still too long for anything but comms by aircraft and ships.

29. Sky Waves, Continued

30. Space Wave Above 30 MHz, ionosphere will not refract E-M waves back toward earth. Above 30 MHz, ionosphere will not refract E-M waves back toward earth. Energy tends to travel in straight line. Energy tends to travel in straight line.

31. Electromagnetic Spectrum

32. Max Range (LOS) Max Range (LOS) - Due to ducting, certain electromagnetic waves can transmit farther than the “visual” Line of Sight (LOS). Max Range (LOS) - Due to ducting, certain electromagnetic waves can transmit farther than the “visual” Line of Sight (LOS).

33. Max Range (LOS) To compute the maximum detection range between a target and electromagnetic transmitting antenna, the following equation can be employed: To compute the maximum detection range between a target and electromagnetic transmitting antenna, the following equation can be employed: H T = Target Height in METERS H T = Target Height in METERS H R = Radar Antenna Height in METERS H R = Radar Antenna Height in METERS Resultant Range is in Kilometers! Resultant Range is in Kilometers!

34. Example Calculate the maximum theoretical range of a surface search radar with an antenna height of 25 m and a target height of 50 m. Calculate the maximum theoretical range of a surface search radar with an antenna height of 25 m and a target height of 50 m.

35. Transmission Range Factors Antenna Height Antenna Height Target Height Target Height Ducting Ducting Losses Losses Spreading Spreading Absorption Absorption Constructive / Destructive Interference Constructive / Destructive Interference

36. Transmission Losses Spreading: Energy per unit area proportional to: Spreading: Energy per unit area proportional to: where R is distance from transmitter Absorption: Molecules of medium absorb some of the energy as it passes through. Absorption: Molecules of medium absorb some of the energy as it passes through. 1R21R2

37. Modulation The process of encoding information on the “Carrier Wave”. The process of encoding information on the “Carrier Wave”. A simple Sine wave. A simple Sine wave. The Sine wave has 3 independent parameters: The Sine wave has 3 independent parameters: Amplitude Amplitude Frequency Frequency Phase Phase

38. Energy Fundamentals Review Q1. Define the terms frequency, wavelength, velocity, amplitude and period as applied to wave propagation. Q2. Describe two types of interference. Q3. Describe the three propagation paths of EM waves.

39. Questions?