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D l - tJ ' V
p .6 -2
/2 6 -3
E,:a+#;.4 Zrr=f E,,t l-J1
cl tvL: - #'-PAoto's ' Vr=-jt$,
:
lL- : = Yi, : - J-@E"ih- r, 0*i)--a ,1+ju>L Zq (p+)'ul) .
WsT/n-r<. -:G.ry ing /-i"lJ,
ancJ Mo.xwe/ l ' s Equa, ' / ions
t: -I#'o'rJ
- -{*(vxi) 'a;5: -,f # dz
/j =d- 3 cc,s (unro"t - iny), /o-€ ( rl.
f a.u ' l : [o ' t -us re c<r3 <os (sr icz+-lrgtt :(4o./dy)
a < t f - . T
?: - vr Lrt"
( 5rr /a't -o. /n) _s in grro?t lxni'(wt).
ar : ftJF ./F :a. sft:or(;rto"t-o.trr)-cotrnrdf, u).
- 1 / t ^
. ^ r - - r .i : f i : 0 . /g lcos(sr to?t-o. / r ) -c-os g2,rc71
- - 0 .6L3 s i n ( rn to l t -a .orT) CA)= 73 = in f 9-rr tort - 1" ) (nA).
Lts ig photor wi th a s /ne r " f , " ten<e,
fioz,A f "'!,Zr Jd
-7-
4#1"(t +yS.
F. e -+ ; = &L-.b , - - 4 r - z ? t .
TrJuced emJ ' i , t /a ,o1 ' : - f ( i l t x E , ) ' JL- r .
----7 U -- !';'#'-'(* - #*)'
- L* ,
l/L- - _ : _
in a- c/o"k,'vise. J,'r.c-*'on
H t ; ! ^ I t t o t 7R- 2nd(4+-,r)
a. ) LF L :O:. t
, , , ( . = V
(ux ! ) . gaoo . t )
: * ( r cn^o ,o4 )xo . / s i n , J t
= 0 .251 s i n / oo? t t (A ) -
b ) j { L : o .oo3E (H ) :t t t L = l O O " t x O . o o 3 g : i . { ( t ) ,
)
O,.',x /o ( w't).
, dl tD.
rc"tf
I
P e -e
/{u:qT:. (/oT x ao4)fo! = in (qtt _ 6 9. {")t, : *---7J67-
: o, to+ -sin (toov; - 49.6") 6).
t t207 / '6e . ! : '
It-)
E : Ec+l ' Stt l --9 c.,s cat x QL (o.?-z-): -Cas ta{ [o. 7 - o. t t(/ - e-us ,^rt )J- -O.39 cos c , : t ( 1+ c -os u t ) ( ,u t ) .
. / dA It - -
z * : -
t o 'zsoo( 'srn r i t +sir t2ut)
- - / .7 t d (s in A t + s t ' n Tas t )
: - / -?q u S in a t ( t + 2 asd t ) ( * f t \ .
3?
P e -z
P <-g
b) .f ,,
\a.)
COndretion Current 4en-s,4y: rE
-D i sp{--ce^m.r# c., rrenf den-si *y : S' uD -J utgf,-E
f or eTua/ tn agni /u4e : f = 2zr€o€rf ,
o r f : ^ 5_^= o / r \
2r/ (€o€,,) = /9 x to' ( +) (/Q.
S.owa1er: f : /sx/o7 (+) : /oE(,1) : / (a l )
Moisf .sc, i | : f : /s x /o? ( j9 :Ztx/06(Ho),or Z z (Mllz).
I 7 \ ' ,| 0 isp lacemert <urrer tI
I Coaduc-*ion czrrent= (zT"loottoetr=bxt61
.f-7o x lo7
s o Lt rce- { rzeR - r rFa . - L ,
: q.7s x'/o-3.
Condctc fo r :
a.) u€r
4
Vx
8 u f V . F : o , E f .@ becornesV'F + rVxF:o.
Co*Aining @ a.n.l @:V"g - ]@f rF: o.
P46-1 t i , :d ;o+dr4o+drzo . g .n=8 , . * r r I r r
dn,.^ (F,- F,)=i lr,"-lni:;^"'"* z, ^ ( 4;o + dr44 - Fr):4rS .n HaE- 30 , Hr r - 4 5 .
38
V'x E :_i-f n:; /i ,-VxlD: Vx Vx lq : V (3, F)-V 'U- rVrE.
@/i.\U
o
@
a) Fr= d,3 o 3 f + a,/o (A[^) - b) 1- 2f a F2 ft).
c ) 4t- t,. i ' Jtol-9' -- 69.:o. a) "at= L;,
- / O .
--J
7if,-E
-.!FF---
)
' /- It ' ,
q*l2/
)
t n
o
P 6- to Mediro | : Fr"" tpa.. ,/{e-l iurn ^ ,
,/r*&. H, husl le zero so ,n"l ,F;.,., j ,,,11n
f z::"1,::i , d-r F,- j-,, B n: B,n.E,o: Er, , dnr. ( E- Dr) : f" .
P. 6- /3 E(" , t ) :Jo c-os(zrr /oqt - kt) 1v/^) io q. i r .
Eo -- so (v/m),
f : /o7( l l ) , T :+ : to ' "Cr) ,^:f,:+#:o.z(,I),tr':+: ?o
a) A( Z : /oo . l zg^ , k r :2oc .25r r , wh i .h i s sq rnens 4 r kz : o -257 , o r T r /4 .
Tf i -s a, p/ot tF ECt):5o c4s 2rr /o7 ( t - r /s) (v/n)
b) A f 2 = - /od . /z -gx , i { i s o . r t /o foF
EG):_ro cos 777rc7( * +r/ i l (v/ , , ) ,
c) At t- r/4, we plof ve-7ss, z ti"fo(b',,r;ogsincts oi 1 o-l 4u nc-*ion :
E (2, {): to cos G *t*qq =50 cot [- a6 -]lJ: So
"ot f f (z-o.ozs) (v/ . ) .
P.6- r+ U-te pbasors qn4 cosine- r="fere.ncz.
.€-: %Eoui*, E, :4ro^oSri tr ' rz ; Er-dro,o+d. i :A
E : E, * 1:at [o.c,3; i" /o+ o.a+; iv/21: dn t- j o. 03 + o.a+( ! -i9)J-d*0.o(,r;i7''""
-+> Eoto .068 (V/ r> , , / r : -72. { " .
37
n , - Fr 6 ' ; > L/se pna-sors a 'nc l Ca s ine r : . 'F< ' re-ncL '
- ,, ){, : t-6 b-4 €in/i 1;a+J* 6+ei1H=o* l l r , f i ) - -? ,u v
--'> Ho: /o-4 G1 * 2 d* )-- /cs-* i*.o' a+ j (z s in q - /,
-sr r r c( - I - O - -+ c<:3O] or n ' /e ( rc 'J ' )
: ZX 1g '4c -os -3oo : / . 73 ' l f a (A / - ) '
See 5e cf ion /o- L, PF'+zs-atf , f7t h-4 )
a-nC Cro-Z)
z?( GorJg23 x rcsT
1
H
,D.6- tz
P 4- /s o)
L/ ,l
= 0.4v (r*d/-),t u )/ a :T :
t l I: ar . f t61r = & l l
.) v-,/ ug
H, lar ae aa
/ =..; - -Ll z -a-= :F)E v ̂ > - */,1 u: '! az
lE, 0 0
:hd*# : 4h()L!* rto":;;*+.ikz - q#v";ioarz G/,n
r-: drffi* e
: - tA -2 np- Er
"-Jo'4r'z/2-O-lTb "
r=
tI '
(A l^)
(n/-1- lt l
v a l- l r - - b c
:+.i1
(rc,c.)
* ) .
P.6-rg
P.6-zo
t7x t r
E-l l -n-
k- +: #g - 29v' e.^a/t^).7 r - - -
, 1 , twHn
,
o-/ .sin (lorr4 t)f z. o
sin (yonx) + doo.{ ({oir) .osftow)JJ[
' In th*o, for-
f, o- Er. Q-rr)
tit ^il,sart s in e. e/'
:4#.sino ;)/z
ln lns*ao4oneou's .{or,n ,
1-1 < n, 6 ; D : * #*R--s i n s.,u' (z rr/o?t - zo n p' /) &/'t.
sin0a
F0
In pL'r*or {or-,
E:dru---:!-orr
) r/o. ?
a t -: fuLa'io'tf
f _ :L-ftoVx H
: dl #rltto,l '*pl
s;. (totrx) ;;f " @
l : , . a t F A l t . l n \ z - 2 , L - t , , 2 . t 2+Tu qt(n3 q/ e\r? . l @ : ( tozr) '+ f '
- 'V6'o: 4oo T:-...+
f :m ?r:54-4 (*dfi).
F,om @ : / tC+z;t) : fu_( i* ; 'ut)- - 4 2. 30 x lda -s i nl1st) c"s ((n tt'et-s+.+ )
- 4 /-t tx tia cos (roz*)s;n(rrro\-s+.tz) 616
'A/,,)
'A l-).
' ' t / l,F/m/.
4l
P E-zr H ( *,2 ;1) = df 2 <os (tst:4 s in (€t' rcet - f ")
({1/^)
Phasor v<ritf i sine reFerence-:
H : oy 2 cos (/S..T x) ,'f: @
t _+ v 'xH7a'-o
t f
* ,La* jf cos(rsnx)dr4-7, /sirsin<rsrr)ii1.@
n:-fu?xt:Ll= L*-*)i
Q7tnl"/t -,
F=
@: 6/ .Tnlt,rnS' . Flcos (rsn x)' ia'/t'
Cc,m,a"-ring g and @, we reTuire
(/51-)'* F": uy'o*o: W( 7 , l o t ) '
---r+ f
: /3. z7r - 4t. 6 (r+d/n).
Frun @, w. hono
Ec+z;il - L(E J'r)- : d*411 cos (trtz)sin(6tto?t- 4L 6z)
+ d"Slg s in (/Etx)cos (tr/o't-+t.< rS
4z
<vh).
----i''F--
,1."
rn
WP/ore E /ecf ronaenet ic Woves
a) Jn q. soLtrce-.{.ee, con4ctcfina me-Ji",r,t wi+hconsrilq4ive p6rari1e4ers <, y'J, a.ncl tr,
87, (z- 6z)' i y E - ' T * 2Dv - - ' t
d t
: trE + e t '9-. : L
P.7- /
@EVs.(s-/eQ V,'& (7 -6 ( ) : FrE: FV.E -F'E
2: -/ fr(v^I) ' @@
v/^).
/.Jqbsf i luf ing @ in @ and no+ing lhaf V. E:O: weobfqin fhe- wa.ve. e..Tualiooin 4,rripafive rn<d/cs-:
=2 = > , : -Fv L -t(6 7 - re jf": o. o
Si^e ; /o-r(y {or i-l .
b) F", l ioo-ho*nonic {i./4s ' * *0'u,)
"nd }i*(af),Wo,ve. e-7uah'a,-r @ con verts lo /{e/nrho/t-'s eluai,bn:
V"E -7@/rE + k'E:O, wAere k -uF.
Af:+:o.3xrdicr.
R:+.:#'^3*tf= 4s x loz (m),
or 4t (k-).
j , - Rsin € : 45 x /O3 sin 19- 9": /2-x /O3(^), or /?(k) ,of : zf (#)ros/s.s..
'-: tftry = +f o-s (n/'), or aLvut 1.? Mneh.
4s
L
7-z
2 Z-S Atr r , f t>e- (h" . r FcB\ l - tos +1,e, - -Fr . , - * , ,,711 (n \ :
Th",. , Fro.n Ef- (G-gcb)
Eril= J-)
qte
= {jd€
t ,: - G (u$t< ) aox 4-145 ,
E ( i l : - 7d*x l l cn)
p 7-4
or
. / -U e- )k Ct " ' k' t o
v x t-t (.e)
(-j \) e, x /1(.e.)
z \
l -1 = d, 4x /d6 <os (rorr t -1y"{) t ,a/^) .) 'o : u$\ = # - +: o. tos ( rad/a) .l : 1 l t / k r : 6 e ( n 1 .
At t = 3 x /;3 (s), we re?e;rc fh* r3u,nerrf af cosine- i,t F ,/ o " n ( t x t o - ? ) - * V + { = ! n l T . ! , h : e , t , 2 , . . .- . *
J= x3on-7 .s [+n) :Zz ,S+nry2 0 . , ) .
b) Use pA.uors wi* c.osine. rr$ez-ence-..
F: d, 4x tdL " iGy'ov+t/+-)
f ,o- -itrt< re sc,lf of problen, p. .Z^z ,
E : -lo d, x Az 4 x /66 TGkoY+'r/+)
: - do 4 x tO6 lo e?'/- o. /o.9y r 7T/4)
: _ d* /. s t x /o-? € c- o.rtsyftr/+) (V/il.
Th. ins,a.ntar?eous erryercian {o, E ir,
E fy,t2= -d* /. qt cos(ro?vt - o. {osy+ o/+) (*u/*).
( A/*,\,
++
D n -r . / - 5
11 a /r I - 6
a)
U>e 1 )ho t - so rs A l ; rh Cos ine re$e rence
E rt): dr2 "-iz/G
* dy,' "-
a ztq Q/n)-
e t : / o s ( r a J / s ) - - - - - - > f : / O " / 2 ? r : / . 5 9 x / o ' ( k ' ) ,
F -- t/n (ral,/^) * A:zn/p : 2JT n (m).
u:ft=t- ",:(1e)':3,L e-l- t -- h o n.! e I | ;r:+i'-2. I ly po/a ri z-e d.
n : l Z _ l z 0 r r _ , z o 7 r / 6 \( \//€ .rc: v-E \\JL) '
F -- + drx E : fur i rz ea'z/E- a,; di=/rj ),R r ^ . -
- i
11tz, t ) : &14*, in( tcgt - z/ .n + drLcos( io6t -z/n) l (A/r , ,5
r {: .lo
t-
S r
S r '
S r n
> / t l
b x-:=- tc
i-IrII
\ 2, \cas ' { , I :
r t,/
r \
; l l
t-t e t q t l :
1 t ) - .
) .
, ) .
) .
e t - ' " r )* / '
L e i a 1 :
r -E _
:
0 ) t - k z .
d o E r o s i r t a . *
6o En n zrE,
: s ino<, ?- 2 0
d rE ros in (<+V)
k +^{)tr
b,7
E;
( E u E tt - -\ Ero Erc
Reor re .ng /ng :
(-lz--\'\F ro s r 'n ! f
cas t / + cos4s in {
cos t "@; 's in zhI Eb /
E. E, cos{r - 1Tq si ; l r
- I ,
/ r r z l_(f l l -s;o."9.\ -t4/ I
/ r \ : .+ I - \ l - 2'
\ E , s inY)
which ls *h<- e-Tctdion d an .l l ipre'r 'r ' , E,-Erplaoe.
4S
ez:z G i,,en:
r r ) f * / -u ' / Eq . ( Z - l ' z ) . ' d :/
Co pf er
Kro-s s
3 x /o, (t{) , €r:2. t,
5.: { =o'oE.
ane" lV e) /G" \ /Tt ' l?': 7(7 )7 : j '48 (u7i^)
; -
l 4n
u-n=: t - x =
; - ln L: o.LZ1 (n)o) €T.(r-+q) ' T_: J 4, ( t +;S):)3s1/-+3, (e)' t e - i€ r l -zo t '
' d 7 -< ' ,
E7. (z- 4il : p = ,fi\, , *(f)',: ,,.riiiff;r''''\: + : a' o 63 (tnl '
a
'F= t : l . t?Tx/c7 (ds", .
t , c f . , * , , , t j eug:
T :
E= Ll . ?(?)' | :,- s?Yx tc' in7';. \ ,4t x:o, E :dyr i r , ' l R: +d._.r t
:2"o.21o*i(*-o.oosir)
H r+r, =dz a. z lc { t ' (*t e, 'n-(4 t lar i -z r . 4 Tx+ o,ez r d\(A,/,n\-
2,2^ s 13 +A, .oppe.r anJ /.*, at.sood conJu.{ot,/ r l r - . , - ,
'(fr)->> / , "1 :@ , t: * , ?.: (/ +) #.
9 f: l (MH=).
a-) L) | .< <48h) S ft.',)
iW
/ . = f x / os
o.4 7 x roe
6.6, / t, /{;
/ 2 . 6 x t c '
2,6t (ttj)xtd
Ttf r+j2xt64
/.9/ xrc4
o . / / x t o l
b) f =/(+H).
d6
46
'/ c- * (Np/-,) & (48/^) 5 (-)Coppe+
prn"s
g.zs ft+t)rlE
1. f t Q4)xto l
l .zqxtd
2 .T (x td
4. !6 x ro6
2- (K x 16e
2 .aq x l i
3- qq v rd'
)L)
, )
P 7-q a) 5: ffiT n: ,fur:o.e? xloe (s/,-)'.
6) A+ f : /o? (Hr) , a-,|@n : l.?{ xto4 (u7/^).
2o Logroe'n": -3o (4i l . --> 2 = #*
= 1.75 xro-a(n)--a.trs (n^).
P. t -/o A^,- le (/r\o: to-' (W/cn').
a) lEl: ' /aoza^- 2. ' /s (v/r^):275 (vt*),I t+l- le l / i ; - 7.2s x to- '(4/cm): 0.zzc (ar/ , ; .
L) F^,: lEf/z'lo: /3oo (W/m')'
lE [ : g?o (v / rn) , l r ( l - 2 .63 (A/ , - ) .
P l- f t / rtrr*" cir cu/a.r/y po/ar;zol p/one wa.ve-:
E ( r , t ) : d* Eo Lot (cot -kz++) - tdyEosin (at r ' /<zt#) ,
H ( z , t ) : = , #
cos ( u t -Lz *q) - ' -+ s ;n (c , r ( . 'Lz+4)-
Poyrrh'ry vect'or, 6:E t U :4# [."t
'(t 'st'/"2*4)* s;n'fu+-/.*+]
: Ur+ > q c'ansfanl inJeped.ery{ of t anJ z.
P.7- tz E-drE"*7+Eo,
n: +v*x e : trcr E" - d"Eo)du- ta-( r, ̂ -u*) :ao*( Vol'* leJ')
P.7 ' ,3 Fro- Gaur r ' s /o , , r t , E-a ,v*T , 1a f ie re ,? rc |he- / ioecharge densiy' on the- )nne.7 c-op4uc+or.
vo : -1*, . dF : * L, (+),* E :a,#r,
Eo^ AnpbreC circ<,ta./ /aul, ft- 4#Poynfirg ve.cfor, F:E, F:ar7fu
fo,ru"r lroo-tniff e4 ov'.r qross -.secliona-l a'rea-:
P -[F.di - #[*I 'G) rdr d(:Vz.3
Y / . / .Itn/s ).
-n.oos r)
tzr r r \Q4,/'n\.
47
l
L
I
PJ- /3 E, c94 = dyLts t pho-soy^t wi.l-*l
4'c'S: dl
F.r- air (me-J,"u.
&, 3-tr) : H, (z) =
aL// * rc__
' 1 t 'b
Y/.: @,: LT^:24ot 6L)( 1 , J € r € r - l o. : d, t"r-o .--
ix/:' = ar. Zr-rr ;i:r,
-io sin (/o*+ -f fi (v/-) .I
Q-- =('ne- fe-F<r.en.o- .
so {)f,vl ) t A - Q - : l o s ( , . -,) /-t c, -,fu :
; (rd[n)
T,: 7o: /a?"r (L)
F-. f o s t f -s = yneJrL>t L: fi : u' |Te, - g h4 - t ( r*J/-1.
/ \ , n fb) f : t , T-t+f :+e
/3
Fr: d,, # "2"/z , {<r,:) -dy{s;^ (tott + x/s) (u/-)
g,-- +GelxE,
* H, rryt;=-|r*t,;s;n(roTty') (A/^).
^ { * [ -J : - 1
_7 72 .
^ \ F / n C \ - - S ' i . Yv// .t : \t tr;o ) q/ e
--/ *' j Er(1t)- a, ls ;. ( tost - ax/z) (v/^).
tlV s ;n (,,ott - 4xb) C4^).Ar: td*xE*---', il.rc-,+): dn
U: /9 # : : Zoq >>l (GooJ.onJ,t*4,,r).a) S ki, cl ep+h S: #F-
- o. o €,3 (m) * 6- )."*) - *
7 . : O* j ) + = z .?6 ( t+ j ) : S . (o&- / i l c l t ) . : * .
b) fr .cr, t) =d, o.3 "-ts ' ' t t ' " .or( lo*t
-- /5.7s2,) (n/^).E ril = - rl"d", Rro) -* f r =,t) - 4 /. 6 g i,r.r trc o, (ort - t f. r s z, ! ) (vt^).
O n. : f*- (E* R') *1 t'T'o't . 'tt '7"cos{ :6, o. t 'g "-t,-7"
(w/^r-
*
4g
rn)
"Jh))
ix/z
P.7- t6 a-) r:+- ; 0
b )
-, l,-H ., . ,o
+ : E r a" E ;o
H+o-4
P.7- t l e iu.n E;: Eo (d* - j ar) e- iq.o
a) Assume ref lecled qtrl - (4Er** a, E.rS .)f."
Borndory con.!i+;on a.f 2=0 : E (o) + lrlgS : g- -> ErG) : Eo G a t + yd .ia) df") df
' a, /ef t - h and circq{ar I
polariz<d Lt/ave in -z 4be<lion .
b) dn,, ( F, - i lr) - { .- -a"xlH;to> + u,cil): 4, (Fr=o ;" !#J::,:)
t U u- * dy) , H,to1: ftca">' E,ftca">' E.o) - t(id.*, dr)
R, {o) - R, to1 * H,{o1 - # ,iu, + dy) ,Js : - dr, F,,q- +'lu*-1ur\.E,tr, t) :6QnlE;tz) + Erur)"t- '
,{;r;
c))
I
(vf^).
Ca/*,).: dr- Eolta.- i ar1 €)/"* (- a, + i a;
"if'f #
:Q- €ol-z2t"r-idy) t;,., f ")eie- 2 Eo s in
f z (d- s;a utt - d.,co" ot ).
n o r r n a . / , ' n . i d e n c e - :
1 + f - t , wh-r . l f l
I_+ l " l = l f l , f <0,an4,1,---"--"" '?, - 3\" - lf l : *5 :
#- -1. '--'-r' Sar:2o(osro3 :?.s+ (48).
41
P. z- tg Fo.
G.
a(vr^)'w/,*)
st.' l r : 2 ' l t '
P, i - /1 [ , t i :dx . /c i j { " ( , t / ,n) .- /O ' i6z
+ r1. (z) : 4 / jT e- 6 / - )
t
o- i r : i l , : I = '
+ ' + r-<) : 6c. - / - {x/c?Ga}/s)
{ossy m-J iu , . ' r , { ' } - , = 2 .25 t Ton f , = {
- " . ,
.
E7 rt-42): o,: #)T: +(!)+: /.ss( t - rs) : I =a. t . l f r f ,u 1f l f
t= , f . ' ' ' , , ' * ; tV) : : 7- i o
&pt^)(ra.A /r-,).d^-7 '
Eo.
I '
(z^+q), 2,: E (,* i *) : # (," i!):zs+i"in)T - - n . i t c q . q c
_ __. ! - :__i ,_L : A . t Cg e, ' -
, - '
nr * i t w ' - \
: 4 + f - : O . - {Og . r rD .O ? * : O .goE . i l ' t '
, : :) E,ir) - A*- z,og e' (62 + te7'1's
(v/^).
J.et = t , r -d;x
E-t") : j , ? a"x dr) z.n8 ui , l t ' * rgt .?o)
= - dyo .oosS s i (e7+ teJ ' r ' ) (a / i ,
Er[r)= a* (, Er) e' '""€if '" *d*&os {^tt". ' i(?'toz-s'r ') 1v/^).
ftrfO: ay # '/ ' t t z
"-a'(7'toz'5' /")
-/. ts z. - i ct . taz r 3. +o) (A/^): qY o ,o3z e
/
- | + l f I- \ :{ - t r l
l +o . t cg| - o . zog - t ' > t .
(6 \ :\u avtt ig* (E; ̂ -ui + E-,r F:)
# i2'?o"cag s.so
(w/n).
(q)=\ varl:
:
7n(Err4)=d,-2.rOz
4 o Q , l L 7 e
SO
F_
)
)
P z ' zo G in .n E , { . , 2 ) = dy lg s tGx+ rz \ ( v / ^ )
4 k.:6, k"=e --* k: p:,[Q*T, - to (ra//,-)-t-: t tr/k- ztr/tO= o,6zg (-), f - e./s-*tgstot(11'); b: Lc:3xto1(rad/s).
0 F r { r , r ; t )=ay /o cas (s * /o t t -6 ' -92 ) ( v t4
F, k,zy - f"4,, r, l4:.: k
: d*o.6 * 4o s ,') ,,,: krr,0,1* Qo.r) *al lo "-)(€-rt"':(+m,4*;r-i(6.'*sz)
F;G,"; t)- C 4r 'r : 4#) 'o '(3x 1o?7 - 1z - {z) (A/n) '
d Cos 9 ; = 4 -n i '42 : (4 ) Or= o . t -F 0 ; - .o r - 'o . { -36-?"
d) E;(r,o7 * E, (*, O-;' - E.{r.z) : -a> to d}'(62-sz)
Fr t r , - - t : a roar rxE. {42) " .d r r :
d ' , o '6 -6 ' "0 's ' )
: - (+h*a,h) 6 iG'-rz)<) E,G,z): E,(.ri l ' t ,rr,o>--'ay to ( a-it '- e28z);;6t
= --? izo d)"* s; n tz ( v /^) .
H,(z,z)= l l l ,z)+ Hr(x,r1 = -(a'fu cos 9z + orfr s;n t)€i6' A/i l.
+ oi8'si rrtl ' - ' , -
) p/,,1.P Z'zt SnellL /o,o o{ reFlec4ion i €r: o; =3ol
Sn"-$L h" +I re.$ra-c$ion:
0 r : / 9 . 4 t ] cas g *= O .943 .
T, : 'Jo- 372 (rr7, T,:e : #:25/
(r l, l '
a \ l - , _ T *cos€ , . - l , eose t : _0 ,24 !
l " cosha? . t cose ,aL: 1 + l t - 1 -o .211 : 0 .791,
b) F,on Ef C7-l+D' QC*,,):4rT€io "-il^(x'sine'+zcaser)'
f,- ,6r, * Fr(xrz$)* dr/s-z cos (zttft -t 'osx-z'7ez) (Vl-)= 1fta4/n) rc. ./,
F, o - €y. 0^ /+ z), \ t r, ",
: #( drco s €, +dos i, er) € 2 (./'ot 2( + 2'e 1?)
-+ Rrk,z;t) : o-odG dro.g+l +aro-zzz)cos{znro?t - logz'2.?&l@/-;'
sin gr: ,[2*t,n er: t
5 ' l
P l - zz Fro n , p roL f , ,n P .7- i { ;
€ r :6 i - 3o " , Qt - /7 .+z :
' / l 7 9 t t d - ? 4 3 . + 3 " ? x o - E 6 d
,,t)
?1 : 377 ( JL ) , T - : z r l 6 : . ) .
c) Frorn f q. (z- / rs) t r, : -a" cas 9t - 17' c'as 0;7 ' t { ) lncvs €, + 1, ios ?1
7 t / x 0 . 7 4 3 - 3 2 2 x 4 8 6 6 : _ 0 . / S g .
f rom €7. O- /5a) :
T, - ( t + r.\ ?. ' .e+ : o. 772'-[ \
' "ll./ zo.s €.
X; tnz) : ZZ o,oEl "4'G
s'raoi+ r 'ect6')
n es ln'x lcf 2:r/f , : T - - ; ro t :T
r--
f r r -q l7 ' i ;o-V€nrf r :T
i , r t , z )= d"o-os3 u2( '74+rz ' / i )L /
'/ (a/*,).
i r, -, +, e -,' 9 o ), f,r-- cx, z ) : / 9. i s (a1. rc{' lo. r7 [r' (' at " tr z/'d6
v/a.l.
Ern : T , E ;o : O . ?Z t x l i . f z - - / 5 .+2o * t a I Vl F.1,/ .
rr f otr) E,
- l O - 0 - t g
'ot. (z-/r+) ond (z-ts-r),
Eruri - /f, 1z ({ra.7+l -,4anl) "-i
{r-or' * x.t6 2)
l
t;I
( "aJ i ,n ) .
( ro" l,-). tu
7rut, wiy'h a. --esin'e re,kranEe,
\ f tz;*): /5. (z (d-o.7rt- +o-stt cosQzaf*-/-or7-z.7tz) fvr-).
o 4 / cos (zt /o't - /. osr- z-?( t) '
C{4w
g2E!r
fEL*__
lF--
P. z-z+ =""r:
t ffrom f7.(y-/iD'
u)f ro^ Eq ft-i4.?):
: fvlz on4 €t' : 60o
7,/1,<4t;r:-i yo/,tt , ?r/?o = -i/,|r.s in €r- P s in e, - - j /2 , cos gt=JV/2, co: er=/ /2 .
' t [o L
f , - ( . \ b / . 4 o ) ( o t E ! - c o s e t : o ) ) o 7 o
( 1 F / n ) c o s 0 t ' * c o s € ,
- l'(n/r).
'o
) rvn).
L
Fru. 87. (T-/4t): 7 . : ' r - 2 (7? / rb ) . coss ; - - o . s " i t s . s "(l p/1)<os o1 f cas 0t )
b)From Er.(v-/sg: r,,: ff i ,* ")zt"F.o,n 87. 0-ltf l ; zu
lfrl: l4l: t , Lut lhe phaseshif t o{ l l .- re}/ec-ted L^./ave.dep<-nds on t'he polariz..alion of fhe iociJ<.a* wa,ve. fh"re
Qre sfa.nr l in3 tA/Ave.s in i l ' te. a. i r anJ expone-n{ ia/ ly o 'ecoy-
ing l ran-smi+ /e^J \Na,ve t in +he- ionosphere .
P z- zE kr) * kri : t: : r^i7o€, -jat7ofr. @Conlinuily con4ffions a* z=O h. o// z aa4y feTuito:
krr: krr: atffi sinQ; : fr-z.o?rrc1 @Lrr : f r r - ja, O
Comb;ning @, @ a.nd @, wo caa solve {gt dzzand Fzzin fermso{ a , /o ,€2 , %, a rd
fn . .8u1 , s incc
fi .. 0tVo1 ,wo hone dz=422=
Fr, =
f -r/tr;a"q - o.3?74 (;t).
a) o, - to,-' f
= b^n ffixfi1 it;.:r;.r-' (rad)
s3
b) fr l l =. L
o-o j93 (tr) t Ztz cos 88oz o.olst (l+2) - o.c2H ein/!
c) t o l ogn? -4 t z : - 3o . - zl - q'
W:8 '6? (n) .
S n e l l i / a r v '
S i n e . I: _ ,S i n g 1 n
€ t = s i " , " ( * s ; " e ) .
Cos€) ra lm
l ,-IE:E.taae-,dffi= ##: E sin (9; - e) -
#T (sin -a,. cas 8r- cat O; sia gr)
=dsine,ft- f f i ]
_ Z 1 r c o t € ;'lrcotl 1
Tocos e;2 x o . o q q t ( l s i )
fr r, nis-o.oes3or11.(os €r- bs o.o3a Z | .
a)
b)
,) j , - 6D
P,7-zr
t,
a ) S i n o : / 8 . 4/ E V € ,| in er -Je sin e; ) I {c, Q.}€.,cot o, =-jrlTffi\;4 .
Fron €7s. (z-t4t) qnd C.l-/+z):
4rt ,z) = dy t ro. ' * t " 4 ' i f " t ,
sF, t,,21=
f (o, i n, * 4{7,s;n e,)i"'" eiluI
IywhsTs
f-,- frsin tr - AIE sin e. ,
"r: f, / (+) stn'q.-t ,
{ro- 87.(r-r+st.
D (a*;r,: t CI* ( Ery rtl, ) : o.
.r+
t . :to |/
nErr!
_ _ , L
,D .7 -26
Z t, cos a.. E iory, c os e; -i7,
rl-@^,a - t
(r,j).
7-
,2 -? -28- G iv . , 0 i=€ . . - - - r - - 4 :T /2 , cos0 t -o .
a) Fron Eq 7-t'+'s ): ( f.ro/E;), : 2 .' , 5 )
F ron Eg (7 - /s '9 ) : ( E ro , / E : ) r t : Z r1 rh , ., ) F, . (x,z i t ) = dl E;o cos w f t
- ! ( r s in g, .+ z Cos ur) f ,
E* t ^ , r ; t ) : dy2 E .oe-n ' .os u ( t - ! x s i r - r€s )= dy 2 f ,o " - "= cos u( t - ! x s in€r . ) ,
where " : ry@;;r j t
-6 ,when o-o, ,
F.z-zg
b)
P.7- to
. \
d )
a) O .= S in - , rm , , - s i n - tm =6 .39 , .
e ;=zoc >ec . t ; ne t=Gs ine , : J . gg cos g * : - 72 .9 t .
,- .,8, cot g: -I , : a_ , : : , " o t
o , - u i t g ' = z i o . (6' v /€r , coter '+ cgs et
z = -- !- /dt !ot ej-- = l .g? ,s?t ' - / . t i c io. t ,L G , c o s e , . I c o t e t " e J e
The /ransmilloal wave in airlvhero
At/e,nuo*/on in qi" {or each= 2o logro e'arLo - | s g
varics as "'<^z
a')fux=
*(z.eD.r,<tava/angil1
(d 8).
'*u'
Wh", |heincidar# l ;ghf { i ,sf s*r i les lAc Aypo-
* e n L t s c | u r { a c a , 0 i - O t = O , 1 = # ,
(fo)r, - 4o T.t : . 4,rorl,
,(o"-); 'lz ' (,lr' 7r)'
Total ref/eclions occur inside fhc prism a*both s lan l ing sur faces bccause
0; - 4 t " ) o .= s io - ' ( * ) - -10 . .
ss
On oxil {ror.,
(Oo).
frt \\ v a v 4 l
. (o*)2(@*),.
*hc 7rism , Tr= ffi,
- 3- n' : .4tX-?o z (72*?) '
f 4 %'h 7' r 4,/7, 72- 16'1 =l oq, -6'7e
a) no s in €o : h t s i n (96 " - A " ) - t l t cos Qc
: n1,[i4.: ',rQ7trj =,msin 0o- +tF4 :,f;ft (no= t)- ) l
P.7-3 t
b) N . A . : s i t - t en :vm = 0 .196 / ,
€a_ : . f i n - t o .?861 : go .4o .
= s i noa ! . - 9 * *e * * t t / 2 .
D rro, Varallal po/arization and €, * €, .
P. z-sza) For perpend;cu/qr po/arizc*;on and
/u,* Vr:s in e r t= fr@
Llndcr condition o{ ns re{lection:
o,sq=/tE-' ' r ' -u
l t * ( tS
sin gr, _ |
cot et -
= S in 9 rU _ Or , en=n /2 ,
s6
Y_a
P. Z-Sl Fo r f wo confg u 6 Lts med ia wi+f i eTct a_/
perrute-a-bi/t+y a-nd f ermit+iwities €, an./ <, \.,y,e
ha-w e {ro* Er, (z -/zo) e<:. -sr o- GJ",, d.oJr4 rom f,7, (Z - / E+): OB|F fon4Qe,
. " . s in e- : ton 0n,
< t / 1 2 Qst
/1
o.5Ill
4s
{ o
;"4 9 "30"2 o.7'
t c.+'
?o"c4 7 "
{5 '
3 ' . 3 "
il.€
t7.5 '
t
I
E7
I
triI
T
!i '
t.
[.
a lW' - lI rans t r l t ss t on L t nes
.2 g:- t 5q bsl i {<t t , , ' .g f f t . (s- /7) anJ (c- r { ) ' 'n E7'G-+9"
n-4re-zr= T, / <
d':'[T d -
t fw:E*
v^/' = 2 u/.
a1 Dr Parr
q- .
.Ji. parf g .
{o - po* . .
: r 7 = d l -V : d lZ-L i t 4 0 w r , l 2 e u l V ' €
- \ 7 - 2 "1 l - t t - : A ,17Y , ' 4 t w / i i - W V 4
. tA / ' - d { :
: U b o,' ,/,f'< i
u?b
up.
.---+
: +t6 /, /L-
"p/,iz
, \ A
l ' { ' Z Q i v e n :
j ' s ' x rc ' (H i l .
R- *re': t.tt (tt/^).L=f * - o . t i 7 (yu /n ) ,
G=t t a o .oos (S /m) ,
C =€ t
: o . r , t (aF /n) .
l l-t tEfr
= lt - 4.t57rto'r.t t L = 4 7 3 . 5 > > A , L ) C = 0 . 6 6 7 > ) C .
> = j ' , [G [ , . * (# . : ; t ) ] -o ' t2 j ' j t t -14 (n ' t ) ,
zo',/E [,. i &- #)] = 27.27+2o.t3 (g-
5s
4 = , ' . 6 r lO ' (S /n ) , w = O .oZ (m) , s ! * , 2 .5 ' l o -3 (a ) .
Lo*/ diohctri" slab : / -f o, €,- j , 6'- 1ti ' 6/n).
a)
b)
c)
-
t
(g-+ 9.
P. s-s
P 8-4
6) Fo, coaxial {rancm&sian /ine:
z,- *,8 l, (H 1,r',. h e) = rs*= n . t , - b : J . 9 t , / o ' t ( ^ ) .
From E7. G-crs, 4 - 4[7: .
' f f i1-3oo (tL).(n).
e: - J
/ )Fro,n Ey.@-zE)a.nd (s-z/.. o( =
f rom /<A/e . ? - / ; L - * f *
A.r - E t b
Z n { ' e L ^ d
. * )
t t )
o ) .
: 2.6 / x /o-4 (fL).p - L .€Jx to ' i 7 | ( \z7r - ( # " ff)* ror- o. os (e).
# : /. o6t r /o-t (t(p/*,): ?. z, x /d3 qAB Iil.
7.: [email protected] V Ca rjut)
P. e-s
R- = aZo- d.o sl1 (nf, .) ,
a=+*t-23 (f s/^),L: + : o.2.o (f urt ),e: +'Fo (pr/^)
sq
For coppzr q.t / (/tt1), A.:
€7 G^ts)'
Giv.n Zo:50" io UL)-1>- re ly r . . . l ,t9r1 (z): 0 --+
*: * - L (Oistor/,on/e,, l;n").
G i ven' i : :. :('i'!!/r;,"'f :i.{
ruBr^)
F'o'n rr f:!?; li;ril ^--# , p=@8, zo=,tg
tr (obx 4t rd7s. g, /o"
Ps-s ( P^,)": ( P,),
P 8-7
P.8 -g
= l v . l t 2 ; ,(Pr*2;)'+ (xr+x;f
h naximize ({ . )L , sei t++
=o.
and u" f : ' ' : o
Mor . (P^ , ) ,= ! ' : l ' - (P -'L 4 Rl , ,o")r, .
- ! a-[u, zi ] z;v; :4vg- V .l i : f r '-t -''
I o, =or, X,=-xj)
o, z;=Zi.
a) -{-ez , - .#=n,
| -+=- pGv,t d z -
| !#:a.EIV(z) : Vo+e-<z * Vo ' c " ' ,
7.G) - I lo t t a I i c - ' , . ( - , f f i .
4- +=Ro:E
r i t
a)
b)
+ Max. powo.r- l ran#cr c#i u 'cncy = 50% .
V(z) - Vrt.'" + ('e1, ,
I121: I| ;)' + Ii er'.
z=O ; V(o)-V; - Vo* * \/c , I(oS- Jr.= Il * I; = ltu,,-US.--> Vo' - t
(4 * J,Zo), V-, = * ( U; - l,Zo1.
V (z) = * U, riZ) oj>" + ! tu, - z, z) 1",
L Gt = fio(v, ,7,so1 i'- +(v, - r,zo1e'z .
V {27 - V, c rh 7z - J;Zo sinh }z ,a 0)- Z; coshr, -
t s inh^rz.
I
b)
)&
?r, n,Vo* Zr.
6 l
-7-
( i = - X j
We- have V(4 = t(ur* r;p);'z
z(z)- +H:rr;)o-"wherc \
2. '' i - &vc
anc i
c) For an in{;nito l inc, 2,- Ro '
Vtzl - #r .qrru ' ' " , rh)
+ f (u;-z,n)eal
- ! (#,-',){',t - .-.-h-
V. -12: T;70e
P s-q
d) Fo, a finitu lino o{ lnnglh / {ermtn<fe4 rh4t'
Q;:4#ffi
Lis*orl,anlctt /inc, 4o=rff : So (l;-), 2 - o.s (tL/n),lv' 'uo)l
"avt"^ ({t) :tan (#) - o. oott.- # = o.oots; 3 =gooortxo.oolS=4e.2= *-L: # : o.o/t (H/^), c- #
:4.42 (Vrtd.4:
h = o.ola (Nf/n), p:u,/E:5.s5 (rad/m).
a-) V{21- #t "-<z "-}pz
: #
;o'atz 6is'rrz ; .re)= #.
. ' . V(z, t )= 5.27 elQ'atz s in (gooorr t - 9.952-o'322) (0,
f (z, t )= o. los €o'o 'zsin (goooTt -s.stz- 0.rzz) t l>.b) A+ z : So (m): V(to,il= 3.Zo Sin (Sooort- O.+lZr) (0,
I (ro,t): O.o6$sin (goootrt-O.L?zv) U\
c) (Po,)L= ;tulurtil
- / (s-^o, o.oe4) : 0./o2 ( w).
I
,,, V,
V.* Zr.
( i = - X 9
f l' 9 '
-7-
e) For an inf;nito l ine , 2,- Ro ,
VtzS - +-uru''", r(z): ffi; ':d) F", a {;nitu lin. o{ lnnglh ! {e.rmin<fcd thA"'
2;:Pr#ffi
L isforl,anlc"t line' Ao-E - so (JL), P - o. g (lL/n),
Wc have Vtzl = t(U.. z;R);"z
J(z)- +(Y^:rz;)o-"
Y - ffiu, and
tf (u;-z,n)eal
-; G'',)r''whorc
:ur''uls)),
U
P 8-qt"" (&) :tan (#) - o. eot{.- f? = o.Oots; 3 = gooorrx O.ootr = 4e .2 = *.L: #:o.ou (H/^), c- #:4.42 (pr ld.4:
h = o.o/o (Nf/n), f:es,{E
=5.s5(rad/m).
a-) v{27- #z "-<2"-}pz :
# {4o/z 1i*srz; rQ)= #.. ' . V(z, t )= s.27 € 'aoft s in (Soaorr t - g-e5z -o,32:-) (0,
f (z,t)= o.los €o'o'z s i n (gooo?rt - 9. s52 - 0. 3zz) tl>.b) A+ z: So(m): V(ro, t )=3.2o Sin (Sooort-Q43Zt) (0,
7 (fo, t): o. 06l s in (trooorrt-0.+?zv) U).
c) (P.u)L= ;tu| urtil - / (s-"o, o.oq> : 0.'toz ( w).
6 l1
P. s- :o a) , co r a sho r f - c - i r cc t i t ed l i ne r Je . ( Zc=0 inE< ; .G-? -< )
lc ob*ain J -2>zZir : ZofanhU : \ f f i t f .
Ftr ,L: )-/4 , /:.L: rr/2, d)./z << | .
Z;r:".--;ffi=zoffi= 4 2.., /ax .
b ) Fo r . r n opon -< i r cq i r eC / i ne , se t Z r - ->a i n
to ob ta in :Z ro: Zo cot h7.,2.,= Z, ffi-
For A:A/+, z;o: zrffi z)":,jt-:t!r o - o / - e 'a y a (1-a;-fiz Zoax/+.
fL: ! ! t=+-4eoo,f ^^
/ l - lon 4goo = - / .732 ,
Z. = z z+ - t! 9"fr? - so G-2'it.d'i.tc.(tttz)aa t r r l z s tan rg . { - - @
= ?6.3 ' iq .s t &) .
G;ucn , Z a : Zo cofh >l - 2So /'s9-" Ut) ,
Z;, = Zo to.n 1! = 35g / 20' ( lL) .
20'6Zo = 3oo &,o = 2s?.8 - j tz .e &) .- f q
t^ A >2 = rlt
- 1.2 /]5' = o.grs +i6tr =tanlrQJ'1/D.
, .1 -=4(m) . . - * 1 : o . t39 (N1 /n ) ,
F = o. z ts (rad/m).
,= [@- n - , f f i{ e+ iuc ' r= '@)
-.-+ 2+jaL =)2, ) G*j ,oc - 7Ito
Q - f c
= O . 2 3 5 r 3 x f O o : a 7 o - f x l O t
we obto;n: R - sg.6(a) , L =o. t t2
G- 0 .246 (mSfu t ) , C * r2 .4
t7 G-i.*)
D Q - t t
P8- /2
a)
b)
f.( r a d f t , 1 .
tp4/^),( f F /E) .
62
i t7.G-7e)
7-t
ii
!
€7.G-tx)
P. s- ts
P.s-/4
a-)
b)
a) Since ihe l in. is verY shorf compa'ed lo a '
we.velrrglh , ye AoZ use Eit '(s'f l) and (t '83)'
, : #,:9 x 1s-t' 1s/^r, l o _.[, :74. s GL).
L-- 4y - s x ro'', (H,/^) j ^, 't c
LC
/J€ : LC --+ €,: f f i : 4.05.
F : +p= 2rrx /o',8 - 0' 42 (rad/m); f L=?'f :: o'':?!iJr.
X,o- -R.ocot Pt' - 'h - - 2g o (JL),
Xr,: QotanflJ uL/ ' - l9 '2 (n) '
fo , /ooJ i -p-dancc
Zt: R"* jXr '
l * - t l , f ( r r -qst*- /l Z z t -
1 4+ t | ,f cr,-, r)'-xtI t t O I
p, /zo onJ t t : X t /zo .
Wh"n - t vL
'z)B
l r l : s - l =l r I
s + l
whore
+ k L
IIt -IIL
- 2
fL
- J -
- +J (to rr- z r]-s)/s
b) S:3 o .nJ r " : /9o/zr :2 .
LL: * ' 'El '
Yt : PL Zo : + 71.8 (g) .
,:_s 4! Fo,
lr l"a. loss I .t" J i. "- , Zo- Qo .
_ | (a,-p) . ixL. l ' _ (cr- t ) ' * x l| (21+Q)* jX, l - T.rhf f i ,Rt ' ' 2r ) " *X ; 2
, ' \ . ' , r i - r i a'-./ _. et ., _t : 0. + Ro _ jT: *t(4 ,-;.r)'lr. S c()pres1)ondt *-^ c- lni,.t'oruo,, lt-I .
Fo" Z, - 40 + A to (I>),, R.o - ,f4-"-3d : .5o (llr.
b) Min. ir l :,tW =,1@ = +.I ' V 4 ' P r V g o + 4 4 J
( v l ;n .S : t r * * :2r - = -
L'!:* Lott lrtu lin. oF chc",ra eferry4i Fes ;r1or-,<e_ l?i ,(e.-rg:th.L' on4 fe-rrxinxlrAg in 2L , (f,-orn tq X-rq)
zi_R; ffi,*#;,zt: P;$;-e!t
Ai- iz i t
l r /a v, s et Z; :5o (Jr) +n d
to + j/o - po' t##
t -'f,rn frL'.
Z t -10+J /6CJ \_> ,
-* {h1iL lo4
.So /..t in1 :
a n e {
+ |oot : So pJ,- zooo t= - (R ' ) 2 t .
a /
Ko :36.7 ( - f - ) ,t : tqnF. l ' :A7zS-
I
.I-'- o. tos ,\ .
64
P. g- t t r , \Lq . ( g -7? / : ^ .
/ - | k ; +2Xr. _ p Rt * i Ro ton B/-'-o ,4,o + ?' Rt b; f,g_
x,- p,E,
, , : t , d.nJ t - -*n
: 1+ i 1 . _I + 1 , r . t
z - L
Let rc . - Rr-RD
, /.- --I p/
- -*1"( t +zc; t ) : \ ' 't f ( { - r t r , ) : x ;
So /u i n? , w - o /> /a - ; n t
l ' - t t tL ' L
6s
#: er-z7zl
: O . 2 7 .
P.g-rs a) lf l :#: #77 I;n 4 €, , vvril< 87. Cr-7il a_s
v ( z') - i',' ;.:3:' :,:7,:i,: ::',:,'r'' 3
: +(zr+R)ei f { f r+[ f l r i4f ,Vo ffag. /x rvrinimqm wh-n 4 : laf ,
or wh.n oe: 2 (gx o.3, \_TT. ' , f =
* e?o.2 i r : o -27o+5o. rq6.
I: - ,3
D 2,.-po (#)=3oo (ffi): + 66 +. j zo6 CSL).
Tti___
e s- !L Q;uen
* )
F.o,4 F;3. r--s,
z.{o , ! -
U; : o | /o" <v), zs- Zo - So {!l).,,4,r: 25 (,fZ) : o.5 Zo . I :
?r : 2 t - P a : - L' L ' R , + t l . o 3
F'L , -
- 1 a
7 r , V a '- o ' * i r
T V "/ - : + r
< .{-o + ..Q2.
Z . + J t * " , f l \-/ 4 i-*.ry7/t
. t O. . , /1/ !1 t , - . - i ro* E7-(E-Zs),
Z i : 7o o's zo +; zot^o f !' = 2^ l-'i-2&ag-
2o +i 0.5 zoA"f& oo 2--+ i r^- /Bl
: -3 *:;-a' |;- '/ - 2 /3 i6 ( r+ j+J^ ,3 j ) ' s 3 L
(v).
( -A) ,
+, f.t:(*)+: T, {onf,t:7V: *(ff i) - o. s2? /*/8.+' (u)J;=3 (+#r)= / .os4,r-/ tr .4" (^A).
l rVLen T/S is cannec/eJ lo*he l ine, o vc/ lon+,/ !a.ve #
.eo arnf i;4ud+ #,W 4.a-ve(s towqrd iO. ,o^d p.L,
erc ivin3 v+,i+h qi oLp/,'+,tJu V, = #dil4 6rAic6
C-a,cr se,s a re$/ec-leJ v<q,'re vsith on a.nptlude-V.-: CV'-7he ref Iec*e.4 wdve 4raveb Lactr hwa,rd (6e qenera.lor and
is nol re€fec-fed lhe-re bec;a."r .se- Z€- Zo, ancl Fc=O
.'. Vt : }ft nift (t +t-r) - + e4fl - q 03 i /-45oSin,;/a,/y. 7r=
#r€;# (-C): + e-ifL --t.33s1-as'
5= #: s=.( Po, ), =
{ A. ( u, tf ) = + ( S) G, k;t) = 2. z L x o r (w)= 0.a 4 (m w)
z l f t= zo- ,so( tL) , F" :0 . (P^) "= #" -c , .o2s (nw) .
(mofcheJ <o^di ( ion)
(0.
(rrd.
b)
c)
66
P s-zo I - 2 r ld (Hr ) , A- f= tscm) .
Apcn-<i rcu i la l l , rm, ,4 - I (n) , lh- o .667.S,ori+h cAarf : Sla,l {roo fl, on tAe dxlrottc r,gAt, rolzltc/ocl<wis. on3comy'olc rouo/u],bo (az'- A/z) andcoajiauc, u, {"r an a,!4t1|ona/ o. 167J- /o o.4lr-\ on
fh o " wo rc /e" lA 1z vat d gi n < ralo r
".
o/., A_e.a.dx--;io.t7f. - Z, - /s x (-)o.r?s) --j+t.r &).D.ran a s#aiglrr lioe f.orr, tit (o-jo.s?t) pohl tArcugh*Ac cs.n*cr and in{crsccl ct! (o*jt.7+) on /_1c oTTosikside e{ l to cAar}. _-._, y - +t $r.74), jo.ozt2 (g.Shor t - c t rcu i ted l ino, I = o. t i3 , . ! . / .+-o.s13..f*arl {rom {te cy/raoo /cf/ poiol pr, , rcfalc clockw/tcone eompltlc r<volu/ioa a6r1 cor,lia;e oo {or an &dite,tal0 , 0 3 3 J . ' l o r s a d
D raw a sfra,str i::r;:i i;:li,i,i!,7 ii;i u2)
*ho ccnler aad iniorsccl at (O-i+.rcjon$cop{uAsidc o{ **e c$er / l * v -
* ,Ojdzt )= j i .o4t G) .
a)
b)
F. g-z t,{ , r - * ( n + 4 r c ) = 0 . 6 1 j o . 2 .
a) l . Localc 2r-0.6+jo.z on5.ri+h charl ( Po;.t pt).
2. WiiA cen*ar al O draw a lfl-eirelc 4treugh p,, inletocliaEO P e a t 1 . 7 7 . - t ' - . ! = 1 . 2 7 .
b)
c)
v L -
anJ
ot (nw)
lv).
nA).
r - # oitle'- o.zg cir.l '
l, Draw line OP,, inlcrtecJ,hg thopor;phery al Q'.Aca4 o.0+6 on nwavo/tagtAs
lowaed gcncralor'lcalq
2. Move clocL*i t t by o.1o11 h o.t l , (Po;^tpl) .
J. Jorh O and Pr' , inltrsecltngthc lff-cirele al Q.1 . & .ad z ; - | + jo .sg a t p r .
2,. - SOr; - go +jzg.g Cn).
67
J) Exl.. td /;r* pr 'pro lo Pt. Lcod f;- o. ls-, io.el.
\:' lT l; = o,ots -jo-oog 6).
e) Thoro is
h -
/ . 6 ' : z
P. s-23
t.) l. Draw i'iac 0Q , ialcrscc*ing |hopcriphcry al F;' '
Load o,+t+ 9n ryuta'velengths 1z'^.-tg gen<rzr:'2"'
S c a { e .2. lVore r . iockwit by o./ . t^ fc o.c-Eg (Po;rt 4 ') .3-Jain O and Pr ' , inhrtu<l ingt6e l f lc i r<le- ot 1.
4 . R c a d ; , 1 2 o . 6 t + 1 o . 2 3 a t Q .
Er - S0 z ; = 3O,S + ;L | / .9 @) .
., i) fylcn1 /ioe dr'Pro lo P, . R-cad /;:/.+z-ia.s+.'{;-
* !;- 0.02g+-2'o.o/o8 G).
0 Thu. is a voltag+ ninitaum at ,!'o.oJ6,\.
no vo/.lag4 77ininu4*'t on lhc/inc-rbuf '1<Vr.
zr= * ( ro -1 to) - o.6 ' jo.2
d) Lacale zLu 0.6- jo.2 on S^,1+1,
chari ( Pt;^t P,). ttVi*h
cenlar c;j O draw a- lf l<.;rcjc/1r.o u3h 1, inlcrt te* ing / inc
APr . a i / .77 . 4 S -1 .77 .
S ) f a o . 2 t r i z t l '
x / 2 - 2 l , A n ' f , ? ( < m ) .
Firt* vollz.ga nr'nirn.tr,rt Qcc-urs af t!- * - O-t t\.
a) l. Slarl frorn Pr" and ro{arfcCaun{crcjoc.,wht o. t o r\
fornard thc loa,d to Pr',
2. Droq fhe lf l-cireto,inlvstci-ing linc oPo, al Z (S.Z).
3. Ioin ofl', ialorsccling l*e lrl-et ' relo al Pt.
iI
I '
" 2S^;4t
rh'kicr,lt
;ng L'nc. t .77 .
l x .
,9'l-
4. 2oad zr.= o.6ts -jo.lts.
+ Zr-9oL- 3j'75-i2t'7t (n).
6) f=+lf t ,=*" izst.s. 'c) If Zr= O, *hc f;rsl voltago ninimun would be at
Zi=\/Z - 25 (c^) fro^ *$e shat-cireuil .
P I -z+
a . )
f = 2x tos (H ' ) ,
-\. = /. 5 (,^). + I : ?
- o. 3,/5(^)
C horor*er is/ ic )rnper/n-nce of Tctctr ler-
; , ,v i re ' {vwo-r,y ire
l r o n t , n , ' s s i o n / , ' n . , 2 ^ : r / z 3 A ' 3 o o - - / 4 g ( L ) .
Co, o /ort/e's air //ne., f,rorn E7' (s'ss ) a-n4 (r-z+),
7 l LH , - ) t :'o = lt - +/{: cosh-' (*)
/+ g -- 7y6: corl"-, (*)
Qiron D : 2 (c-) - a(wire roJ;,r) = 0. 94 (cn)
P s-zs zt = (2s +2>r)/so = 0,9 t j o . - 9 , y r= / - h ,
See con"/rc.e't'ion.
P , t Z " -0 .g r i o .E .
Pr : Yt= / ' i / = YsrPr t Y r r= l+ j l ,
+J , : o '
* Jz : O. /6 L^+ (a. s-o. ? I il_\: o .324 ) - .
^ l l
G : bu= /, -rl,=(o.z;*ot2s)^-: O - 7 T S X .
$': bgr=-? l.u{- (o. t7r- o.2 s))_-= o-/acx.
ttF
&tII
t"_
6g
, '2
S-,4t1
rl)'kicr.ir,
i rrg h'ac
. t . 77 .
l x .
\,
iJ,
't-
*. 2oad zt= o.6ts -jo.tzs.
* Zr-jozt- 33.75-j2t.7g (n).
6) f :# t ,=*" i :s t .s . '
c) If Zr= O, *Ao firsl voltagc niainun would be at
Zi- ^/Z ' 2f (c^) fro^ +$e shot-cireuil .
P I -z+ f = 2x tos (H. ) ,
.\ = /. S ('^). + I : + : o. 3'/F(^)
C horor*er) s / ic ) rn leJnt ' , re # 7 ucrr ler - i ,v i re ' lvvo-r ,v i re
l ront ,n |ss ion / , 'n . , 2o: r , fETTi{ : /48 (L) '
,Cor o /otr/er', air /,'ne, [.o,-, E7' k-:e ) an4 (r-z+),
"o= lT - +/t: cost>-,(*),/4y = Ac Lorl ,- ,(*)
Q;ven D : 2 (c-) - a(wir. roJ;rr) = o. 94 (c-).
P g-zs zr: (zs +;: .r) /so = g ,g t j o .S , f r : / - * .
a.) See conslrcaetion,
P , t Z " : 0 -5+7o .9 .
P " t / t = l ' t / = Yg t - J , - 0 .
P t t Yn r= /+ j . 1 ,- dt = O. / 6 L + @. s- a I I d,\
-- o.32+)-.Pr", brr= /, -+/,=(o.zstoet)x
= o -J7Sx .
$': ber=-?1.*1,:(Osrr- o_2 s))_
-= O-/2sx.
51
P. g- ze Fo, Zo- ZS ( ' - f I ) : / .5.20
y , : * f ,_0 .667
/ h - re?u i re4 f lo r145, [ i2 .4 s ]u 5 c<1u i#a_nce-s a re
bi,: -4,: tt- : I /.e.The- /occtf ioo*rf p-irt l t 1* and Q'are-ncLl J;&-nt
ly'le- hove t 4'= o. 4c4 ^. ^,..,J 2i- O. o 7.4,t,Ti, e-r e a.re no c6ong,u" in 1$- /acs*'o,rs aty'$e s{ubt,
d , ' : J , : O, o - , -J 4 r ' : J , : o .324 L .
t r!J_ G iv.,', ' ?
7s (n) , ,S : 2.4V^in of o. z ? i (,n) atn cl t. 2 3 g (,-) f.o,-, /oJ.
-A . :2 x ( t z 3 e -d . 3 j s ) = L so ( - ) .@. t(,0) Fi"s i V-,n a-t +# : c. i s4x
hrom luod .&- - L/se a- Srr','+h cAa.rt.
/ D"aw a, cen{ered ci"c/e (4oshea)" 'throug,A S =2-4 poini.
2- Loca,{e point Q {or 2, {ro,nY,;^ (po,nlon e x{reme. /e{t ) o- lg 4x (c/ock*'i 'e.)' loworJ 1$< /aa.d. L= t .31- j 6.?S .
a ) a - + r -*/ ./.1: -/5 z"* 1o4.3 - jrz.s (jL)3. Lccxl. 4A. drao,.lr|.o/, o/fosi.t<-
p o t.'nt P^ 4o {,.n j lt : 0. ai g t j O.}4.
/2 .o.4 o.04+^- aJ l ta inr Q' .4- L(s.'fh" Snrith chs.rf q-s 6(n a&nithne cha.r* anJ T|nJ
+he- inlec-:ecl|on o( ah.l1l-c-ir<(e wi+h tL,e- g=t circleo-+ P,t /B= ' t + jOtz. R"cJ 0-/60;- q{
G,D Loca.i ion qF =4.'b O:or:r*&f-
"effr i-O.076\-o./73(h).5' h or I - <:t' r cuile 4 slu L / e. ng/ h 1a g r' v.- be=- o. ?z : / = o.3 izx- o. 29,-
=O. /)2A--O.23C6,)
70
I' I Compctred fo
V ) P " o b i ' e n , P s - 2 t
t -
----I
IItt
I
'\,
P. g-Zg Llte Smith chqr'f ar a.r ' t irvp<.da.ace. cha-rf .
,S'-rr.e conrt 'ruel ion q-s thql )o pro-6/em pg-2g, e.xcept point
Psc wou/d be.al lhe. exlrerne- /e,ft (mor/<<J 5y o ,) o' ' .(
I ' h - S : / c i r c l e becomes 4 r= / C l r c - / e - .
P , t 2 "= (2s+ j ze> / so = 0 .9 + j 0 .5 .
T wo ryoss i b la 5 af c tTJctns :
At Pr ' zsr - t+ i t .---+ cl3 - (O. t(Z x_ O. ogf).) : e. o7+ . .
At P" t zs t= / - i / '- - -+ d r : (O . lSg , r - -O .OCg^ )= O .29o) . .
k ^ci. ieve a. rno-fch \,vi+h - Seriee s{ub h<-uing
^ / 354: it Ro , w< n"ed a ncrrna.Jized s{<tA reoe{a-nce-
-)# -- -2'/.213 $er so{e&;ln c.orrzspa,iing lo Pr. Fronl
5p,ifh chor-f ,.ve tn4 *he- re-oui.e-Jsfub (*5*h
/ r=o ' 347^ ,
5;r ;/<r-, ly dor' -so(q1ioo @r.e-spon4,'ry 12 P^, d 5*u/krryth
rxith o.-no.rnaliza4 fea.lon.e- -S'/.43 is nee.Je4rwh;-$
c " fu ) re t a - s lu$ / " ->g th . / r= o ' / s i ' \ .
7t
,lt
)
J(m).
;^-
30i.
q? a= at
I
,, tx l!
z
,D. q - / ' We- c,se- f7". (q-;+t
respec f i ve ly For c t ) r , 7
(ur/u)
I
eb^ *s: q
Wa r tg u i de.s a nc i ,Qeso, ' ,a lo , 's
crnJ ( f -s?) - fo . Zru anJ Zrc:1o : / 2o " t ( r ) - - 377 1 l L )
a) The narrha/rzed w€\ve
/'ft P. Ja nces- ct re y/ o#e.t
c<s skcwrn.r \ / - rT r tb ) oTM= t t o l '
t - - / '
'7 4r- kT€
/ t f : r . , f" , /@ --4,117.
Zr r : o ,4 /7 r lo : lgZ (9) ,
Lre= =hT - gol (g).
At f =2.1f. , /ryf :r/,4*.J- o.s?/.Zr. : o sq| ,?o:3J<&). 2r r= #:+23 GL.) .
P o-Z F.orn €7 ("t-tg), F = k/ r- c7' : #/ t -1*;'.(^) ta= -p ( r-G,/tf
I r -:42;:uJ/-(+)'(h\ ' * ( - f , \ ' : t\ . , ( , /
. \ f Iw h i.6 i,t <1, col.s t'o-f +4eg raph of (u"/"<") ploaad versus(*" - /+) )s a- 'un i* l i rc le .
a) uj
1/F
n/J)
7;
b)
QA)
ie: 2n
T (j) ,t/ - (tJ;r2 n p t
zAtrI - / t :
'
v r - (f./tf
i Zre
\ ve -
#e.l
A
O",,' 1r4,
(e).
lL)
t / /a \ /9g-r ic le. r 'n Ft ra . V-
aycra-Jion f-r Ult) '
d )
b)
e )
P 9-3 Fo, TF vtt<vzs
|roph shewn an fh.-/<Fr.
) At I /f" = t-2e,u, /" t : 0.6a, )g/x = / .62,
u , /u t . : / . (7 .
e-/vvec+: in(;n ite- p <cr^ al I e./ - p I a-)e.
) txe- -sqlve +Ae Fo//o,*rh3
. l 'Af l l t* h-Hlry):o,d y ' ' i
with H"(y, i l = f l lct)?7 foupJoT con./ i+, 'o-.s lo
be :q. l is l i <J n/ th* conJq.h ' "5 p/^ /<s a-J-e :
dH!rv)fr
= o a-{ y-o anJ / :b.
Prop{ 5e/u/ron, H: V) - Bn ,"' (ry) ; h = T, tt-12,3;,.
fro,-, f7.(7-24), f"- # =
#Fror-, TE, moJs, n=/, (f,)rrr- #
Inslo-n/at+?-.,ur; fic-lJ expre->siun.s &rr TE, rntQa,
ko1v, z; t.) = 8, .o, (H cos (a)t-fiz',, F, = ̂ F@
K, (y, Ljr) -- ff s, s in ( ni9 s in (q1q -f,r)
E* (y,z;t)-- # P, sin (#) s;. (*t-f,z).
7s
(, / f")
P?- t_ Pa , r i s (a ) c+oc l Cb)-s)mi/s-r 1o Prcb/e^ P. 7^3a.) Phut" exp.esrions .4r d'e./J conpsnert*s o{ fe modes,
l"(y, z) : Bn c"t {:"rz) " tf"L
,^,i " - &h< / / -(+) ' ' n= / ,2 3' ' " '
!J, (v, z) : .j.* Bn ;in (!#) n- i/"".
t* (y, .> - iff Bn s in (T) e-if,',
b) F,-o,n f7 ( t -26), hn: #c ) S u , { a c e c u r e . f f s . 6 5 l t i e s ; f , :
Cn low., p lefe: Jr l : a,-x f r@)
0n upper p la re , 1 - : - rx t tC t )
Pq- ; o- )
Enx i ,-"€ r
= i* 8, a jf"".
= dr 1-rf "8,€ if"o! r a t .
- l J s t 1 4 r n o o a \\ - I s l * . n c v e n .
L " - : 2 o , : ? x Q . o 2 e : a , O S G ? ) .
( q - z c ) q n J ( q - 3 t ) : ( * ) ' : 1 2 7 L, ^3 / 7 - t ,
^* #;, to1= !:ii i;r*,9b) LJs= Smith chart. )n",* l r l - #- j . , - . bfhrougl> s=2 Fiot.
,Sh,l+;ry \ 1o*va,J fo*d /.,y #: o.trl+
p/<".s ?"i"t & /,nrr. (/te boy' fu.5-o.tSilx,=o.3$l A g low.-d {L eg-r-rertr,
,L-_-,J 4-: o.qg + jort.
zr€ot- ff i = ##-t4761)-* / r= (Q-?q t 2o.at) x 511 - t44 + ilio <9) .
1"^r- lo (r- *) - 8. r7 (w),
74
A S : 2 x 2 . ' o 5 : 5 . 3 O k m ) .
fo. TE rc mode : f . :
Front {ct.
J:
*9-= J* l {= :5d/o1 (Hz) .2 a . 2 x o . 9 2 5
c-)
- )
Hz)L
t.
f
0.6ilr,
Pq'6 TM,, -uJe io a i r - { ; ( (eJ recr \ngu(ar \ ,vaveguic le
Oleral i ,-tg zt a-r3u/or {.t .71'/ency u:zrJ (re. Ff.?-1s):
a) E)tr ,y)= Eos;. ( f f : )s;^(T)
Jap+ing 4-o in [7 .s ( f - i r ) l l - ro1sh (?- r+) '
H)r*,y) = +# =ffP)Eusin(T)r",(uu ),
H| t,,fi : - # u; = - ff H Eo cos (X),;n (T),
Ef,t*,y)= - #,'#:-#El E4 co'f#) s;"ff).,
d ,.r,= - #,, # - *r@:, , ,, ,,ry) .., (!),,.*hu,. h,l = (+)'o (€-)' , f,:1/r^ty'e
- h). t/aria.lions
i n z -d i rec ,+ ion are deswr i6er / by the y ' ' c fo r , " t4 lz
b) Fro- 9.cr- zd, (4)r.,,: fi" - ;fTV,(x - i , ,=* - : -L=1 c'1Mtt (f.)r,,1,,
. ) - T ) - c '- = : : : e : - -' 3
F , , r ' t - ( f . / f ) ' { f ' - f . '
P q - l Rec fangu la r wavegu ide : Q ' : / ' 21Gm) , b :3 '4a ( cm) '
E7. (9 - as ): / ; 1 - 2t-\s/1nn_
,m
Mod"s wi*h lAe -rhorlesl A" ( S (cm) a're:
Mode TEto T E,^ T Eot TEt,f TM,
A kn) | 4 ,4 7.20 6.s0 5. ls
A - lo (<m)"t /he only ProPaga{ingmode is TErr.
A = 5 (crn)t fAe. p.opa,Safing mod"^s *re:
TEo , 7Ero , TEo t , TE4 , and TMt r -
T5-
a) Forb) For
IIII
I
IL
I
Modes F&rr,n)
7En
7Eot, TEzo7 8,,, rH,,
7Eo,7M,tTMaz
I
P.q-s
? q-q
= #F(^,n).
b) a: b, F(^,r2 =JT6.e) a:2b, F(m,n1=/ffi
2
J?4
Jii,l2o
. f - S x toa (Hz) , x- r / f -o . f (m).
Lc.f a.=kb , t (kcz. ( f , )^,= 4\m,.(r ', L lt tot\ lJrr= ff hr fhe dominanl TEroaodc .
t -o r f > t2 ( f ) tu . ' a>o .o6(m) .
Thc ncrf h;ghe r-ordcr aodc is TEo, wlsh Cl,>rf Y.f r , f <o .g ( f )o t : b<o .o4h) .We cAus. a= G.S (cm) and b = 3.9 (cm).
u. - $.a - 4.To x lat Ca/) ,r { t -(Nzaf- . txs-
mEff.= o.ts7 (r,) = fS.7 (cm1,
F: + = 4o.l (rad/m) t
' n
(zrr\o- mt'- 5?o (fr) -
a)
b)
76
7E,r ,Tt4r , | ,12TEor ,TEro | 2
-l--III
/
[ *
Pq- to Q iven : d = 2.Sx lo'2 (m), L =f.st lo'2(t^), f '7. s , toe (Ht).
a) -r . - f :#-o.o4(m),
4=rlm =o.Go, .\S - ^ /F , - o .0667 0 r r ) o 6 .67 ( cm) ,
F = Zn/xr= Q 4.2 (rad/n),
uf "/E
' ,l' lot (r'/il,
\= c '1 ' l ' t x lot (m/s) '
(Zrr)n= , lo/ i :2oott = 629 ULl.
#.b
b) X=?-b-o.o233 (m),
Fr'=@ =o'g2e ,^S - ^'/F, - o.ot+3 (m) = 3.13 (cm,,
F'e 2n/^; = f93.2 (rad/m),
' i= u/6 ' 2 '57 r la t ( m /s) ,
ij = t '4.= t'?s t lot (rn/s) ,
(Zrr).= h-323
(tL).
P 9 - I t Par* G-) Ao.s been cJone
i l Llse- E7, ( t- t t) *o { in4 th"a lonq /he wo.ve2eta is .
in frob)em P. g'6, parl h).
av?+d.le Po\^/er I ransmi*fed
P 9 ' tz +) Er{*,Y,2;)=fosin (toonx)s;tt(/oory) cos(2np'or -f z)
Eos;n(4) t;r(f, i co' (2ro'orfz)-
M od" d ope rof ian : T M, t4 : 2nf : Zzr /oa (rad/s).
77
-"i
. j
- l / , - \ 7 , a - , , / - - . . - - - -b) ('.!.),, = ?J (tl'*(4)' : +/ ##: i .+ g x ic, ( l {") .
F : ,4/'-Gii 7. G-zz) ( Zr*,),
: #[t -H"I: /// (raa/ra).
P 9-. : TE qode in C.o25Gn)xo.02t( t ' . - , , t ct i r - { ; t / . r /^s7.rar?
W. : \ \ /egU ide :Hrr4/.,2; t) - h,s <,tr(#) ror,lfx)ros (at_f z)
cL: ry : 8o?r : #,, -':::"n:::)cos (d+ -2goz)
--+ TEo, rno-le.
b) Fro,..n {f - ( 7-< s) :(f;0"='
? * =
* -
#- /. 2 x Toto (H,) = t z (gll").
Fl.om E7.c?-3s): P:?,F@ - Z*,ffi:.
f : J74'14 = - /. Y,t ta''elo)7 t ^ 2 - a
: / 7 ( & H ) ,
Zru= ffi: J#.-Sdd(tL),
' / \q113/'
A! : x/C@T : c/yuQ@ : 2.24 x ri t 7,o7 : 2. 2 4 (co,).
c) p, =+fbfbl+f r - . r . .=afpn'Ht fb-v 't ro.v = T )o Jo trrex 4Y
4 zr" Jo -;o'(ffx) Jx
: (zrr).,ab ui (+,) _ zgo (W).4z tx \2 ' /
78
?, F€l :3zZy/,--r '
37zxo . ' i 3 -Zoo( ! , ) .
3 x / c "f f i ; ;
: O.0566 (^)=s.ss(.^)
(fQre
e")
,o
)
'cm).
o
j_
P 7- /4a-)
Subst i lu t ing E7 G-fz) , ' , 9 . (7-24) ;
- r vv,'(-)*,) -h'f''": i r[a7-n'{, - irlq (rrV, -h)-'
l''"x i/r '*n, {,-
'T'o @7.-h')-'t
Fro- f7.G-ze), @r: aJFr@.
f te i "e , y=d4ni f ,
wi rh 4 . -Qf1 . r | = %4
rr) j=T'/z@*r
A/' f - + t (o1 (fu), TEro E '/hz on/y />raf c,-e*fi-\s,rna4e ,^tAic/> 6o.t q eu{c>t$ fr*/u.n.7 #
(f.)rr,o: # : # : ta';'g.1{# -- 3x roe G{-).Th-r, d4= }ffi : o.oo?e (ny/d- ooz4 (+8D.
P.q-rs (f.)*n= ilffia') (f),o-
* ' t' \i"aie = 1x /o1 (H): 6 (Qu).
Ncxt higA.t moJe: b -42id b ' = 4 5 O a b=0.79a
(f)or #(f.)t,= *i/,.GftyJro= t
24
>1.7
@| 3.+
@
(tto
t L
Llsa6 lez b q,J,n;e+h is o,8.9 ,| |L o.a9x12 0.6 l8
*oa / . / f , 1 :6 .9 (eH) loz l o .L / o .L e .a (61 ' t z )
P+rerisril/o lanJsi4tz* 3.t(ard 3.rlatl) xfjiS
b) Fro^ t7.G-toD, pa,- I,rgr-2t.3+(*).
+ Pou: 9. j (w) &r b-o.ze a, and to .Z f tD {or b -o.Soe.
71
CGHz)
( *(+)(Gtlz)
e _ = O . A g k n ) , b
{ '^- .: /. g x los F(n,-,f),t ^ n ?
E ryrf /o-r" . / -6r der t4oJet
: O, O6 (m), d = O. QS (n).
f(n, x, f ) - too/ (7)'. (?S',(gy .a rtJ /f>e., 'r re tonanf f.e9uen.,i.r,
P. q*;z
W:: I F (m,n,P) f -n* ;n (&Hz)
TM: to I :o .g3 3 . / zgT € r o t 23.5s 3.57sT E r t t 26 .o3 3. no,
jE ' , r , TMr , , 28. ss 1t- 3tLT t4yo 3c . og + Ea7T Eer t .3 2. 02 4. gozT Mtzc | -? 9. 60 9 .3 40
cx ) S ince d >a ->b . , *he /owes f -o rc {e . r t ?son46 ff t iode is 7€ro, r - rode.
r - e F - - artot - T/ ;r, 4 - 1. Bo, x rg, ( 11)= l.Yoz' (g.F{z).
b) ,:ram E7 (e-/2o):
D : v {,o, ,/ ' to o-bd (a} +41)*tot- P-rf2@
- , f f iW a.64(a. '+ d ' )
: 6 '861.
From E7t.G- /(4) e.nd (g-rrs):
W" - *roFo' -t I
o f,:, H: : o. 07z3 x t6tz g7S= o.ozztet),w^- fr ob4 (# * r) Hi - 0.o773 (f ;r) -we .
IIIII
II
Il-IIIIJ_--
80
P. g - /s
P q-te
a)
A )
c)
1 r :2 ' 5 .
r - t * l t l: -) t / t L { a, 4t
n : l ( n \w(oJ (€r) ' /a\"tot/go
W_ (W)ru: o.
ta '. | : :
v { T f t o t l o q
: t
( f , , , )g: 3.r 32 (Gtaz).
= 5 ,162 .
oz73 (pr)= W^.
r : s l = - ar (o t Z la :
- , /Va -
t
a') 4,-* - +Jn"/m :6.soo
/ q, s oo (21'/+ - /a+ a - - O . o 2 g q G n ) - 2 . 9 q ( c m ) .
b) f*, - &
: 7. j+ (qU") .c ) For copper , 6 -5 . to^ /o7 G/n ) .
Q,o, o G .To.,- 6,s ool 'r i i - 12,443 .
P. 9-zo n ,[ffi"r a-bd (at+ d')*{o{ -
a) For a . -c ! : t . sb - o .o31 f ^ ) , b -o .o2 (m) .
i ,o,= +{{ry - t .r7q,toe(L)-s.sqxto1 (Hz)
Qto t - 4o .zz , /VF - l l ,O l g .
b) Fo, Q'rn- l .2o Qrct --r 6'- l .zo2b : /-44 s o. oL- O-o2ss (ft) = 2.g? (crr.).
o
g l
WAntenna .s a .nd An tenna- A . .ays
From EV. (/o- /z) a:-rd Qo-/4) :
a- ,9, 6) - 4n8t ?o-L T g t r ! 1
P. to- t
b)
P /o-z a)
t l
Mqximum E, of 4, occur at €- n/r .
o - DP, - Eo' .'j aw 4 zAt ,r?o
, 7 - 2 - > ? o D P .
1 1 - / F ^- o Z 1 T Z , ; D : 1 ' 5 , I
- -+ Eo- o :ogzz (v / - ) - 9r .zHo: # : O.Zsg Q, .A/m) .
a o
^ - U^o,"_T
frIuao
- o,/ox /E x /o3 (w|
(n v /^).
l .- J , ' f ^ t
2 - i , K r '
---* -a_ 2 P,Kr -T :
-i
Uno* - 50 .
T-rc.zcstl.
#L"[o{r,n'n cosgsine de d4
= 2.6s ( tu/s , ) .
- - " r> D=#=lg '95, or l2 '7 'GD.
L{.^t: +P, :4n Uon- 4?rx2 .4 , -33 -3
g2
.P. /o' I fq.ra*ion/
- Q) t -
P ro-4
t 1 / . f L
tsowe-r losf , fL:
Conf inu i t y : V -J : ' j -_e. l 7 t - \-T'
^ 7 o+ F : = - : S t n 2 7 T Z
1 c
d;pole.
g3
of
j_(A
^) Z (z) - Io cos zarz
F=+:271 Lt/ovelenS th z, - | Crri..
/2) i rz) - zo ( , - *t zt) + f": t:lH 2i'"'.oo
a )
6)
w).
^: #:3oo(n), *- #- j ; . . t (41../z;on J;polr).pod;oh;on re^sishnu, Pr: f ,orr2(*) ' : tgz (n).
Eq.( io-3o), 4: , f f -W :2.6tx t ;4 l .s} .E re-( to '2?), PL-
| . (#) : o.r r , (e) * \ , : &-gs.s%.
E7.(to-zey: P, = r'(d!)'- ^' )
87. (ro-,o7' 1r;;*!$e;'${i * lt'l"-"'- *{*"= tq (^v/n)'
rr (t?)=?f r_j'1 : S. o /, /.6, 6D.l .17 t rc"
-?:#-3(-).Di p olt bngf h : /- l Cm)* 2, - 73. | (sD.
c)
I+T
.:
h f '^+
(zoco'/z)zJz
#-6t/:: (AsLx rr= o e?s(F)(*')8,:7r.t (*).
.1i. t-il.:t'I
!1
P, lo-e
P. /o- r
a.) Ee -,i W /fT'( r - #S eir'co'e dz
- .m c'jf| Frs) ,un'i -
fu"-jP"FG),FG) = s;ne[t-ct!(tt gasdJ .
In case f hr r , , cos( fhcosl )a t - { ( fhcost ) ' , an4
Ftcl * *(t ' 's;n e'E, = # oile 6 ptsine) ='ry r"4-iVa sin e,Ho - * r-ifa g fh sino) -
i#trttlA sin e.b) P, - *{T"r ri r'siae dad{ = $ [nrr,(+),J,
R,= P,/(*i l = Zan'(*) ' 'c), =
ffi * qh:rc + raloe o-t.o@s1.
l : /eo x bt ( H) _>^: ?: #
: 1 ,647 ( ,n) .
h: 4O (m).<<)- ,,^tilh /riarrgctlay, cu.rcnf distribuf,bn.
a-) /r,-o'-t P-oLle,n .P; /0-6, tse ha-we , ( fg= +)
l l" l^,^r7 -*ro- ff i ^ioo: r.rr(av/^).
b) P,
lH+l^or: f ItJ^^,- ff: 7, s I x /o-'(A/d= 7st(y,</^).
: +I"" I;": zntsine Je - $rf^'"tl*2;"?ede- # (f rq' (i) = s(f h z)-: ! l+'"'GI l
= ryx +ori (#V)': , , t36.s(w)= r. r+ (2w).
, ) 2r= Zp,,/ t i = o-227 (f t) .
r4
-v
P 'to- g - l F t4) L ' P(one pa f te rn {unc t ion {o r } f e r4o 'o ,nclipole is , from E7. ( /o- rd,
F^( e) = -s in €.
Mo*. Etu) : { at €o - ?o"
T; _' : :': ;' :7,"i,, : F- ( 4) =*
-+ Be -a ,nw i4+h A€ : O r -0 , -?oo, \6) t -plane pay' lern {un.h'on hr ho?-wz,ve 4ipo/e-
i t , f rom €7. (ro-sr),
F^rc)- cos{(v/?)coseJb\v.
- ---7^ a
lVlo" 6 (6,)- I qt Oo=7c".
fb. I I ^ P otars, Ooiofs al
-+ B"oavv id th A0 '=
P. lo- to Ltse E7. (to-27):
f5(€,'):$ {ei) =t .0r'- ei- / 27"- S/"- 7gi
).
85
F(e) - cos(fAcos.e)- cos.PAS r n O
For 2h : / . 25A- ,
l f fe>l - lcos (r.zsn cosel - cos (r.zsi l |t r r ? r l - t f l
lU;a+h af mainb.a,n Ae{*.rnthc- .first nulls= 2 x 5 3 . / 3 ' = t O 6 . 2 6 " .
i.i-:rf
*-_rj-..{:l,l
P io-r t Use 87. ( /o- to) for Her lz ian d ipo/<s.
- a : E, rc) ' t E,@): ; i ( zh )- #1/'i,r(#_#)
-rAo _ _"-j|r'
I t l ^ - / n n ILn (be far zor1e, P- ; R- <l cos O.
a-) Ee= t# 7o p sine A/2' (l * la'f 4coseS
= +Prf ,iPrc-lcosdF(il,
where F{e) = sin€ cos ($ro, e).
5.1 4 =)./z ,
lF@l - ls ; n e c o s (! c os gl.
: ) d= : . ,
lf?Sl -ls, ne cos grr eo, il1.
86
p/o- /L
P. /o- tE
o)b)
/ ior an a.rray o{ i .Jenlica/ e/ernenls sf a.e4 .<
c/r'-tf aoce c/ c\pc<rf , we 6ovu, {rom Ff . (/o-g+),
It i : # tFc1t)l l*, *1, ;eo
\vhe- rc ( - - fJ s ingcos /+ f .
In lhe H-p/or. aF a. d;po/e , e : r/z , F (!, 4): /<t-) J=4,9-+'
I,q, oil -- i, +i=1, * lI t,,.- +)ll ., \ r 1 z \ , - n 'D t a = ? , ? : : '
. . t | , n n . + t r llA@) l = lcos( f fcos( + t ) l .
IJatt
Five - elemenf broadsi{e- |inomia.la-rray.
P.otaf ivc cxci la* ion ampl ihtdes: f :4:6:4:1.
I r ra,y {acfar : /A e | - | cos(!c." g)11
c; cos(*cot{)=QV). ' /o
€ g = 7q.c6".
Hal{-power f,eamwiJ+/1=2 (go'-74.96'): jO.29..
For uai{orm a"?4v , {ro^ Eo.(tt-Eil :l l sn (Fcu l l ( ' '
r .TtWSi -E- i '7*3t '
Half -po*c, beo^wid+h {oc S-alct*rr{ llnifonne*AwitA 4a tpact 'r! = 2(go,-7E.6t.) - 2O.78..
g7
P to^ lq 7ne n< Trna./;zc4 a.rra.y SacaaT at iAe{;u._e/<r'ter# ra.pzre-J arrqy 1j
iAc^.ili = + I / * zei!+3 J2** z {'3* + e;+{!
- t l ";,*
[z + z, ei i + { iu) -, (" i '*+ ;;"*)Jl:
+ l 3 + 4 c .os, l t + L cc, z{ Icraph tF V<"fSl r" . ! i t shown befow cntAe./e.Sr.
-n -n / t
Fot b roaJt ide- ,opr ro f fon: g : O , . ,J , =
f d .o"+=1rcos$.
l ' i ( i l1 = + lz + + cos(v cos d) + 2 cos(2 j r cas +)1.
T'hrs is 2lot+ed a6aue- om +he rlgh+ . TAe {i .rt siJe,/o,1c,{e.,rel| t 0.// ,
"" .b(ugr{//o. l t) = /r.2 (dE) a,awr, {.o* fhe mo,.n_bea.m
rq d/a-1|on . Th is < o"r,p<l-rz, ,.vft6 O.--, or y'? (d B) Cown frr r1he
.ive-- . /err ' ,en-( qnf#rn broa-ri=, 'Je- o.r.a7 shown ,h t] ,g./O-l/.P. ' l t - /5 F,o* -Qr . ( to-3?) and ( /o-6d :
llol: ry e'jtp l"'t3,7, A,H;)Ay6t)l
T )
where A*(U):; !ff i,A (*\: t d!z*hL.. , / , t y t
N2 s i n (79V5 ,
, l i - $*t ino casf ;, D )
7t : i;' sine cosdt v -
t
l r G,6t l = INtNz I serq,"'d1 si " (#). s ;" (4b) | .L sine J sin(f , t3;"(g I
8g
o
I
It/r.
1371/z
-r
P to- ta-h
a-) / l ertzi^n dipole ofJ,(z) *- Z@1 ,
, S dt/+/" =
J_orr" cos f
z dz -
l? to - t t A-
l '{^/f - w^\/e dipole wir| srhcts6,1'q/q/ cqrrenf ch'strr!>qhbn
Z(z) : J (s) s.r ' . f ( | - lz l)
- J(o) cos fz.
r 1 1 ) - + r ' r
\ fT=t)
Frorn E7 (/o- (g) and P.ob/.,n P. /o- /6 6) , l.= #.f rom €V. (to-s€), vve hono,{ar 0 = 17/2,
1 : + r' @) P, n r@7ry-F =z+,,u,).lE,l= ###: 2-?6 (v/m)
l4"l= le,LI: 2.?6 x $ = o,v4z u).
/eng*h c//.
t-!at, s;^(rs#l= f +.&.
b) l/a-/f - uvave 4,'p.o/e- ,uith h = L/4 ctncl J.rz):r(o) cos pz.rx/4
/ . = f - - ' =co ,pzJz : * s t r o ) t - 2 ^- '_^ . / , - - f - - - -
,B - '^ \ fT) : p
- ?r
c) l lo l { -wo' . te dipo/e ,y i th A:/ /+ anJ a(z)=r(D(t-4t21/r) .r A/4
t": [:;* ( ,- +tzt/x) Jz = ,I^'*r,t - +z/,t)d, : t .
t-#='t (m)
l.- h/' r<z) dz .
Fo, rnolched loal,P: V: : o '7+i '' L gR , gx?3 .1
a)
b)
= /. s a x lo ?(w) = /.52 Qnw).
II
s7
P to- rs , q . (io-sd' pt_: ##r,
f : / fe(m), Pr :2x(o3( t* r ) , ^ : - f =##: /h) .
c ' ) P a r a / / e / h a . l f - t A . / a w e J i p o / e r ; 4 : D r = / , 6 4
Pr: ff i f f i{,2,/oj: /.s/4 x /c: / . 5 / 4 ( * ,
b ) Pora / re l l {e - r l z ian d ipo les : D , : Dz : / . - tO
P, = / - s t4 - (#) ' : / - 267 (mw).
P. /o- rq .Froq E1s. (/o- /z) ancl (to- t+):
G_: 1nU(e , r . i l _ 4 t rR 'F" ,V ' D D D' r . r
l l . r1-; ' in! t q". (/o - 40) an d (/o- 12,), r( - - l c r l : r / ^ i : cs (4cosdfz .) D r ' ' . , - t ' O . f I_
L s i o ) I
- :' (w)'"v)
,h.Q:
a ) Su,6si i i 'q f ins @ / 'n €Z ( to-7s\ ,
l"re): #ecel= o./3*
Occ<trs af O
c) M o-r. yo. lu e o*
b) M ox. vo-lue o.F A"(e) for .f : /O* (H),
f cos(*co'dlzL st.'d -l
A"(g): o. /3x. / -sz =o.2i c* ' ) ,wL; ct, i5.--rr,,1 o.lfor ,%on A.e)&r f =, /o{ft1)becorts- 4re vva.yelergth is shar{er a! if :J/ rcPpz).
?o
>": f :3 (a)
='T' Arq-o./3* = /.r i (m").
Ak) frr .f : 2x /o?(+b), L: /.9 (a),
P. /o-zo A, . t+ennq ga in : /o IogroQ2, : 2o (c B)- GD: /oo '
,f-a) Fo ^/er
d T -" r
P /o- z l
3^ loq(Hz) - :f:3':/-/fi- O. / (m).
{en-, ily a.1 ra-ryef1 - ilu e"
FIr: #ffi:o.ot4r (w./*')
U
b) Power fnlercepi"d Ly large/ = {urf, = /Sx o. O/4? - O.224 (0.
c )Scu t (e red 1 )o rn r t r 4ens i t y ay ' radq . r e .n f enna
Y,= #- Zff i- 2.7rrro-'o (w)Ref /ected po,,ye.r aAsor.be4 by anlennct : 4 A"
= 2./ex to-h (fi c): 2./rx to-'(#, roo) =zzir ' /i" (w)
Er - / o .o /47x2Y377 = 3 .39 (u / ^ ) .
= tz . t ( fD.[ar t 'h rqd i . ts -6 ,39o (k , - ) .
Al.(; lu./" of geosyncAronous sq./elhles - 3 6, f Ao ( L.,)
Qecs yneh"aus orbit raJiu' = 4,lgo+g4roo
t . - t / 6 . sso . : 44 (so ( kn ) '
Y - s , n ' (W iT )=8 .561
{ - 7o ' - { .s6" - g t , *4"
a) Two sqlelllfes cover only 2r(2f)-):.e"< i40:
U"u /hr"e se.lzlfites io eTuqforia(
p(o-ne, 3x (z{ 'S = 4 8?o> 3 60?
Po/or rggioas are naf avared Ae-.aqse
b) L.t Pr- Poru., fcaasmi(lcd ly sa-/e/li.t:e- enlennq-'9'<qoi
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