1. ELECTROMAGNETICS AND APPLICATIONS Lecture 19 Radiation Luca Daniel

2. L13-2

3. L13-3 Review of Fundamental Electromagnetic Laws Electromagnetic Waves in Media and Interfaces Digital & Analog Communications Wireless Communications oRadiation Fundamentals  Magnetic Vector Potentials  Radiation from a short dipole  Near fields produced by a short dipole  Far fields produced by short dipole  Intensity of a short dipole oTransmitting Antennas, Gain oArrays, Wire Antennas oReceiving Antennas; Wireless Communicat. Systems oAperture antennas; Diffraction Acoustic waves and Acoustic antennas e.g. speakers, musical instruments, voice Outline Today

4. L13-4 Course Outline and Motivations Electromagnetics: –How to analyze and design antennas Applications –wire antennas (e.g. inside your iPhone, or wireless router) –aperture antennas (e.g. satellite, radar, parabola TV)

5. L13-5 Wireless Communications RANGE Arm’s Length <100 m <100 km Global Cosmic ACTIVE hearing aids, computer peripherals Wireless phones, remote controllers, computer links Radio, TV, cellphone, collision avoid, altimetry, 802.11 Amateur radio, satellites, radar Radio & optical interplanetary communications, radar PASSIVE Faucets, thermometers Cameras, doors, RF tags, glasses for 3D Multispectral remote sensing Weather satellites Radio & optical astronomy ubiquitous !

6. L13-6 Magnetic Vector Potentials – the formal derivation Note: A is not specified completely. We can still choose as we want! Same as electrostatic potential at ω=0 ! Lorenz gauge

7. L13-7 Magnetic Vector Potential – the intuitive picture q=  dV r r d Charges produce electric potential (as in statics) At non-zero frequency there is an additional wave propagation term which vanishes at DC Currents produce Magnetic Vector Potential (A) Very localized segment of current Superposition for complex current distributions Very localized charge Superposition of complex charge distributions

8. L13-8 Fields radiated from a short element of current Algorithm: y z   -Q +Q r dI0I0 x in spherical coordinates very “short” segment, i.e.:

9. L13-9 Near Field Radiation (kr << 1  r << /2  ) Quasistatic Dipole Fields: Dominate near field, kr <<1 Field expressions:  z Power is Imaginary: Near Field:

10. L13-10 Far Field Radiation (kr >> 1  r >> /2  ) Radiated Far Fields: Radiated power: z y  I(  )  sin 2  x z Intensity or time average Dominate in far field, kr >>1