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lesson_1_-_Waves - = 2A exp(jωt cos(βz Real E = 2A...

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EE3321 ELECTROMAGNETIC FIELD THEORY Lecture 1 Highlights 1. International System of Units (SI) MKSA Length meter m Mass kilogram kg Time second s Current Ampere A 2. Unit Multipliers Tera 10 12 T Giga 10 9 G Mega 10 6 M Kilo 10 3 k Milli 10 -3 m Micro 10 -6 µ Nano 10 -9 n Pico 10 -12 p 3. Propagating Waves E(t,z) = E o (z) cos (ωt – βz) a x E o (z) amplitude Volts/meter ω = 2πf angular frequency radians/second f frequency Hertz (1/second) β = 2π/λ propagation constant radians/meter λ wavelength meters v = f λ = c/n speed of propagation meters/second c speed of light in free space n index of refraction a x unit vector in x direction 4. Complex Notation E c (t,z) = E o (z) exp [j(ωt – βz)] a x = E o (z) cos(ωt – βz) a x + j E o (z) sin(ωt – βz) a x E(z,t) = Real { E c (t,z) }
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5. Sign Convention - βz propagation in +z direction + βz propagation in –z direction 6. Standing Wave E = A exp[ j(ωt – βz) + A exp[ j(ωt + βz) = A exp(jωt) [exp(–jβz) + exp(+jβz)]
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Unformatted text preview: = 2A exp(jωt) cos(βz) Real { E } = 2A cos(ωt) cos(βz) 7. Transmission Line/Coaxial Cable V = V o cos (ωt – βz) proportional to E I = I o cos (ωt – βz) proportional to H Characteristic Impedance Z C = V o / I o Typical values: 50, 75 ohms 8. Time Delay φ = ωt – βz = ω[ t – (β/ω)z ] = ω( t – z/v ) τ = z/v time delay φ = ω (t – τ) phase E c (t, τ) = E o (z) exp [jω( t – τ )] a x 9. Radar, Sonar z = R o τ = 2R o /v R o is the target range 2 R o is the round trip distance 10. Coordinate Systems Cartesian (x, y, z) Cylindrical (r, φ, z) radius r, azimuth φ, height z Spherical (R, φ, θ) range R, azimuth φ, elevation θ...
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