ELECTROMAGNETICS AND APPLICATIONS Handouts Prerequisites Administration sheet 6 002, 6 003, 8 02, 18 02 Subject outline, lecture notes Homework set 1, text errata 6 013(New) Content Wireless communica[.]
ELECTROMAGNETICS AND APPLICATIONS Handouts: Prerequisites: Administration sheet 6.002, 6.003, 8.02, 18.02 Subject outline, lecture notes Homework set 1, text errata 6.013(New) Content: Wireless communications (3.2 weeks) Media and boundaries (1.5 weeks) Circuits (1 week) Motors, generators, MEMS, power transmission (1.2 weeks) Limits to computation speed (1 week) Microwave communications and radar (2 weeks) Acoustics (1 week) Optical communications (1 week) L1-1 WIRELESS COMMUNICATION IS UBIQUITOUS Local Telecommunications Network: Cell phones (who has one?) Wireless phones, data Wires, coaxial cables Optical fibers Link to national net Local cell Homes Base station Other Communications Links: Central office Microwave and optical fiber links Urban network International satellite links Transoceanic links, ionosphere Satellite Radio hams (any here? DX record?) Interplanetary links National Network NATION A Ionospheric link OCEAN NATION B L1-2 WIRELESS COMMUNICATION IS UBIQUITOUS Other Forms of Wireless Communications: Broadcast: Data links: Passive: Terrestrial radio, television, data Satellite TV, radio, data (~40,000 km - ~0.3 seconds roundtrip) WWV Time signals (clocks, watches) Computers to/from peripherals Hearing aids (from CPU) Remote controllers (optical and radio) Wired home, office, factory Pills with sensors (TV, chemical) (what frequencies penetrate body?) IR, microwave (satellites, factories, faucets, doors, thermometers, cameras) L1-3 COMMUNICATION REQUIRES ENERGY AND POWER Power Requirements Typical receivers need: Eb > ~4 × 10-20 Joules/bit Power received [W]: P = MbpsEb (Mbps is data rate, bits/sec) e.g 10-9 Watts permits Mbps = ~10-9/4 × 10-20 = 2.5 × 1010 bps This can send 2.5 × 1010/(8 × × 108 bits/CD) = 4.5 CD’s/second!) Transmitted Intensity is Pr(θ θ,φ φ,r) [W/m2] 2 For isotropic radiation: Pr ( θ, φ,r ) = PR πr W m PR = total power radiated (W) PR [W ] = ∫ Pr ( θ, φ,r ) r sin θdθdφ where: In general: % (&( ' 4π isotropic Pr(θ,φ,r) z θ area = r2(dθ)(sin θ dφ) = dΩ ∫ PrΩ ( θ, φ )[W steradian] dΩ 4π r x φ backlobes main beam [Steradian is a unit of solid angle; [dθ] [sin θ dφ] is in steradians if dθ and dφ are in units of radians A sphere spans 4π steradians] L1-4 ANTENNA GAIN G(θ,φ) θφ Gain over Isotropic G(θ,φ): θφ G ( θ, φ ) = Pr ( θ, φ,r ) PR πr (By definition, PR is at antenna input; we assume lossless antennas here) At receiver: Pr(θ,φ,r)[Wm-2] = G(θ,φ) PR/4πr2 Example – Cellular Phone: If PR = Watt, then Pr at 10 km = 1/4πr2 = × 10-10 [W/m2] for isotropic antenna (G = 1) How to Increase Gain? Focus the energy: lenses, mirrors, phasing L1-5 2] ANTENNA EFFECTIVE AREA Ae(θ,φ)[m θφ Power Received Prec from a particular direction 2 Prec = A e m Pr W m by definition of A e ) ( Say Go = 10 Antenna Effective Area and Gain A e ( θ, φ ) = G ( θ, φ ) λ 4π Antenna Tower Go (to be proved later) Cellular Phone Base-Station – Received Power cellular-phone base station Given: PR = Watt, G = for an isotropic antenna (is it isotropic?) Pr = 1/4πr2 = × 10-14 [W/m2] at r = 1000 km (or 40-dB margin for r = 10 km) Prec = AePr (Ae depends on the base-station Gbs and λ) λ = c/f = × 108 [m/s]/900 MHz = 33.3 cm Ae(base station) = Gbsλ2/4π = 10 × 0.332/(4 × 3.14) = 0.088 m2 Prec = AePr = 0.088 × × 10-14 = 7.1 × 10-15 [W] Data Rate [bps] = Prec[J/s]/Eb[J/b] = 7.1 × 10-15/(4 × 10-20) = 176 kbps Wishful thinking! Data rate per line limited by bandwidth and frequency reuse L1-6 CIRCUIT PROPERTIES OF ANTENNAS Equivalent circuit of antenna Radiation Resistance Rr PR = i Rr Rr = PR Reactance i(t) jX + Rr v(t) i2 - - VTh + Open-Circuit Voltage (Thevenin voltage) Induced by incoming waves Maximum power extractable from the antenna: Prec = ( VTh (t) ) Reactive elements are tuned out Rr Rr Rr - VTh + L1-7 WHAT DO WE NOT YET KNOW? ° What is an electromagnetic wave? ° How does it propagate through air and space, around buildings, around the earth? ° How we launch and receive them? ° How we engineer wireless communications systems using waves? Examples L1-8