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@2 @2 @ = + + @x2 @y2 @z1 @ @ 1 @2 @ = r + + :

r @r @r r2 @ @z1.7. - x E .

, , z, z x0z (..), y H jkz Ex = A e;jkz + B e Ey = Ez = Hx = r r " " jkz Hy = A e;jkz ; B e Hz = p 1 @Ex k = ! " Hy = ;.

j! @z , p v =1= ".

, . Ex = A e;jkz r " Hy = A e;jkz :

r Ex = = Hy " . . " . " , .

.

1 (..):

Ex = e;jk z r "1 z 1 Hy = e;jk z = e;jk z:

1 , r "1 jk1 z R jk1 z jk1 z Ex = R e Hy = ; R e = ; e :

1 r "2 T 2 2 Ex = T e;jk z Hy = T e;jk z = e;jk z:

2 R T. { Ex Hy { . z = 0 Ex Hy , 1 1 + R = T (1 ; R) = T:

1 R T:

;

2 R = + 2 2 T = :

+ 2 ! 0, jRj ! 1, jTj ! 0,.. . , , . , = "1 = "0, "2 ;j, 1 ! "0. r r r j! 2 ! = = = (1 + j) :

"2 r p p ! (1 ; j) k2 = ! "2 = ;j ! = (1 ; j) = :

2 z z z ;j (1;j) ; ;j e = e e :

r = ! 2 (-).

Ex = Hx:

, , .

, . . j" j "0, . Ex Hy . Et = Ht . :

~ ~ Et = (H ~ n) ~ { .

n . -, - , .

. - .

(.. -) "0 :

! , , "0. ! :

5:7 = 5:7 107 ! = = 36 = 6:4 1018 ; 1:

"0 10;f 1018, = 3 10; 8 . , .

! 1, ! 0, Et = 0. . Bn , Bn = 0 ( Hn = 0) . Ht , . , K = Ht . ~ ~ K = H ~ n:

, . , :

Z ~ ~ K = J dz z . , Ht = K . , ~ ~ ~ ~ rot H = j!"E + J J:

~ H y- . @Hy ~ Jx = rot H = ; :

x @z Jx , 1 Z Z @Hy Kx = Jx dz = ; dz = ; Hy = Hy = Ht:

@z 0 z=0 , ~ ~ K = H ~ n:

~ ~ ~ E = H ~ = K:

n , r ! 1 + j = (1 + j) = . , , .

() . ~ ~ P1 = Re (E H) ~ n:

~ ~ E = (H ~ n) h i 1 ~ ~ P1 = Re (H ~ H ~ = Re j Hjn) n 2 1 P1 = jHtj2 = jKj2.. K . , , , 111111111 , (.

111111111 ). , , K .

1.8. . .

, . , , ~ ~ ~ ~ rot E = ; j! H rot H = j!"E .

l = l0 L L { , l0 { . , ~ ~ ~ ~ E = e0 E H = h0 H ~ ~ e0 h0 { , E H { .

, h0 ~ e0 ~ ~ ~ Rot E = ; j! l0 H Rot H = j!" l0 E e0 h Rot .

{ h0 ea1 = ! l0 a2 = !"le0 h .

e0 h0 , , a2 =1. h= !"l0:

e a1, a1 = !2 " l0 = idem:

!2 " = k2 = l= idem:

r ! 1 + j Et = (1 + j) Ht Et = Ht:

, 1 + j h0 ~ ~ Et = Ht:

eh = !" l0, e!"l0 ~ ~ Et = (1 + j) Ht:

!"l= idem:

! =, { , !2 "l = !2 " l0 :

! l a1 = !2 "l0 = idem, = idem:

l = 1, = idem:

l2. 2.1. , z. , . . , z e; z,.. , z.

~ ~ rot E = ;j! H ~ ~ rot H = j!"E:

, . ,.. Hz = 0 Ez = 0. , , @=@z = ;, :

;j! Hx = Ey j!"Ex = Hy ;j! Hy = ; Ex j!"Ey = ; Hx @Ey @Ex @Hy @Hx 0 = ; 0 = ; :

@x @y @x @y :

Ey + j! Hx = 0 Ex ; j! Hy = j!"Ey + Hx = 0 j!"Ex ; Hy = 0:

| , . , . , , :

+ !2 " = 0 :

:

p = j! " = jk :

" { , { .

, :

r r Ex Ey = = ; :

Hy " Hx " @Hy=@x ; @Hx=@y =0 Hx Hy Ex Ey , @Ex @Ey @Ey @Ex + = 0 ; = 0:

@x @y @x @y , @ @ Ex = ; e; z Ey = ; e; z @x @y { x y. , @2 @+ = 0:

@x2 @y~ , E ~ E = ; e; z grad = { .

~ E (Et = 0 , =const).

, , ,, , . . -, - . . , , ( ), , . , | , .

( TEM) p. TEM : v =1= ".

0 1.

, :

~ ~ H = ; rot E:

j! ~ E, ~ ~ ~ rot ( F) = rot F + grad F, r " ~ ~ E = ; grad e; z H = ; e; z ~ grad :

z ~ { z.

z~ , , E ~ H .

2.2. , TEM- TEM | , Z ~ U = ; E d~ l 1 2 , , . .

, , . , I ~ I = H d~ l , , . , I .

, TEM- , , , , , , , . :

U = U0 e;jkz I = I0 e;jkz :

U UZ0 = = I I .

, TEM Z0 { ,.. U I .

= + j 1 | . 1 = = const . , , , . , 1 ~ z E = ;grad e;jkz . r r Ex Ey = = ;

Hy " Hx " ~ H z , ~ E. U I , U I .

U=I = Z0 { .

TEM. , r r " " Hx = ; Ey Hy = Ex:

" " 2 2 2 Hx + Hy = (Ex + Ey ) = E2:

, H2 "E= 2 TEM- . .

TEM- C1 L1 2We = C1jUj2Wh = L1j Ij We Wh { . , Wh = We, C1 j Uj2 = L1jIj r U L= Z0 = :

I C , TEM-:

Z ~ ~ P = Re (E H ) ~ dS zS.. S. r r r " " " ~ ~ ~ ~ ~ ~ ~ (E H ) ~ = ExEx + EyEy = jEj :

z , r Z Z 1 " 1 "EP = jEj2 dS = dS = p 2 " S S = 2vWe = 2vWh = v (We + Wh) = vW W { , v { .

, :

v = p :

L1 C , r 1 1 1 C1 1 jUjP = p C1 jUj2 = jUj2 = L1C1 2 2 L1 2 Z r 1 1 1 L1 P = p L1jIj = jIj2 = jIj2Z0:

L1C1 2 2 C1 P = Re U I :

2.3. TEM , (..).

r :

2 U r 1111 = ln r1 rrln r U { . @ U 1 U=r Er = ; = ; = @r r1 r rln ln r2 rr r " " U=r H' = Er = :

rln r r " U I = 2 r1 Hr=r = 2 :

rln r :

r U 1 rZ0 = = ln :

I 2 " r , r 1 r2 r2 rZ0 = ln = 60 ln = 138 lg :

2 "0 r1 r1 r . :

r L1 Z0 = v = p :

CL1C 1 Z0 C1 = L1 = :

vZ0 v v Z0, 2 " r2 C1 = L1 = ln :

r2 2 r1 ln r , , , , . , .

2.4. , .

111111111111 x , E H b TEM-.

y a b. a . U = b Ex I = a Hy .

r U b Ex b Z0 = = = :

I a Hy a " 1 a Z0 b C1 = = "0 L1 = = :

vZ0 b v a 2.5. , . " 2 C1 = :

s 00 11 00 11 b b ln + ; a 11 00 2a 2a b a :

b " C1 :

ln b=a , :

r 1 1 b Z0 = = ln :

vC1 " a 2.6. TEM , . , (.

.).

dz Z dz 1 U U+dU I I+dI Y1 dz :

dU = ; I Z1dz dI = ; UY1 dz dU dI = ; IZ1 = ; UY1 :

dz dz , , I:

d2U ; Z1Y1 U = 0:

dz = Z1Y1, d2U ; U = 0:

dz U = Ae; z + Be z.. , . :

1 dU I = ; = A e; z ; B e z:

Z1 dz Z1 Z r Z1 Z1 ZZ0 = = p = YZ1Y , . , Z1 = j!L1 Y1 = j!C, p p = ;!2L1C1 = j! L1C1 = jk:

! v = = p k L1 C :

r LZ0 = :

C U = U + U I = I ; I = (U ; U) Z Z0 { . , , :

1 1 P = Re (UI ) = Re (U + U) (U ; U) = 2 2 Z1 = Re (UU ; UU + UU ; UU) = 2 Z1 jUj2 1 jUj= ; = P ; P 2 Z0 2 Z.. . 1 jUjP = 2 Z . , Z0 { (, ).

2.7. . , (..).

, U , I . Z Z0, , .

, U=I = Z . U = U + U I = (U ; U), :

ZU + U Z0 = Z U ; U U + U Z = :

U ; U ZU , =; (; { ), U 1 + ; Z = 1 ; ; Z, ;, Z ; Z; = :

Z + Z :

jkz U = Ue;jkz + U e U U { ( ) (..).

:

2jkz U = e;jkz (U + U e ) :

2jkz U U e . U U , U . :

U = jUj + jUj :

,.. z = =4, :

U = jUj ; jUj:

U z (..). jUj + jUj 1 + j;j = = j Uj ; jUj 1 ; j;j (), . = 1, = 1. , , , .

2.8. , l, Z. z jkz U(z) = Ae;jkz + Be jkz I(z) = (Ae;jkz ; Be ):

Z A B ( z = l) jkl U(l) = Ae;jkl + Be jkl I(l) = (Ae;jkl ; Be ):

Z A B, :

U(l) + Z0 I(l) jkl A = e U(l) ; Z0 I(l) B = e;jkl:

(z = 0):

U(0) = A + B = U(l) cos kl + jZ0 I(l) sin kl 1 j I(0) = (A ; B) = U(l) sin kl + I(l) cos kl:

Z0 Z , Z(l):

U (0) U(l) cos kl + jZ0 I(l) sin kl Z (0) = = = I(0) j U(l) sin kl + I(l) cos kl ZZ(l) + jZ0 tg kl = Z0 :

Z0 + jZ(l) tg kl , Z(l) + jZ0 tg kl Z(0) = Z0 :

Z0 + jZ(l) tg kl 2.8.1. Z(l) = Z = 0. Z = jZ0 tg kl = jX ;0 = ; 1:

.

X l |U| |I| l 1. (2n + 1) =4 . =4.

n =4 . =4, , .

= H Z 2.8.2. Z = 1 (..). Z = ; jZ0 ctg kl ;1 = +1:

X l |I| |U| l 2.8.3. , Z = R (.. ..):

R + jZ0 tg kl Z = Z0 :

Z0 + jR tg kl l =2n =4 Z = R l =(2n +1) =4 Z = Z0 =R.

, R Z0 . R Z0 =R.

= H Z Z0 ZR R R R |U| R > Z > |I| 2 Z0 ZRR R R |I| R < Z < |U| 2.8.4. , Z = jX (.. ..). X + Z0 tg kl Z = jZ0 :

Z0 ; X tg kl :

X + tg kl ZZ = jZ0 = jZ0 tg(kl + ') X 1 ; tg kl ZX ' = arctg, ; '.

Z0 2 , '. , 1 0 , =4. X. X { , , =4, =2 X , , =4.

X > |U| || = l |I| X < |I| || = l |U| 2.9. .

2.9.1. kl =, tg kl =0. Z = Z:

, 1. .

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