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# 5 - (1.46 If t L = t e the line is said to be matched and...

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1.5.1 Power loss in Cables ~n i(z) lout +~ :0;. ~2L V(z) zc· v I ~ z =!f' z I-----------+-----~ z=o FIGURE 1.6 The basic transmission line problem with symbols defined. ( 1.41a) /\ Vel) = /\ :t C-t') :: (1.41b) Phce50~. L If) e Va{ letS! e PhCiXJf LIr1f C: (reI} +

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+ + V out V(z) Ze. v z=o z = If' z FIGURE 1.6 The basic transmission line problem with symbols defined. V(z) = VJ(z) + ~(z) J(z) = vJ~(z) _ ~~z) z; z; (l.42a) (1.42b) where ( 1.43a) (1.43b)
Tt Me D-€ penJ.efl ce : e J 0 r 1: "f'Y1pl;ed /\ /\. Vel:) = vet,) L Bv(tr") ICt) :: \ I (:t)] L B r C2!) f3 = l-;- ::. phee5e CO/)Skrl j 0( -::; A +Jf(l ()~ k;i\ (vJ 5 h f;-f-

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The quantities VJ(z) and Vb(z) are referred to as the forward- and backward- traveling waves, respectively. This is because the phasor forms in (1.41) converted to the time domain become [1 ] v(z, t) = ~e[V(z)ejwtJ = V+ e :" cos(wt - (3z + e+) + V- e" cos(wt + j3z + e-) (1.44a) i(z, t) = gfle[f(z)ejwtJ (l.44b) V+ = - e :" cos(wt - {3z + e+ - e z ) Zc c v- - - e az cos(wt + {3z + e: - e z ) Zc c
(1.45) The reflection coefficient at the load is [1 ]

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Unformatted text preview: (1.46 ) If t L = t e , the line is said to be matched and the reflection coefficient at the load is zero, r L = O.The reflection coefficient at any point on the line can. be related to the load reflection coefficient as [1 J ['(z) = r L e 2cx (z-Sf) e j2 {3(z-Sf) (1.47) The general phasor expressions in (1.41) can be written in terms of the reflection coefficient as [1] V(z) = Y+ e== e-j/IZ[l + f(z)] = Vj(z)[l + f(z)] [(z) = ~+ e= e-jPZ [1 -r(z)] = Vj",(z) [1 -['(z)] Zr z~ (1.48a) (1.48b) The input impedance at any point on the line can be obtained as the ratio of (1.48a) and (lA8b) as f'ilQicht?d Lifl{} (f\!O Re+ftd/Vl) (1.49) 1\-z L...
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5 - (1.46 If t L = t e the line is said to be matched and...

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