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# formula sheet - ECSE 352 EM Waves and Optics Formula sheet...

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1 ECSE 352 EM Waves and Optics: Formula sheet TRANSMISSION LINES Lossless line: β = ω LC = µε u p = 1 Z 0 = V 0 I 0 = L C General transmission line equations: d 2 Vz ( ) dz 2 = γ 2 ( ) 2 Iz ( ) 2 = 2 ( ) ( )( ) C j G L j R j α + + = + = ( ) ( ) ( ) ( ) ( ) 22 00 , cos 2 2 cos , cos zz ZZ Z VV zt e t z z e αα βθ θ −−  = −+ =  PP 0 = R + j = G + = + + Parameter Parallel Plate Two-wire line Coaxial line R w R s 2 s π a 2 π 1 + 1 b L w d µ π cosh 1 D 2 2 π ln G d w σ π cosh 1 /2 ( ) 2 π / ( ) C d w ε π cosh 1 ( ) 2 π / ( ) = π f c / Wave characteristics of a finite transmission line: Reflection, transmission coefficients: 0 0 L L Γ= + 0 2 L L Z τ = + Voltage on line ( z =0 is at load): ( ) 0 2 sin jz sT VzVe j z τβ = Voltage standing wave ratio: ° = 1+ | Γ | 1− | Γ | Input impedance of lossless line: i = 0 + jR 0 tan l 0 + jZ tan λ /4 line: = 0 2 λ /2: = Lossy line: 2 0 2 1 1 l in l e e =  −Γ Γ = + 2 0 2 1 2 Z V P av
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