U=umej(wt-kr)
um = umju ; r - ; k ,
k=w/c=2π/λ
λ .
, It. I, It , T . . .
v .
() () :
z=E/H
u=p u=E , *:
i-^^-^-^^ w
|
. I*U*Z* I* = U*/Z* (6.25)
LI=LU+LZ
** .
LI=101gI/I*, *(6.26)
LU=201gu/*; LZ=101gz/z* I,U,Z.
,
Lit, i- . , Lt,
LIE=LI+101gn
, :
=I/IH
I r W, Ω; I= W/(4πr2) . , ø φ, φ= φ(ø). =(ø). , :
(6.23) k fc, k:
γ δ . um (δ) = umeδr a :
|
|
r
δ = 8,686δ , .
Wx =I*Se (6.28) :
Se Lw=101gW/W* W*:
, . (6.29) , . . , , . , , . 101g .
6.7. , /
- | , | ||||||
,% | |||||||
0.8 | 1,5 | 3,8 | 12,1 | ||||
0,4 | 1,3 | 2,8 | 4,9 | ||||
0,2 | 0,9 | 2,7 | 5,5 | 9,7 |
δ , , . , +20 , δ . 6.7. , , δ≈0 (. ). , (, , . .), (, , . .), (, , , . .), (, , . .) eS(i)
i- . (S = 0), :
. , W=Wg , 1g
d V ck=WgdK 4. , dQ = d5fcos6/r2 , d^ == w^cosOd V(\S/^nr1. 9 d^=" AinOdOdcpdr d*? :
,
Ig=Wgc/4=I/4
, I . I = cw, w . .
|
|
I . , (, , , . .). , , , , .
, , , , .
W (. 6.38) w Wg : W = w + Wg. ,
I=I+4Ig
(6.28). Ig . . W pW, pW/S. , αIg. , W/S=αIg. , . (6.32)
. 6.38.
, , (1α)/α, α .
. , , , . , ( ), . , , , , . . . : , ().
: W- + W˜ = W+. , : , ; . j j:[um]j=[um]. : W= IS, (6.25). (. 6.39)
W , U , , , , , a z k = Zk/Sk (k = /, ).
i , [u,n]i == ^ + "w :
[Urn]} == . Ry ' (/, j) /:
|
|
= 1 + 7?, Ry = Rj,. I +1, 0 2 . (S, = Sj) (6.34) , ^ ^, to == ^) ^ \/S (k = /, /). :
. . , , , . . . Ry t{j. (6.34). R ,
U+ U - ; U .
, 1 (. 6.40) h, 2, , S1 = S2 = S3. , Z1, Z2, Z3 2 h , h . (7, 2) 7 (6.34). +^- U, : U= Rum.
2 , (7, 2), 2 2, 2, U, \ = ^^+- (2, 3) 2 , ^ == ^R^T^e'2^ J. = ^^^ hu-^m. , 7: ^ =2l7l2723^-2u^4m, (7, 2^ 2 us = rzi ^"3^-* /. (1, 2 2, 3)
. 6.39.
. 6.40.
, 7 ,
,
3 , .
, (6.35) :
(6.34) R :
|
|
zi2 = / 02 = o/q. , ,
, ^ ^ . (6.36) (6.37) :
R : = . 2, = 2,
:
= . + + <?., (6.40)
f. ^
^ = (201g^)8A, ^ = 201g|T U = 201g|(l -2V)! , (1, 2) . h , ^ -> 0 w ek +- ^
.
L,(f) ^( (6.41)
Lp(f) = 201gp^(/)/A 1(/) . (6.41) /== 63,125, 250, 500,1000, 2000, 4000, 80000 . (6.26)
L^L-L, (6.42)
, - : = 2 10'5 , 1 = 1012 /2 = 400 /.
p:z = . == 1,29 /3 = 331 / ^ = 430 /(2 ). . 6.8 .
6.8. ,
, | ρ, /3 | , / | z= , ∙ / |
0,084 | |||
1,45 106 | |||
0,89 106 | |||
16,5 106 | |||
41,1 106 | |||
47,6 106 | |||
4900...5900 | (12...15) 106 | ||
2,94 106 | |||
11106 | |||
4,1 106 | |||
0,12∙106 | |||
( | 0,72 106 | ||
) |
. ^ = 400 / , , , 0,9 105 (675 . .) 27 1,013 1015 +38,8 . 2^= lOlg^* , , Lp(f) = Z//).
, (6.29), (6.30), (6.33).
(6.33),
. 6.41.
Z/(, ) , Q B=aS/(l ), S ; ^5 (, (6.29), , S(r) == 4^. (). ( = 2), . Q : = 2 -; = ; Q == /2 , . = (W/ ^)/(W/4nr1) = 4w/Q.
|
|
(6.43) , > 24> ^ .
^ (. . 6.41), (6.43) r= /\i. L^ .
(6.43) , , , . (6.43) , , , (, <, 0,95, = 1,2). : /== 63... 1000 == , . 6.9; /= 2000...8000 : = 1(1oio)exp(25/), 6 . 6.7,
1= 4 V/ Si.
6.9
, f, | ||||||||
- | 0,07 | 0,08 | 0,08 | 0,08 | 0,08 | 0,08 | 0,09 | 0,09 |
, - | ||||||||
0,10 | 0.10 | 0.10 | 0,11 | 0,12 | 0.12 | 0,12 | 0,12 | |
- | ||||||||
; | ||||||||
- | ||||||||
- | 0,11 | 0,11 | 0,12 | 0,13 | 0,14 | 0,14 | 0,14 | 0,14 |
, | ||||||||
, - | ||||||||
, | ||||||||
. 6.9. , (6.43) :
Wf , /-, */ a/; Sa == ^ /*/ i - (i = 1, ).
(6.32) , 41//= ^. , ^ < 1 (. . ), , , ^ > 1 (. . , ), . % = 1 ^ , = = ^/(161) (. . 6.41) ^ (6.43) (^=0):
lj (, ) - L() = Z.+ ioig(4.y / ). (6.44)
. , , , , .
, , , . , . , , , . 6.42, . (. 6.42, ). ( , , ), , . , , , . (. 6.42, ).
, . , , . , , (. (6.18), , . ^ = 0 R = 1. , .
. 6.42. :
; ; ; ,
, ( 6.42, ), . .
, , , , , .
, 250, 500, 1000, 2000 , : 0,2; 0,3; 0,4; 0,5.
== (-5/(1), == (1 ) : kw = In(r, B)/In{r, ), :. /
= lOlgA^ = L^ (. ) Zi(r, ), (6.45)
Z/ (r,B) L^ (r, ) ^ (6.43).
5,
, . == *== '(*Ӗ)4- + a"S^ ' " (S iS) S^ Sa ^dS^a^SS^) + ^. == (" a^S^/Su , aS a"S^ = Sa(*)/S, *(*) = = ^ . &(*)= ^ + ^ Sa.(i)fii, Sa(i} I /- , // . < (6.44) (6.45) , :
e=lOig£/R
(6.43), : L//r, ) ^ L. , ... 8 ( 10... 12 ).
. , () . , . , , , , , . . h (6.39). , . . (6.39) jka, kz = / ,
= 1 Olg[cos2^ 4- 0,25feAi + Zi/^ )2sm2^2A], (6.46)
Zi == pi^i ; ^ = .
(6.46) , ==/^2/2, . . (= 0, 1, 2...), , h = (2 + 1)2/4.
, , piCi , (h^ ^2/271) (6.46)
^=101g[l+(wo)/2pici)2], (6.47)
== ( , ).
(6.47) :
= 20 Ig-^ = 20 lg(w/)const. (6M) 2piCi
(6.48), , , . / , (6.48), , . / /2 , 47,5 .
.
<?= 10 lgl/ == 10 IgW^/y = Lw^Lw. (6.49)
, , W, 1, , , , 2. t , 1, W/[S\(r)} ^ = wib\
S^ 1, 2, W^ = -/ (6.50) :
Lw" , , (6.43), 1^(, ) ^ L^ (e^O)
| Lw ^ zhio ^[/ + 45^]. (6.52)
(6.49) (6.51) (6.52), :
, 7, (. 6.43, ), 2 ( ), S^ = 5'i(r)= 5p (6.53)
. 6.43, 7, , 2 , , 5. , 2 (. . 2?2/(452()) 1), (6.53)
*\ . 6.43, , , 7. , . (6.53) ,
. 6.43. :
; ;
. 6.44.
(. 6.44) . .
N ; N=£2(a^-bd)/'k ( N >: 0,2). , 0. , = 0. ( + ) . , ( d). , , .
, , (, ), . (, , .) () , . .
, ^; 1\ , /2 , ^. (6.49), , W^ , IV . . , .
S (. 6.45, ) W, , , (6.31) / = W/^S. , -" Pdl ( ) dW= oL^PdIn 1,09.
. 6.45. :
; ,
, , . . 6.45, , , ( ). . , - , CD, .
(. 6.46) (), S\ So, /. . (6.46), [. (6.34)] h / (h = k = /):
, kl -> 0 V2, X,, /2 . ., , . Sh. pc/Sz wpc/&, - , . . /. , . , \ , ( dzd\ = V2, 3V2, 5V2 . .).
. 6.46. : ; |
. (. 6.47).
. 6.48 , , , , . . , .
, . : (. 6.49). , . -. . , 1/10 . , . , . .
. 6.47. |
; (3 = s\c/it^v ; *Si sq ;^ ; V . (f^fo)
e=20lg[(α+0,5)/α]
< 0,25 f
. 6.50 = 0,5.
, , :
i- .
. 6.49. : ;
. 6.50. α = 0,5
*. , () :
, , . , 109 106 , , 0,3 300 .
: r > e2 / λ r > 3/λ, l . , :
ε*=ε-jς/ω ; ε μ. ;ς ; k*= ω√με*.
(6.24) (6.54), , z = √με*. (6.54) , ς = 0)
(ε = 0)
, .
. 6.10
. Z0 = √μ∕ε120π,, μ εo so : ε = 1/(36π∙10-9)=8,85 10-12 / μ = 4 10'7 /. .
6.10. ,
μ/μ | ||||
ς 106. / | │*│=√ωμς, '1 | │Z│=√ω∕μς | ||
57,1 | 21,210'7√f | 0,372 10'6 √f | ||
34.5 | 16,4.10'3 √f | 0,478 10"6 √f | ||
7,2 | 75,4. 10'3 √f | 10,47 10'6 √f | ||
4,8 | 6,2 10'3 √f | 1.28 10'6 √f |
, .
Z=Z0(1+jkr+1/jkr)(1+jkr), (6.57)
Z=Z0(1+1/jkr)/(1+jkr+1/jkr), (6.58)
(6.57) (6.58) , , . . ( kr 1),
Z=ZE≈Z/jkr (6.59)
Z=ZH≈jk/Z0 (6.60)
ZE , ZH (. 6.51). , Z=ZEH=Z0.
, ( ) . , , (6.39),
E=20lg│chk*h│+20lg│1+0,5(Z2/Z1+Z1/Z2)thk*h│
, h k* Z1 Z2. , (6.27) (6.56) k* Z2 : k* = √jwμ2ς2. Z1.
. 6.51. :
( μ≈μ0, ε≈ε) Z1=ZEH=√μ1/ε1≈√μ0ε0≈ 377 . Z1 |. (6.59) (6.60)]. (. 6.52). Z1
Z1=Z1E=Z*/jkr*m=1/jωε1r*m
Z1 = Z1H=jk1r*mZ*=jωμ1r*m,
= 2 r* = l/2 ; = 1 r* = ; = 1/√z r* = r (. . 6.52).
k*h, (f< 104 ), chk*h ≈ 1, a thk*h ≈k*h (Z1E/Z2>Z2/Z1H)
. 6.52.
, → 0.
, . (, , )Z1/Z2H>Z1H/Z2, (, , ) Z1H/Z2 > Z2/Z1H. .
. .
ω→0 .
(104 <f, < 109) *
, [ (6.38)] Tn, T c Z1>Z2 : Tn:T:T = 1:2:3. , , (l = 2r 2p). , en = 20lg1/Tn, = 201g |1/T| = 201g|l/Tn| = en20 lg 2 ≈ 6 , e= en9,5 . (Z2>Z1) n::e = 1:1/2:1/3. , , .
, , (f ^ 109...1010 ), λ d, . . λ≥ d, (. 6.53). Z1
. 6.53. :
; ; h1 - 0,01, h2 = 0,001, r = 5
:
(6.63) |
Jn(u () * , ( ). (5.63) (6.61), , Z1/Z2<<1 .
, ,
(6.64) |
Z1 = Z1H ; Z1≈Z1H ; | Z2│ =│ ωμ2σ2│; = 2πh/l
r*=0,62V1/3 (V ); l () ; k1=ω√μ0ε0. (6.64) , kl < 2, l > 0.
, . , , .
=10lg│ZE/Z│+A+8,686C
* 1() : H1 () = J1(u) + jY(u). , : Q1(Z) = Q0(u)1/2Q(u), Y, . [6.1].
, (6.64) (k1l< 2), z d s : = π d/(sd), z =l/G2h*, L*=πd2/4s.
0,01...0,05 ,