2. O

2.1.

, (, , ), , , , . , .

, () . .

. ( 2.1). . , . , ( ), . . , , , .

14

(Stripline)

(Microstrip line)

(Slotline)

(Suspended-substrate stripline)

(Coplanar line)

(Coplanar waveguide)

U (Ridge waveguide)

H (Double-ridge

waveguide)

-

()

2.1. .

2. 15

( ), . , , , . , . , .

( ). . , . 4. 2.1 , , , , , , , U- H-.

2.2. , , ,

, ( ). :

HE = jrot , (2.1) EJH j+=rot , (2.2)

0=div E , (2.3) 0=div H , (2.4)

E , H , . , .

(2.3) (2.4) (2.2), (2.1), .

, . , , (2.1)(2.4) ( ). z- (. , 2.1), 2.2. x y ( ) . , .

16

,

zy

x

2.2.

.

, , () . (2.1), (2.2) :

EE 2=rotrot . (2.5)

EEE divgrad=rotrot , (2.6) = , (2.4)

EE 2k= , (2.7)

=k . (2.8) (2.7) . ,

HH 2k= . (2.9) , (2.7) (2.9) , E H (2.1) (2.2).

(2.1)(2.4) ( 2.3):

0=En , (2.10) s= JHn , (2.11)

s=En , (2.12) 0=Hn , (2.13)

n , sJ , s . (2.10).

2. 17

sJ

, n ED

, HB,

s

2.3. .

, (). : (, z-) , ( z-), .

zt zi

+= . (2.14)

( zyx zyxiii

++

= .) , , +z-. (

z-.) z- )exp( z , += j . , , )exp()0,,(),,( zyxzyx = EE

)exp()0,,(),,( zyxzyx = HH . 1/m. , , ( Np/m), , , ( rad/m).

z ,

zt i= . (2.15) E H ,

zzt E iEE += , zzt H iHH += . (2.16) (2.1)

.)(j)()()()(rot

zzt

zzztzzztttzztztH

EEEiH

iiEiiEiEiEE+=

+=+==

(2.17)

zi E , , (2.17)

ttzzzt E HEii = j)( , (2.18) zztt H iE = j . (2.19)

ttzzzt H EHii = j)( , (2.20)

18

zztt E iH = j , (2.21) 0= ztt EE , (2.22) 0= ztt HH . (2.23)

(2.18) (2.20), )(j zztttz E iHEi = , (2.24) )(j zzttzt H iHiE =+ . (2.25)

ztzzztzzt EEE == iii )()( , , ztzzzt HH = ii )( . (2.24) , , zi . ( ) ( ) ( ) tzzttzztzz EiiEEiiEii == ,

zttzt E= HiE j . (2.26) )j( (2.25)

ztzztt HEk +=+ iE j)( 22 . (2.27) (2.24) (2.25) tE ,

ztzztt EHk +=+ iH j)( 22 . (2.28) (2.16) 22 +=== t ,

ttt = , , , 0)( 22 =++ zzt EkE , (2.29) 0)( 22 =++ zzt HkH . (2.30)

(2.19), (2.21) (2.27)(2.30) .

, , , 022 =+ k 022 + k . , , .

2.2.1.

0=zE 0=zH . (2.27) (2.28) 022 =+ k , == j2 , . , , ( ). , (. ). (2.24) (2.25)

2. 19

ttz EHi = j , (2.31) ttz HEi = j , (2.32)

, , /=j=j . (2.31) (2.32) E H ( tt HHEE == , !) , . ,

=TEMZ , (2.33)

. ( , , .) , (2.31) (2.32) :

TEMZHE

HE

x

y

y

x == . (2.34)

0= tt E , (2.35) 0= tt E , (2.36)

( 0= z , ). , (. ), . , z- )exp( z , ( ), z .

, , (Q') , .

0'1

==

N

iiQ , (2.37)

N . , . (2.11) (2.12), (2.31) (2.32)

zJss = (2.38) ( sJ z-), ,

20

01

==

N

iiI . (2.39)

, (2.39) , .

(2.18)(2.23) (2.21) (2.23), 0= tt H 0= tt H . , , (2.32) (2.35) (2.36).

2.2.2. ,

0=zE 0zH , ( ), H . 0zE 0=zH , ( ), E . , 0zE 0zH , , EH HE , . 022 + k . , , . .

222 kK += . , (2.27) (2.28),

ztzt HK

= iE 2j , (2.40)

ztt HK

= 2H . (2.41) (2.40) (2.41) ( tE tH ) ( zH ). , , (2.30),

02 =+ zzt HKH , (2.42) . 2K ( ). () , , . z- )exp( z ,

)exp()0,,(),,( zyxHzyxH zz = . (2.43)

2. 21

)0,,( yxH z ( x y , , ). )0,,( yxH z

2K . , 2K , k .

(2.40) (2.41)

tzt HiE = j , (2.44)

tzt EiH =

j. (2.45)

tE tH , . ,

= jTEZ , (2.46)

.

ztt EK

= 2E , (2.47)

ztzt EK

= iH 2j , (2.48)

02 =+ zzt EKE , (2.49) zE

)exp()0,,(),,( zyxEzyxE zz = . (2.50) )0,,( yxEz

2K .

(2.47) (2.48)

tzt HiE =

j, (2.51)

tzt EiH = j , (2.52)

=

jTMZ . (2.53)

22

2222 j KkK == . (2.54) 2K , (2.42) (2.49) . 2K . (2.54) 022 > K , 022

2. 23

2c

oo

o

1

=

ff

cc (2.58)

2c

oo

og

1

=

ff

. (2.59)

c , oc , g , o . , 1r = 1r = , g o . , .

. . .

0=z ( )ttAttAta )cos()cos(

21coscos)0,( mm ++== , (2.60)

, (

24

( ).

2c

g 1

=

ffcc , (2.66)

c (2.58).

rr

2o

g =ccc . (2.67)

. , . , , . 2.4 .

( ), , . , , , , , .

2 3 410

cff

gc

c

rr

0

c

2.4. ( c ) ( gc )

( cff ).

,

rrc

o

cc

1== f

cf

. (2.68)

, . (2.59) (2.68)

2. 25

2c

2g

2o

rr 11+=

. (2.69)

:

2c

TEMTE

1

=

ff

ZZ , (2.70)

2c

TEMTE 1

=

ffZZ . (2.71)

cff < ,

12

c

==

ff . (2.72)

cff ), .

. , , . , ( ), . , , cff > , += j , )exp( z . (2.74) )2exp( z .

26

)2exp()0()( zPzP tt = , (2.75)

)(2)2exp()0(2dd'gub zPzPzPP ttt === , (2.76)

gub'P . (2.76)

tPP2'gub= . (2.77)

, ,

dpgub ''' PPP += , (2.78) p'P , d'P . ,

PP

PP

2'

2' dp

dp +=+= , (2.79) , .

, . .

ppppp j)1(j +== f , (2.80) p p , f . ,

pp f . (=2,7182818...) , ppp 1 = f . :

( ) MHz][Cu m66 f= .

p

p

p

pTEMp j)1(

j

+== fZ . (2.81)

,

p

ps

= fR . (2.82)

( )= ps 1R . (.

)

2. 27

( ) 2tgsp *Redd

HnHE RSP == , (2.83)

( ) nHE * ( 2.3), tgH .

=p

d'2

tgspC

lRP H , (2.84)

pC ,

( )tpp 2' PP= . (

) ( ).

"j'e = , " .

( )( ) EEEEEJH ed jj+jj+=j+=rot == , (2.85) d ,

( ) ( )== dde "+j'j+ , (2.86) , . ( ) ''Re ee == , ( ) ( ) =+== edee ""Im , e . '/"tan d = .

. , d'P , ,

2ed dd E=vP ,

=t

d' 2edS

SP E . (2.87)

tEE = , , (2.76),

d

2

Ted

d tan2'

22'

=== ZP

P

t, (2.88)

,

de

d tan2'2=

= , (2.89)

28

=

=

2c

d2

c

ed

12

tan

1

1'2

ff

ff

. (2.90)

, , , (2.90) .

, e .

2e

222e

2 j' KK ++=+= . (2.91) ,

2c

2c

e22

e22 1'j

1

1'2'

j1'j

+

=ff

ffK

K . (2.92)

, , . ( , ), , , "j'e = , " . .

2.4.

( , , ), . .

(2.1)(2.8) , . , . (2.10)(2.13), ( )

021 = EnEn , (2.93) 021 = HnHn , (2.94)

02211 = EnEn , (2.95)

2. 29

02211 = HnHn , (2.96) n , , 1 1 , 2 2 .

, . , . , .

, . . . 2.2.1, = j . , , . .

, , . , ,

tzE E

30

, :

xy H

zE

oj= . (2.99)

z-, )jexp( z ,

11 j y

y Ez

E =

, 12

12 j yy Ez

E=

. (2.100)

z

Ez

E yy

21 (2.99) .

, ( zE ), .

xyz H

zE

yE

oj=

. (2.101)

zE zEy

. (2.93), zE ( 21 zz EE = ), (2.10), ( dy = ).

, zE y, , ,

0,o > y

dE

yE zz , (2.102)

0,o

2. 31

, . , , , .

, , . , , . , .