Notes2-2

Notes2-2 - Notes #2, ECE594I, Fall 2009, E.R. Brown...

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Sensors Point Remote Passive Receiver Coherent Incoherent RF Sensors Transmitter Active Incoherent Active Coherent Proximity to Target Overview of RF Sensors 39 Definition: an RF system designed to detect the presence of objects or materials through their electromagnetic reflection or emission. Hierarchy A passive sensor detects thermal radiation emitted by an object, or environmental radiation reflected by the object. The paradigm passive sensor is the radiometer. An active sensor detects radiation reflected from an object that the sensor system itself transmits. The paradigm active sensor is the radar – an acronym for ra dio d etection and ra nging. Coherent receivers are often based on heterodyne down-conversion (more later). Incoherent receivers are often based on square-law detection (more later). Notes #2, ECE594I, Fall 2009, E.R. Brown
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0 = ε ρ E r r 0 = B r t B E −∂ = × / r r r t D t D J H C + = × / / v v v r r Review of Classical Electromagnetics generalized Ampere’s Faraday’s Coulomb’s Take curl of Faraday’s: t H t B E E E × = × = + = × × / ) ( / ) ( ) ( 2 r r r r r r r r r r r r µ Maxwell’s Equations Constitutive Relations E E D r r r r = = 0 H H B r v v r = = 0 377 / 0 0 = = o Z In free space In free space t t D E E E + / ) / ( ) ( 0 2 2 r r r r r r r r In free space: And we get the vector wave equation: 0 / 2 2 0 0 2 = t E E r r r Sinusoidal solutions: } ) ( ~ Re{ ) , ( t j e r E t r E ω r r r r = 0 ~ ~ 2 0 0 2 = + E E r r r Vector Helmholtz Eqn for E: Analogous Eqn for H: 0 ~ ~ 2 0 0 2 = + H H r r r 2 2 0 0 / t E = r Radiation always entails two degrees of freedom: E r % H r % and 40 Notes #2, ECE594I, Fall 2009, E.R. Brown
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Poynting’s and Sensor Power Theorem 00 () jkr jkx Er Ee ⋅− == r r r rr r % Simplest solution: Plane Wave: Substitution back into vector Helmholtz eqn yields: 2 22 2 2 2 0 kE E k c ω µεω −+ = = = %% For propagation along x axis This is called the dispersion relation: a very important kinematic relationship for all wave phenomena From plane wave propagation we know that is a vector that always points in the direction propagation. To understand what the magnitude means, operate on this quantity with the vector divergence operator: H E r r × ) ( ) ( ) ( H E E H H E r r r r r r r r r × × = × ) / ( ) / ( dt D J E t B H r r r r r + −∂ = (1/2) | | / | | / E JE d t H t εµ =− ⋅ − t U dt U J E M E = / / r r Application of Gauss’ divergence theory now yields × = × s d S s d H E dV H E V r r r r r r r r ) ( ) ( surface vector that encloses volume V So H E r r × represents a flux of power and the the integral × s d H E r r r ) ( represents total power leaving enclosed volume Joule heat Electric energy density Magnetic energy density 41 Notes #2, ECE594I, Fall 2009, E.R. Brown
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ˆˆ jkz XX EE xE e x +− == r % % Poynting’s theorem for plane waves: In phasor form: 0 (/ ) jkz jkz yX HH e y EZ e y + r % 2 2 0 0 () ˆ
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Notes2-2 - Notes #2, ECE594I, Fall 2009, E.R. Brown...

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