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1 1 2 2 2r d 2r d l d (a) (b) (c) 1: I(x,t) I(x+ x,t) I(0,t) I(l,t) V in V(x,t) V(x+ x,t) V(0,t) l V(l,t) 2: 0 x x+ x 3: V in 3 V in x V (x, t) I(x, t) V (x, t) I(x, t) V in x t 3 4 1 L R 2 C G L 0 R 0 C 0 G 1 0 x x V (x + x, t) I(x + x, t) 1 L 0 [H] [H/m] R 0 [Ω] [Ω/m] C 0 [F] [F/m] G 0 [S] [S/m] 1

R L C G x 4: x x x + x I(x, t) x x + x L R L 0 x R 0 x x + x V (x + x, t) L 0 x R 0 x I(x, t) V (x + x, t) = V (x, t) R 0 xi(x, t) L 0 x (1) x x x + x V (x, t) x x + x C C 0 x G G 0 x I(x + x, t) I(x + x, t) = I(x, t) (2) V (x + x, t) I(x + x, t) V (x, t) I(x, t) V (x, t)/ x I(x, t)/ x V (x + x, t) = V (x, t) + (3) I(x + x, t) = I(x, t) + I(x, t) x x (4) (1) (3) (2) (4) R 0 I(x, t) L 0 I(x, t) = (5) G 0 V (x, t) C 0 V (x, t) = (6) (5) x (6) t R 0 I(x, t) x G 0 V (x, t) L 0 2 I(x, t) x = 2 V (x, t) x 2 2 V (x, t) C 0 2 = 2 I(x, t) x x t (7) (8) 2 I(x, t) x = 2 I(x, t) x (9) (6) (8) (7) 2 V (x, t) V (x, t) 2 V (x, t) x 2 = R 0 G 0 V (x, t) + (L 0 G 0 + C 0 R 0 ) + L 0 C 0 2 (10) 2

I(x, t) 2 I(x, t) I(x, t) 2 I(x, t) x 2 = R 0 G 0 I(x, t) + (L 0 G 0 + C 0 R 0 ) + L 0 C 0 2 (11) [ 1] R 0 = 1 Ω/m G 0 = 1 S/m L 0 = 1 H/m C 0 = 1 F/m (10) V (x, t) V (x, t) = f(x)e jωt (12) f(x) x x = 0 f(x) = 1 x f(x) = 0 (12) (10) 2 f(x) x 2 e jωt = f(x)e jωt + 2jωf(x)e jωt ω 2 f(x)e jωt (13) f(x)e jωt 1 2 f(x) f(x) x 2 = 1 + 2jω ω 2 = (1 jω) 2 (14) x f(x) f(x) = Ae (1 jω)x + Be (1 jω)x (15) A B x f(x) = 0 B x = 0 f(x) = 1 A = 1 V (x, t) V (x, t) = e (1 jω)x e jωt = e x e jω(t+x) (16) 2 V in (t) 1 e jωt e jωt V (x, t) I(x, t) V (x, t) = V (x)e jωt I(x, t) = I(x)e jωt (17) (18) V (x) I(x) x t (17) (10) 2 V (x) x 2 = { }V (x) (19) V (x) V (x) (19) V (x) = V i e γx + V r e γx (20) 3

V i V r γ γ = (R 0 + jωl 0 )(G 0 + jωc 0 ) (21) V (x, t) (17) (20) V (x, t) = V i e γx+jωt + V r e γx+jωt (22) (18) (5) (R 0 + jωl 0 )I(x)e jωt = γv i e γx+jωt + γv r e γx+jωt (23) I(x) I(x) = I i e γx I r e γx (24) I i I r I i = V i I r = V r (25) (26) = (27) (18) (24) I(x, t) I(x, t) = I i e γx+jωt I r e γx+jωt (28) (22) (28) V r I r V (x, t) I(x, t) V r I r V r = 0 (22) (28) V (x, t) = V i e γx+jωt I(x, t) = I i e γx+jωt (29) (30) γ γ = α + jβ (31) α β (29) (30) V (x, t) = V i e αx e j(ωt βx) I(x, t) = I i e αx e j(ωt βx) (32) (33) 4

(32) (33) α β jω V i e αx e j(βx ωt) L 0 R 0 C 0 G 0 R 0 L 0 = G 0 C 0 (34) α β α = (35) β = ω (36) α β ω (34) V i e αx e j(βx ωt) Re[V i e αx e j(ωt βx) ] = V i e αx cos(ωt βx) = V i e αx cos{ω(t L 0 C 0 x)} (37) t = 0 t = t 5 V(x,t) 0 x x t=0 t= t 5: α e αx x α βx β cos{ω(t L 0 C 0 x)} (37) (34) 2 (34) (34) R 0 G 0 α = 0 R 0 = 0 G 0 = 0 5 V i e αx cos(βx ωt) t x x V i e γx+jωt x (22) 1 t x v p = x t (38) x v p 5 x t β x ω t = 0 (39) 2 f 1(t) f 2(t) t f 2(t) = Kf 1(t τ) K τ ω (34) K τ K = e R 0 G 0 τ = L 0C 0 5

v p v p = ω β = 1 L0 C 0 (40) (22) 2 x (22) 2 (28) 1 2 V(x,t 0 ) t=t 0 0 x 6: t = t 0 (37) V (x, t 0 ) V (x, t 0 ) = V i cos{ω(t 0 βx)} (41) 6 β = L 0 C 0 2π 1 λ λ = 2π β (42) λ [ 2] 1(a) r d L 0 = µ 0 2π ln d 2r C 0 = 2πϵ 0 (43) (44) ln d 2r 1(b) r d L 0 = µ 0 π cosh d 2r (45) C 0 = πϵ 0 cosh d 2r (46) µ 0 µ 0 = (1/36π) 10 9 H/m ϵ 0 ϵ 0 = 10 7 /(4πc 2 0 ) F/m c 0 (3.0 10 8 m/s) 6

R 0 G 0 L 0 C 0 L 0 C 0 = µ 0 ϵ 0 (47) v p 1/L 0 C 0 v p = 1 µ 0 ϵ 0 = c 0 (48) [ 1] 1 GHz λ 3 1 I(l) 2 V(0) V(l) 1 2 l 7: F 3.1 F 7 l F x (20) (24) γ jβ 7 V (0) (20) (24) V (0) = V i + V r = V i V r V (l) I(l) (20) (24) x = l V (l) = V i e jβl + V r e jβl I(l) = V i e jβl V r e jβl (51) (52) (49) (50) (51) (52) 7

e x e x cosh x sinh x e x = cosh x e x = cosh x sinh x sinh x (53) (54) (51) (52) V (l) = (V i + V r ) cosh(jβl) (V i V r ) sinh(jβl) (55) I(l) = V i + V r sinh(jβl) + V i V r cosh(jβl) (56) (49) (50) V (l) I(l) = V (0) cosh(jβl) Z 0 sinh(jβl) cosh(jβl) V (0) = sinh(jβl) + cosh(jβl) 1 sinh(jβl) sinh(jβl) cosh(jβl) V (0) (57) cosh 2 x sinh 2 x = 1 V (0) V (0) = cosh(jβl) sinh(jβl) 1 V (l) (58) sinh(jβl) cosh(jβl) I(l) F β = ω L 0 C 0 F A D jω B C jω AD BC = 1 F [ 2] F AD BC = 1 I(l) V(0) V(l) R l 8: 3.2 8 l 8 Z in = V (0)/ (58) Z in = V (0) = Z cosh(jβl)v (0) + sinh(jβl) 0 sinh(jβl)v (0) + cosh(jβl) (59) 8 V (l) I(l) V (l) = I(l) (60) 8

(59) Z in Z in = R cosh(jβl) + sinh(jβl) R sinh(jβl) + cosh(jβl) (61) Z in R R R = Z in Z in R=Z0 = = R (62) R R = 0 R = Z in Z in R=0 = sinh(jβl) cosh(jβl) = tanh(jβl) = p (63) cosh(jβl) Z in R= = sinh(jβl) = tanh(jβl) = p p p = tanh(jβl) = j tan(βl) (65) L 0 C 0 (63) (64) p s (63) p (64) p (64) R 1 1 I(l) 2 V in V(0) V(l) R 2 1 l 2 9: [ 3] 8 R = 50 Ω = 100 Ω l = 3λ/4 Z in λ 3.3 9 1-1 2-2 (20) V i V r V i e jβl V r e jβl Γ S Γ L V i + V r = V (0) (66) 9

V i V r = (67) Γ S Γ S = V r V i = V (0) V (0) + = Z 11 Z 11 + (68) Z 11 Z 11 = V (0) (69) (61) R R 2 Z in (60) (60) V (l) = V i e jβl + V r e jβl (70) I(l) = 1 (V i e jβl V r e jβl ) (71) ( R 2 1)V i e jβl = R 2 + 1)V r e jβl (72) Γ L Γ L = V re jβl V i e jβl = R 2 R 2 + (73) Z 11 = Γ S = 0 Z 11 (61) R R 2 Z in R 2 = R 2 R 2 = Γ L V in R 2 Z 11 R 1 3.4 9 V (x, t) (22) V (x, t) = V i e jβx+jωt + V r e jβx+jωt (74) γ = jβ (73) V r e jβl V r e jβl = Γ L V i e jβl (75) (74) V (x, t) = V i e jβx+jωt + Γ L V i e jβx+jωt = V i e jβl e jβ(x l)+jωt + Γ L V i e jβl e jβ(x l)+jωt (76) 1 2 1 V i e jβl e jβ(x l)+jωt = (1 Γ L )V i e jβl e jβ(x l)+jωt + Γ L V i e jβl e jβ(x l)+jωt (77) 10

1 x = l R 2 2 (76) 2 β = ω L 0 C 0 V stand = Re[Γ L V i e jβl e jβ(x l)+jωt +Γ L V i e jβl e jβ(x l)+jωt ] = 2Γ L V i cos{ω L 0 C 0 (x l)} cos{ω(t L 0 C 0 l)} (78) 2 Γ L V i cos{ω L 0 C 0 (x l)} x 3 x V real (x, t) R 2 V real (x, t) = (1 Γ L )V i cos ω(t L 0 C 0 x) + 2Γ L V i cos{ω L 0 C 0 (x l)} cos{ω(t L 0 C 0 l)} (79) x = 0 x = l V real (x, t) V max V min V max V min (76) x (76) Re[V i e jβx+jωt + Γ L V i e jβx+jωt ] = V i cos(ωt βx) + Γ L V i cos(ωt + βx) (80) cos(x 1 + x 2 ) = cos x 1 cos x 2 sin x 1 sin x 2 sin(x 1 + x 2 ) = sin x 1 cos x 2 + cos x 1 sin x 2 V i cos(ωt βx) + Γ L V i cos(ωt + βx) = V i (cos ωt cos βx + sin ωt sin βx) + Γ L V i (cos ωt cos βx sin ωt sin βx) = V i (1 + Γ L ) cos βx cos ωt + V i (1 Γ L ) sin βx sin ωt = V i (1 + Γ L ) 2 cos 2 βx + (1 Γ L ) 2 sin 2 βx sin(ωt + θ) = V i 1 + 2 cos 2βx + Γ 2 L sin(ωt + θ) (81) θ θ = tan 1 (1 + Γ L) cos βx (1 Γ L ) sin βx (82) (81) cos 2βx x 1 1 V max = V i ( ) (83) V min = V i ( ) (84) ρ ρ = V max = 1 + Γ L V min 1 Γ L (85) 3 = L 0/C 0 Γ L 11

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