Ws T/n-r<. -:G.ry ing /-i"lJ, ancJ Mo.xwe/l's Equa,'/ions D
J'V
-I#'o'r
t:
l-t
J
--{*(vxi)'a; 5
: -,f # dz p.6-2
/j =d- 3 cc,s(unro"t - iny),
/o-€ ( rl.
f a.u'l : re[o'tc
ar : -
i
/2 6-3
Lts ig
:
ftJF t^ 1/
fi:
./F:a. sft:or(;rto"t-o.trr)-cotrnrdf, u).
.^r-r. 0./glcos(srto?t-o./r)-c-os g2,rc71
-- 0.6L3 si n( rntolt -a.orT) CA) = 73 = in f 9-rrtort (nA). 1" )
photor
E,:a+#;.4
with
a s/ne r"f,"ten
f "'!, -7Zrr=f E,,tl- fioz,A Zr Jd : 4#1"(t +yS. ' Vr=-jt$, J1
cl t vL: - #'-PAoto's
lL-: --a
= Yi,
,1+ju>L
: - J-@E"ih-r, Zq (p+)'ul) . 0*i)
F.e-+
;
b, -
= &L-.
- 4r-z?t.
TrJuced
e m J ' i , t / a , o 1 ': - f ( i l t x E , ) ' J L - r .
----7 U -- !';'#'-'(*
- #*)' in a- c/o"k,'vise.
-L
--_:_
*l/L,
Ht;!^Ittot7
R-
2nd(4+-,r)
J,'r.c-*'on
a.) LF L:O: .t
(. =
,,,
V
(ux!).
gaoo.t)
:*(rcn^o,o4)xo./sin,Jt = 0.251 sin /oo?tt )
b)
O,. ',x/o ( w't).
j{
L:o.oo3E
(H):
tttL = lOO"txO.oo3g:
/{u:qT:
, dl tD.
(A)i.{ (t),
tt207/'6e.!:'
(/oT x ao4)fo! . = in (qtt _ 6 9. {") t, : *---7J67-
rc"tf
: o, to+ -sin(toov;
P e-e
- 49.6")
6).
--9 c.,scatx QL (o.?-z-) E : Ec+l' Sttl : -Cas ta{ [o. 7 - o. t t(/ - e-us,^rt)J --O.39
(,ut). c o s c , : t ( 1 + c - o su t ) . / dA : - I o' zsoo( ' sr n r it + sir t2ut) t - t z * - - /.7t d (sin At + st'n Tast) : - /-?q u
I
Sin at (t + 2 asdt)
t-)
3? I
(*ft\.
P e-z
COndretion
Current 4en-s,4y: rE
den-si *y : uD -J utgf,-E S' = e T u a / 2zr €o€r f , f or tn agni/u4e : f
-D i sp{--ce^m.r# c., rrenf
or \
a.)
:/sx/o7
(/Q.
f
M o i s f . s c ,|i :
f : /s x /o? (j9:Ztx/06(Ho), or Z z (Mllz).
I 7\'
,
|I 0 i s p l a c e m e r t I
o/r\ _ ^ = = /9 x to' ( 2r/ 5(€o€,,) +)
S.owa1er:
P <-g a.)
:^
f
/ (al)
u€ = (zT"loottoetr=bxt61 r .f-7o x lo7
Coaduc-*ion
(+):/oE(,1):
: q.7s x'/o-3.
b) .f ,,
s o Ltrce- { rze C o n d c t c f o r : Vx R - rrF 4
-
a.
L
@
,
V'xE :_i-f n ,-
VxlD: Vx Vx lq : V (3, F)-V'U:;
/i
8 uf
V . F:
/i. \U
o
rVrE.
Ef .@ becornes
o ,
V'F + rVxF:o. Co*Aining @ a.n.l @: V"g - ]@f rF: o. P46-1 * n
g.n=8,.*rr
ti,:d;o+dr4o+drzo.
(F,-F,)=i dn,.^
I
rr - /O.
lr,"-lni:;^"'"
z, ^ ( 4;o + dr44 - Fr):4rS . HaE- 30,
a) Fr= d,3 o 3 c)
@
4t- t,.i'
Hrr- 4 5.
f
Jtol-9'
+ a,/o (A[^)-- 69.:o.
38
a)
b) 1- 2f aF2 ft).
"at= L;,
-.!FF---
-
P 6- to
J
7
Mediro | : Fr"" tpa.. , H, husl le zero so ,n"l /{e-liurn ^ , ,/r*&. ,F;.,.,j,,,11n
if,-E
d-rF,-j-,, Bn: B,n.
f z::"1,::i ,
E,o: Er, ,
) '/It q*l2/
',
P . 6 - /3
c- os( zr r /oqt - kt)
E (" ,t):Jo
Eo -- so (v/m), f : /o7(ll),
)
dnr. ( E- Dr): f" .
T :+
^:f,:+#:o.z(,I),
1v/^) io q.ir .
:to'"Cr),
tr':+: ?o
a)
Z: /oo.lzg^
A( Tf
b)
Af
i -sa , p/ot
,
kr:2oc.25rr, ns 4r kz:
tF ECt) :5o
o
tn
c4s 2r r /o7 ( t- r /s)
(v /n)
2 = -/od./z-gx, i{ is o. rt/ofoF EG) :_r o
c)
whi.h is sqrne o-257, or Tr/4.
cos 777r c7( * + r /il
( v /,,) ,
At t- r/4, we plof ve-7ss, z ti"fo(b',,r;og sincts oi 1 o-l4u nc-*ion :
E (2, {):
P.6-r+
to cos G *t*qq =50 cot[- a6 -]lJ : So (v/.). "ot ff(z-o.ozs)
U-te pbasors
qn4 cosine- r="fere.ncz.
.€-: %Eoui*, E : E, * 1:at
E, :4ro^oSritr'rz; Er-dro,o+d.i:A [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>,
37
,/r:-72.{".
n,-F
r
6';
a'ncl
L/se pna-sors
>
-
H=o*llr,
,,
Ca s ine
r:.'F<'re-ncL'
1;a+J* 6+ei1
f){, i ) -:- ? t-6 , u b-4 v€in/i
--'> Ho: /o-4G1 * 2 d* ) -- /cs-* a+ j (z s in q - /, i*.o' 1
H
- O --+ c<:3O] or n'/e (rc'J') -srrr c( - I (A/-)' : ZX 1g'4c-os-3oo : /.73 'lfa
See 5e cf ion /o- L, PF'+zs-atf , f7t
,D.6-tz
h-4
)
a-nC Cro-Z) P 4-/s
o)
z?(GorJg2 = 0.4v (r*d/-), x rcsT
tu) /a:T:
3
ae aa ,lar / =..; - -Ll z -aH = :F)E v ^> */,1 u: '! az lE, 0 0
L/ ,l
: 4h()L!* rto"
:hd*#
:;;*+.ikz
.) v -,/
I : a r . ft tl 6 1
ug
-
:
lr-- b
: drffi*r-
e
G/,n (A l^)
r=
r=&ll
-l tl val
- q#v";ioarz
- t A -2
npt I'
-
Er " /2-O-lTb"-Jo'4r'z
(n/-1
c
:+.i1
7r---
,1,t
wHn
'In (rc,c.)
- 29v'e.^a/t^).
k- +: #g
P.6-rg
t7x tr
E-
for-
th*o,
f, o- Er.Q-rr)
ll
n-
^il,s
tit
s in e.e/'
art
sin0 a
-
F
*).
0
:4#.sino ln
;)/z
lns*ao4oneou's .{or,n ,
,
In
pL'r*or
{or-,
E:dr u---:!-orr r/o 'A/,,)
:
)
.? at-
f_:
l-).
''t/ l ,F/m/.
o
sin(yonx) + doo.{({oir).osftow)JJ[
fuLa'io'tf
L-ftoVx 'A
o-/ .sin (lorr4 t)f z.
: dl
H
#rltto,l'*pl
s;. (totrx);;f "
(tozr)'+
l: ,. a FA q/ e\r?.lt @ : qt(n3 +Tu
-'V6'o:
lt.ln\z-2,L-t,,2.t2
-...+
f'
f F,om @: /tC+z;t) :fu_( i*;'ut)
:m
@
4oo T:
?r:54-4 (*dfi).
- - 4 2. 30 x lda -si nl1st) c"s ((n tt'et-s+.+) 4 /-t tx tia cos (roz*)s;n(rrro\-s+.tz) 616
4l
H ( *,2 ;1) = df 2
P E-zr
x) ,'f: H : oy 2 cos (/S..T
F= +
t_
@
v'xH
7a'-o tf
({1/^)
,La* jf cos(rsnx)dr4-7,/sirsin
*
n:-fu?xt :Ll=
Q7tnl"/t
L*-*)i
-,
: 6/ .Tnlt,rnS' . Flcos(rsnx)' ia'/t' Cc,m,a"-ring g and
@, we
@
reTuire
(/51-)'* F": uy'o*o:W ( 7, lot)'
---r+
f
: /3. z7r - 4t. 6 (r+d/n).
@, w. hono
Frun
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.<
4z
rS
----i''F--
W P/ore
rn
P.7-/
,1."
a)
E /ecfronaenetic
q. soLtrce-.{.ee,
Jn
Woves
con4ctcfina
me-Ji",r,t
consrilq4ive
p6rari1e4ers <, y'J, a.ncl tr,
87,(z- 6z)'
-' T * 2D iv -y- 'E t dt
: trE + e t'9-
@
.:L
EVs.(s-/eQ V, FrE: '&(7-6(): @
/.
wi+h
FV.E -F'E
2 : -/ fr(v^I)'
@
Jq b sfi l u fi n g obfqin
@ in @ and no+ing lhaf we V. E:O: fhe- wa.ve. e..Tualiooin 4,rripafive rn
v L= -t(6 7> , =2
-
:-F
o
re jf": o.
Si^e ; /o-r(y {or i-l . b) F", lioo-ho*nonic
{i./4s ' *
*0'u,)
"nd }i*(af),
Wo,ve. e-7uah'a,-r @ con verts lo /{e/nrho/t-'s
V"E -7@/rE
7-z
+ k'E:O,
eluai,bn:
wAere k -uF.
Af:+:o.3xrdicr.
v/^).
R:+.:#'^3*tf = 4s x loz (m), or 4t (k-). j, R si n € : 45 x /O3 sin 19-9": /2- x /O3( ^) , or /?( k ) ,
of : zf (#)ros/s.s.. '-: tftry = +f o-s(n/'), or aLvut1.?Mneh.
4s L
2 Z-S Atrr,ft>e-
( h " . r F c B \ l - t o s + 1 , e , - - F r . , ,- * , ./ ,7 1 1( n \ : 'Ut o e - ) k C t " ' k
Th",., Fro.n Ef- (G-gcb)
Eril= Jqte
v x t-t(.e)
)
={
(-j \) e, x /1(.e.)
jd€
: -
E (il:
or p 7-4 z\
(u$t< ) aox 4-145,
7d*x ll cn)
l -1= d , 4 x /d6 < os( r or r t- 1y"{ )
)'o: u$\ l:
=
- +:
#
t,a/^) .
o . t o s( r a d / a ) .
1 lt / kr: 6e (n1. t = 3 x /;3 (s), we re?e;rc fh* r3u,nerrf /o"n(txto-?)-*V + = !nlT. { !,
At
-.*
b)
-
t,
G
pA.uors
Use
wi*
c.osine.
rr$ez-ence-..
d , 4x tdL "iGy' ov+t/+- ) -itrt< re sc,lf of problen, p. .Z^z , E : -lo d, x Az 4 x /66 TGkoY+'r/+)
( A/*,\,
- do o. /o.9y r 7T/4) 4 x tO6 lo e?'/-
: _ d* /. s t x /o-? € c-o.rtsyftr/+) Th.
h:e,t,2,...
J= x3on-7.s [+n):Zz,S+nry2 0.,).
F: f ,o-
:
af cosine-i,t F ,
(V/il.
ins,a.ntar?eouserryercian {o, E ir,
E fy,t2= -d* /. qt cos(ro?vt - o.{osy+ o/+)
++
(*u/*).
Dn-
r. /-
5
U>e
1)hot-sors
dr2
E rt): a)
F
-- t/n
(ral,/^) *
r\ ;ll
/ I -6
a
n:lZ_lz0rr_,zo7r ( \//€ .rc:
Lei
/O"/2?r:/.59x/o'(k'),
: 2JT n (m).
/\\JL) 6\ '
v-E
i rz ea'z/Ea,; di=/rj),
^ .in( tcgt - z/.n + dr Lcos( io6t- z/n) l
a1 :
0)t -kz.
r-
doErosirta.
E_
t-
:
tetqtl: 1t)-
Q/n)-
"-
",:(1e)':3,
1 1 tz,t): & 1 4*, 11
a ztq
L e-l-t -- h o n.! e I |;r:+i'-2. I ly po/a ri z-ed.
F --+ drxE : fur R r r
f :
* dy,'
A:zn/p
u:ft=t-
re$erence
Cosine
"-iz/G
------>
(raJ/s)
et:/os
Al;rh
b,7
E;
).
( A /r ,,5
* drErosin(<+V)
6o En n zrE,
tr
.
-i
:
sino<, ? -20
Sr n
S> r/ t'rl { c a s t / + c o s 4 s i n { bx :. -:= - t clo
,). (Eu
Et
t--
\ Ero
k +^{)
Erc
,\ \2
c a s ' {r t , I
:
,/
i-
c o st " @ ; ' s i n
zh
I Eb/
/ r rzl
Ir t-_(f\ -t4/ l l-s;o."9. I I
I
Reorre.ng/ng:
(-lz--\'
).
\Fro et-'"r)
*/'
which
sr'n!f
/r\:.- \
+' I
l-2
sinY) \ E,
ls *h<- e-Tctdion d
4S
an
E . E , c o s { r -- 1
Tq
si;lr
I,
.llipre'r'r', E,-Erplaoe.
ez:z G i,,en: ur r')/
f*
/
-
E q/. ( Z - l ' z ) . '
;-
3 x /o, (t{)
l4n
5.:
u-n=:
o) €T.(r-+q)'
-
t,
e) /G" \ /T 7(7 )7 : j '48 (u7i^)
t'l?':
t
€r:2.
=o'oE.
ane" lV
:
d
{
,
x = ;- ln L:
o.LZ1 (n)
+;S):)3s1/-+3, ' d T_: t e - iJ z o (t € r l -4, 7-<' , t'
'
(e)
(z-4il: p =,fi\, , *(f)',: ,,.riiiff;r'' E7. ''\:
: a' o 63 (tnl'
+ a
: l. t?Tx/c7(ds",. : ug: :,. E= Ll ?(?)' | s?Yxtc'in7'; T E :dyrir,'l R: :2"o.21o*i(*-o.oosir) +d._.rt iW 'F=
t
t
,
.\ ,4t x:o,
c
H r+r, =dz a. z lc {t'(*t
f
.
,*,,,tj
e
e,'n-(4t lari -z r.4 Tx+ o,ezr d\ (A,/,n\-
2,2^ s
13+A, .oppe.r / rlr-. , -
anJ
(fr)->>/ , "1:@ 9 f:l
at.sood ,
/.*,
conJu.{ot,
'
, t: * , ?.: (/+) #.
(MH=). a-) Co pf er
2,6t (ttj)xtd
Kro-s s
L) | .< <48h) /.9/ xrc4 / . = f x / o s
Ttf r+j2xt64 o . / / x t o l
S ft.',) 6.6, / t, /{;
o.4 7 x roe / 2 . 6 x t c
'
b) f =/(+H). '/ c-
* (Np/-,) & (48/^)
Coppe+ g.zsft+t)rlE l.zqxtd prn"s 1.ft Q4)xtol 2 . T ( x t d
46
5 (-)
4. !6 x ro6 2 . a q x l i 2 - ( K x 1 6 e 3- qq v rd' d6
n: ,fur:o.e? xloe(s/,-)'.
P 7-q a) 5: ffiT 6) A+ : /o? (Hr) , f
a-,|@n
2o Logroe'n": -3o (4il.-->
: l.?{ xto4 (u7/^). 2=
= 1.75xro-a(n)--a.trs (n^).
#*
P.t -/o A^,- le (/r\o: to-' (W/cn'). a) lEl:'/aoza^- 2.'/s(v/r^):275 (vt*), It+l- le l/i;- 7.2sx to-'(4/cm): 0.zzc(ar/,;. L) F^,: lEf/z'lo: /3oo (W/m')' l r ( l - 2 . 6 3( A / , - ) . lE[: g?o (v/rn) ,
)L)
,)
P l- f t /
Y/. /. Itn/s ).
rtrr*" E (r,t):
cir cu/a.r/y po/ar;zol d* Eo Lot (cot-kz++)
p/one wa.ve-: -tdyEosin (atr'/
s;n(c,r(.'Lz+4)c o s( u t - L z * q ) - ' - + # '(t'st'/"2*4)*s;n'fu+-/.*+] Poyrrh'ry vect'or,6:E t U :4# [."t : Ur+ > q c'ansfanl inJeped.ery{of t anJ z. H( z,t): =,
-n.oos r)
t
zrrr\ Q4,/'n\.
P.7-tz
E-drE"*7+Eo,
n: +v*xe : trcr E"- d"Eo) -u*)
du- ta-( r,^
:ao*( Vol'*leJ')
, 1afiere,? rc |he- /ioe P.7',3 Fro- Gaurr's /o,,rt, E-a,v*T charge 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) 3 47
l
L
rdr d(:Vz.
PJ- /3
E, c94 = dy -io sin (/o*+ -f fi I
Lts t pho-soy^t
wi.l-*l
Q-- =('ne-
fe-F
: fi u'|Te,- g h4 - t (r*J/-1. Y/.: @,: (1
,J€r€r-
. : d,
&, 3-tr) : H, (z) = aL//
* rc
d,,
#
, {
"2"/z
g,-* +GelxE,
^v// \
fn :t, f
.tF
U:
/9
#
-
:
(tott + x/s) (u/-)
:+ e
72.
/nC \ \t tr;o ) q/
Ar:
-dy{s;^
H,rryt;=-|r*t,;s;n(roTty') (A/^).
T-t+f
- 1{ * [ _7 :
lo
/ 3
'1 t'b
Fr:
LT^:24ot 6L)
ix/:' =ar. Zr-rr;i:r, t"r-o .--
__
^ J:
.
,.: ( (rd[n) ; /a?"r (L) T,: 7o:
f o stf -s = yneJrL>t L:
/\, b)
.
4'c'S: dl so {)f,v l)t A - Q - : -,ful o s (me-J,"u. ,) /-t c,
F.r- air F-.
(v/-)
td*xE*
e
- --/ S'i.Y
*'
( ls ;. tost ax/z) (v/^). ---', il.rc-,+):dn (,,ott - 4xb) C4^). tlV s ;n j Er(1t)-
: Zoq >>l
a) Ski,
a,
(GooJ.onJ,t*4,,r).
- o.o €,3(m)* 6- )."*) clep+h S: #F* : * . : 7. O*j) + = z.?6 (t+ j): S.(o&-/ilclt). b) fr.cr,t) =d, o.3 --/5.7s2,) (n/^). "-ts''tt'".or(lo*t E ril = - rl"d", Rro)-* f r =,t) - 4 /.6g i,r.r trco, (ort - tf. r sz, ) (vt^). ! t'T'o't : *1 O n. .'tt'7"cos{ :6, o. t'g f*- (E* R') (w/^r"-t,-7" 4g
*
P.7- t6
a-)r:+
-;0
-,
l,-
, .,o H .
rn)
b)
Era E;o
+: "
H+o -4
"Jh) )
e iu.n E;: Eo(d* - j ar) e-iq.o a) Assume ref lecled qtrl - (4Er** a, E.rS .)f."
P.7- tl
ix/z
Borndory -->
,{;r;
con.!i+;on a.f 2=0 :
ia)
E o G a t + y d .)
ErG):
E (o) + lrlgS : g df"' a, /ef t - h and circq{ar I df polariz
Lt/ave
in -z 4be
.
-a"xlH;to>+ u,cil): 4, (Fr=o;" !#J::,:)
b) dn,, ( F, - ilr) - { .-
u-* dy), H,to1: E, - t(id.*,dr) ftca">'E.o) ftca">' t U
- # ,iu, +dy), R,{o)- R,to1* H,{o1
Js: - dr,F,,q-+'lu*-1ur\.
) I
c)
(vf^).
Ca/*,).
+ Erur)"t-' E,tr,t):6QnlE;tz) : dr- Eolta.- ar1 €)/"* (- a, + a; # i i "if'f :Q-
€ol-z2t"r-idy) t;,.,f ")eie
- 2 Eo s in z (d- s;a utt - d.,co" ot ). f
P.z- tg G.
a
(vr^)
'w/,*)
Fo.
,'n.idence-:
norrna./
1+ f
- t
,
wh-r.
l f l st.
f <0,an4,1,I_+ l"l =lfl, --"--""'?,- 3\" lf l: * 5 :
'lr:2'lt'
:?.s+ (48). -1.'--'-r'Sar:2o(osro3
#-
41
P,i-
/1
:dx./cij{"
[,ti -
+ t
e-
r1.(z): 4/jT
: o -i r : il,
(,t/,n). 'i6z
/O
I =' + '
6/-) r - <: ) 6c. - /- { x/c?Ga} /s)
+
Ton f, =
{ ' } - ,= 2 . 2 5 t
{ossy m-Jiu,.'r,
E7rt-42): o,: #)T: -d^7 ' ( t - r s ) :
T- -n. __.!-:__i,_L :
_
-
+(!)+:
. ".,
/.ss &pt^)
lf I = a .,tf..l'f r f' ',,u,*' 1 ; ft V ) : : 7 - i o t=
(,*i *) : #
Eo. (z^+q),2,:E I'
{
.t
A '- \ C g w
(ra.A /r-,).
(," i!):zs+i"in)
i t c q,.- q 'c e,'-
nr*it ?*: O.goE.il't' 4 + f-: O.-{Og.rrD.O (62 + te7'1's ,::) E,ir) - A*- z,og e' (v/^). :
J.e t =
E- t") : j, ? a"x dr )z.n8 ui,lt' *r gt.?o) t,r-d ;x =- dyo.oosS si(e7+teJ'r') (a/i,
Er[r)= a* (, Er) e''""€if'" *d*&os {^tt".'i(?'toz-s'r') '/'t t z /") ftrfO: ay # "-a'(7'toz'5' : -\:
-/. ts z
{-trl
(6 \: \u
qY o,o3z e / | + lf I
avtt
(q )= varl: \
:
ig* (E; ^
l+o.tcg | -o.zog
(A/^)
- t' >t.
-ui+ E-,rF:)
7n(Err4)=d, 4o Q,l L7
ct.taz r 3.+o) .- i
-2.rOz e
SO
#
i2'?o"cags.so (w/n).
1v/^).
F_
P z'zo
rz\ E,{.,2) = dylg stGx+
Gin.n
--* 4 k.:6, k"=e
(v/^)
- to (ra//,-)
k: p:,[Q*T,
ztr/tO= o,6zg (-), f - e./s-*tgstot(11'); b: Lc:3xto1(rad/s). Fr{r,r;t)=ay/o cas(s*/ott-6'-92) (vt4 -t-: ttr/k-
0
:
)
f"4,,
* 4os,') l4:.: k : d*o.6 ,,,
r,
Qo.r)*al lo "-)(€-rt"':(+m,4*;r-i(6.'*sz) - 1z- {z) (A/n)' 'o'(3x1o?7 4#)
krr,0,1* F;G,";t)- C 4r'r:
) d + oi8'sil '-',rrt-
F,k,zy-
C o s9 ; = 4 - n i' 4 2 :
Or= o.t -F
(4)
-36-?"
0; -.or-'o.{
- E.{r.z) : -a> to d}'(62-sz) d) E;(r,o7* E, (*, O-;' d ' ,o ' 6- 6 ' " 0 ' s ' ) Frtr,--t: aroarrxE.{42) ".drr:
: - (+h*a,h)
6iG'-rz)
<) E,G,z): E,(.ril't,rr,o>--'ay to ( a-it'- e28z);;6t = --? izo d)"* s;n tz ( v /^) . H,(z,z)= lll,z)+ Hr(x,r1= -(a'fu
) p/,,1.
P Z'zt
/o,o o{ reFlec4ion i
SnellL
h"
Sn"-$L
+I re.$ra-c$ion: 0r: /9.4t]
cos9z + orfr
l-, _
T*cos€,.-l,eoset
A/il.
€r: o; =3ol
sin gr: ,[2*t,n er:
t
c a s g * =O . 9 4 3 .
T,:'Jo- 372(rr7, T,:e a\
s;nt)€i6'
:
#:25/
(rl,l'
:_0,24!
l"cosha?.tcose,
aL:
1 + lt -
1-o.211 : 0.791,
b) F,on Ef C7-l+D' QC*,,):4rT€io "-il^(x'sine'+zcaser)' * ,6r, Fr(xrz$)* dr/s-z cos(zttft -t'osx-z'7ez) (Vl-) f,= 1fta4/n)
rc. ./, (./'ot2(+2'e1?) : #( s €,+dosi, er)€ 2 drco r, t z), /+ €y. 0^ \ F, o ", - logz'2.?&l -+ Rrk,z;t) : o-odG dro.g+l +aro-zzz)cos{znro?t
@/-;'
5'l
P l- zz
Fro n, proL f ,,n P.7- i { ; €r:6i-3o", Qt - /7.+z: ?1 :377
c)
(JL),
Frorn f q. (z- / rs)' t r, : t{ 7
T-:
zrl 6:.).
- 17'c'as0; -a" cas 9t )lncvs €, + 1, ios ?1
7t/x0.743 - 322x4866 : _ 0./Sg. 79t t d-?43.+3"? xo-E6d
'/l
l
f rom €7. O- /5a) : - ( t' + r.\ ?.'.e+ : o.772' T, -[ "ll./ zo.s €. \ ,,t)
X; tnz)
: ZZ o,oEl es
n
f ,:
T
t; I
s'raoi+ r'ect6') "4'G
lcf - - ; ln'x rot:T
2:r/
("aJ i,n) .
r--
( ro" l,-).
frr-ql7'i;o-V€nrfr:T
(a/*,).
i , L / r t , z ) = d'/" o - o s 3 u 2 ( ' 7 4 + r z ' / i )
: i r, -, +, e -,'9o ), f,r--cx,z ) / 9.i s (a1. rc{' lo. r7[r' -E l Or n :
r
r f otr)
E,
T- 0o , *-Ettg;ao : O . ? Z t x l i . f z
'ot. (z-/r+)
\ f tz;*):
(' at " trz/'d6 v/a.l.
-- /5.+2
I Vl F.1,/ .
ond (z-ts-r),
Eruri - /f, 1z ({ra.7+l -,4anl)
7rut,
tu
{r-or' * x.t62) "-i
wiy'h a. --esin'e re,kranEe,
fvr-). /5. (z (d-o.7rt- +o-stt cosQzaf*-/-or7-z.7tz) o 4 / cos(zt /o't - /. osr- z-?( t)
'
w
C{4
g2 E !r
fE
L*__
lF--
P.z-z+
:
=""r:tf 7,/1,<4t;r:-i yo/,tt, ?r/?o=-i/,|r.
u)f ro^ Eq ft-i4.?): 87. (T-/4t):
Fru.
E! - cos et (1F/n)cos0t'* cos€,
(.\b/.4o)(ot
-
f,
dep<-nds Qre
(l p/1)
t , Lut
ing
P z- zE
-l
'(n/r).
kr) * kri
)
"its.s"
")zt"
lhe phaseshif t o{ ll.- re}/ec-ted L^./ave. of
\Na,vet
in
wa,ve. fh"re
fhe iociJ<.a*
tA/Ave.s in il'te. a.ir
lran-smi+/e^J
Conlinuily
ffi,*
on t'he polariz..alion
sfa.nrlin3
o))o7o
zu
87.0-ltfl;
lfrl:l4l:
:
7 . : ' r - 2 ( 7 ? / r b ) . c o s s-; - o . s
b)From Er.(v-/sg: r,,: F.o,n
c o sg t = J V / 2 , c o : e r = / / 2 .
s i n €'r - P s i n eL, - - j / 2 , t[o
from f7.(y-/iD'
'o
€t' : 60o
on4
fvlz
anJ
expone-n{ia/ly
+he- ionosphere.
: t: : r^i7o€, -jat7ofr.
con4ffions
a*
z=O
o'ecoy-
h.
o//
@ z aa4y
feTuito:
krr: krr: atffi sinQ;: fr-z.o?rrc1 @ Lrr: frr-ja, O Comb;ning @, @ a.nd@, wo caa solve {gt dzzand Fzzin ferms o{ a, /o,€2, %, ard .8u1, sincc fn.
fi .. 0tVo1 , wo hone dz=422=
) rvn).
a) o,- to,-' f
Fr,
= b^n
=
-r/tr;a"q - o.3?74(;t).
ffixfi1
s3 L
f
it;.:r;.r-'
(rad)
b) fr
_Z1rcot€; ll= 'lrcotl 1 .L Tocose; 2 x o . o q q t ( l si ) o-oj93 (tr) t Ztz cos88o z o.olst (l+2) - o.c2H ein/!
c) t o l o g n ? - 4 t z : - 3 o . -
z
, D . 7- 2 6
a)
nis-o.oes3or11. fr r, (os €r- bs o.o3a Z | .
'
l-q
(n).
W:8'6? Snelli
/arv '
Sine. : Sin g1
_I, n
€t = si"," (*
b)
,) j ,-
Cos€)ralm
l,-IE:E.taae-,dffi= ## 6D : E
sin (9; - e) #T
=dsine,ft-
P,7-zr a /)
s;" e).
V€,
4 rt,z)
sine; ) I {c, Q.}€.,
coto,=-jrlTffi\;4
Fron €7s. (z-t4t)
t,
ffi]
|in er -Je
S i n oE : / 8 . 4
(sin -a,.cas 8r- catO; sia gr)
.
qnd C.l-/+z):
= dy tr o.' *t" 4' if"t , s
F, t,,21= (o, i n, * 4{7,s;n e,)i"'" eiluI f Iy
whsTs
f-,- frsin tr - AIE sine. ,
"r: f, / (+) stn'q.-t, t. : to
Z t, cosa.. E io
ry,cose;-i7,
rl-@^,a
-t
{ro- 87.(r-r+st.
|/
D (a*;r,: t CI*( Eryrtl,) : o.
.r+ n r E
r !
__,
L
7-
(r,j).
,2-?-28- Giv.,
0i=€..---r--
cos0t-o.
4:T/2,
a) Fron Eq 7-t'+'s ): ( f.ro/E;), : 2 . ',5) F r o n E g ( 7 - / s ' 9 ) : ( E r o ,E/ : ) r t : Z r 1 r h , . ,) F ,.(x,zi t) = dl E;ocos w ft ! ( r sin g,.+z Cosur ) f, E * t ^ , r ; t ) : d y 2 E . o e - n ' . o su ( t - ! x s i r - r € s ) = d y 2 f , o " - " = c o su ( t ! x si n € r . ) ,
where
F.z-zg
a)
O.= Sin-,rm,,
b) e ; = z o c> e c .
L
d)
t;net=Gsine,
G,cose,.
The
=6.39,.
:J.gg
c o sg * : - 7 2 . 9 t .
cgs et
v/€r,
ej--
= --!-/dt!ot
z
- sin-tm
.,8, cot g: o, a _ ,: - uitg' = zio.(6 :, "ot coter'+
,I ', :
.\
-6,when o-o,,
":ry@;;rjt
= l.g? ,s?t'- /.ti cio.t, "eJ e
Icotet
/ransmilloal
wave
in air
varics
lvhero
=
At/e,nuo*/on
in qi"
as "'<^z
a')fux
*(z.eD.
{or each r,
P.7-to
Wh",
|heincidar#
* e n L t s c| u r { a c a , (fo)r,
(o"-);
'*u'
-
4o ' : 'lz T.t
l;ghf {i,sf 0i - Ot=O,
s*riles = 1 #,
lAc
Aypo-
. 4,rorl, ,
(,lr' 7r)'
Total ref/eclions occur inside both slanling surfaces bccause 0; - 4t"
) o.=
ss
sio-' (*)
fhc prism --10..
a*
On oxil
{ror., (Oo). frt
\v
\
av4l
*hc7rism, Tr= ffi, - 3- n' : .4tX(72*?)' ?o z
(o*)2 -
.
16'1
(@*),.
P . 7 - 3t
a)
no sin €o:
4 %'h 7' =lr 4,/7,
f
ht sin (96"- A") -
: n1,[i4.: sin 0o-+tF4 -)l
b)
N. A.:
oq,
72-6'7e
tltcos Qc
',rQ7trj =,m :,f;ft (no=t)
s i t - te n : v m
= 0.196/, € a _ : . fi n - t o . ? 8 6 1: g o . 4 o .
P.z-sz a) For perpend;cu/qr po/arizc*;on and /u,* Vr: sin ert=
fr@
Llndcr
condition
o{ ns re{lection:
o,sq=/tE'
-u
'r'
= sinoa!.-
D rro, Varallal po/arization sin gr, _
lt*(tS 9**e**tt/2.
and |
€, * €, .
cot et = S i n9 r U _
s6
Or, en=n/2,
Y_ a
P . Z -S l
Fo r f wo perrute-a-bi/t+y
ha-w e {ro*
u 6 Lts med ia wi+fi eTct a_/ a-nd €, an./ <, \.,y,e f ermit+iwities confg
Er, (z -/zo)
e<:. -sro- GJ",,
d.oJ
r
4 rom f,7, (Z - / E+): OB|F fon4Qe, . ".
sin e-:
ton 0n,
Qst
/1
?o "
o.5 I ll
4
s {o
t
I
E7
I
c4 7"
;" 49" 30" 2 o.7' t c.+'
{5' 3 '.3" il.€ t7.5'
t r i
I T
al
W
! i' t.
[.
'-l
I ranstrlt sst on L t nes . 2 g :-t
( s- /7)
5 q b sl i {
anJ ( c- r { )
' ' n E7' G- +9"
zn-4rer= T,/ < d':'[T d :r
7 = d
Li
t40
-\
4t
Y,' .t A/
wr,l
l -V
:
2e
7 - 2"1l-tt-: i-
w/i
'-d{: ,'
d ul
lZ-
tf
w:E*
V'€
A ,17
W
:
Ubo i
: ,/,f'<
.---+
u?b -
up. , \ A
l'{'Z
v^/' = 2 u/.
V 4
+t6
/,/L
"p/,iz
a 1D r P a r r q - . .Ji. parf g . {o- po* ..
=,'.6r lO' (S/n) , w = O.oZ (m) , s! *,2.5'lo-3(a). 4 -f slab : Lo*/ diohctri" o, €,- j , 6'- 1ti' 6/n). /
Qiven:
j ' s'xrc' (Hil. a)
b) c)
R- *re':
t.tt (tt/^).
L=f*
- o.ti7 (yu/n),
G=tt C =€
a o.oos (S/m), t
: o.r,t
(aF/n).
ll-t
= tE - 4.t57rto'r. lt fr ttL = 473.5 >>A,
L)C =0.667 >) C.
> = j',[G [,.*(#.:;t)]-o't2j'jtt-14
zo',/E [,.
i &-
(n't),
(g#)] = 27.27+2o.t3
5s
t
P.s-s
'ffi1-3oo (tL). (n).
(g-+ 9.
6 ) Fo, coaxial {rancm&sian/ine:
z,- *,8 l, (H he) =rs 1,r',.
*=
P 8-4
b: J.9t, /o't (^).
From E7.G-crs, 4 - 4[7: .
Fro,n Ey.@-zE)a.nd from
-
n.t,
/
(s-z/.. L-
o( =
*f
*
A.
r- E Zn{'e
tt) o).
#
P.e-s
€7 G^ts)'
- J
e
/)
.*)
For coppzr q.t / (/tt1), A.: p-
:
t b L^ d
tr (obx 4t rd7
s. g, /o"
: 2.6 / x /o-4 (fL). L . € J x t o-' i 7 | ( \ (
z7r # " ff)* ror-o.os (e). : /. o6t r /o-t (t(p/*,)
:
?. z, x /d3
qABIil.
7.:l@.
no
V
Giv.n
Zo:50"io t9r1 (z): 0 --+
Ca rjut)
UL)-1>-rely r...l, - L (Oistor/,on/e,,l;n"). *: *
Given' ruBr^) : :('i'!!/r;,"'f :. :i.{ i F'o'n rr f:!?; li;ril ^--# , p=@8,zo=,tg R-= aZo- d.osl1 (nf,.),
L: +
: o.2.o (f urt),
a=+*t-23 (f s/^),e: +'Fo (pr/^) sq
( P^,)": ( P,), -
Ps-s
=
lv.lt 2;
(Pr*2;)'+(xr+x;f
h n a x i m i z e( { . ) L , s e i and
l-iV: .
,
t++
P 8-7
(, P ,o")r,
Max. powo.r-lran#cr
V(z) -
Vrt.'"
I121:
I|
=o.
u"f:'':
M o r . ( P ^ , )'L, = ! ' : l ' 4 Rl +
z; v;:4vg
! a-[u,zi ]
o
I o,=or,X,=-xj )
o, z;=Zi.
.
c#i u'cncy = 50% .
+ ('e1, ,
;)'
+ Ii er'.
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",
ri t z=O;
a)
f-tr ' -''
I
i'L Gt=fio(v,,7,so1 . +(v, r,zo1e'z b)
V {27 - V, c rh 7z - J;Zo sinh }z ,
a 0 )- Z; coshr , P.8-g
a) -{-ez t
t
sinh^r z.
, -.#=n, | -+=- pGv, dz-
| !#:a.EI
b) V ( z ) :
V o + e - < z* V o ' c " ' ,
7.G)-Ilott
a Iic-'
,
.( -,ffi.
4- +=Ro:E
)&
-7-
We-have
?r,n,
V(4 = t(ur* r;p);'z +f (u;-z,n)eal
z(z)-+H:rr;)o-"-! (#,-',){',
Vo
* Zr.
wherc
\' i -
2.'
a n c i t - .-.-h-
&vc
(i=-Xj
c) For
an in{;nito linc, 2,- Ro ' V. r h ) : T;70e
V t z l- # r . q r r u ' ' " , d) Fo,
a finitu
lino
o{ lnnglh /
Q;:4#ffi
lv''uo) l
"a
v
P s-q
Lis*orl,anlctt
t"^ ({t) #
L: # 4:
a-)V{21#t
h
/inc,
{ermtn
4o=rff : So (l;-),
-12
rh4t'
2 - o.s (tL/n),
:tan (#) - o.oott. = o.oots; =gooortxo.oolS=4e.2= 3 *-
: o.o/t(H/^), c= o.ola (Nf/n),
: "-
#
:4.42(Vrtd.
p:u,/E:5.s5 (rad/m).
;o'atz 6is'rrz; .re)=#.
.'. V (z,t)= 5 .2 7 e lQ' atzsin ( gooor r t-9.952- o' 322) ( 0, f (z,t)= o .l o s €o' o' zsin ( goooTt - s.stz- 0.r zz) tl> . b) A+ z : So (m): V(to,il= 3.ZoSin (Sooort- O.+lZr) (0, I (ro,t): O.o6$sin(goootrt-O.L?zv)U\ - (s-^o, o.oe4): 0./o2 ( w). c) (Po,)L= / ;tulurtil
6l
-7-
Wc have
,,, V,
Vtzl = t(U.. z;R);"z tf (u;-z,n)eal
-;G'',)r''
J(z)- +(Y^:rz;)o-"
V. * Zr.
Y - ffiu,
whorc (i=-X9
e) For
fl
'9'
an inf;nito line , 2,- Ro ,
VtzS +-uru''", d) F",
and
a {;nitu lin.
r(z):ffi;':
o{ lnnglh ! {e.rmin
2;:Pr#ffi :ur''uls ) ), U
P 8-q
L isforl,anlc"t
t"" (&) f?
line'
h
a-)v{27#z
- so (JL),
P - o. g (lL/n),
:tan (#) - o.eot{. = o.Oots; = gooorrx = 4e.2= O.ootr 3 *.
L: #:o.ou 4:
Ao-E
(H/^), c-
= o.o/o (Nf/n),
: "-<2"-}pz#
#:4.42
f:es,{E
(prld.
=5.s5(rad/m).
{4o/z 1i*srz; rQ)=#.
.'. V (z,t)= s.2 7 € ' aoft sin ( Soaor r t-g- e5z- o,32:- ) ( 0, f (z,t)= o.los €o'o'zs i n (gooo?rt - 9. s52 - 0. 3zz) tl>. b ) A + z: S o (m): V( r o,t) =3.2oSin ( Sooor t- 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).
6l 1
P .s - : o
a) ,cor a shorf-c-ircctited lc
Ftr
J
ob*ain
line rJe.( Zc=0inE<;.G-?-<)
Zir: ZofanhU : \ffitf
-2>z
.
rr/2, d)./z << | .
,L: )-/4 , /:.L:
Z;r:".--;ffi=zoffi = 4 2..,/ax .
b)
For .rn opon-
s e t Z r - - > a i n t7 G-i.*)
/ine,
Z ro:Zocoth7.,2.,= Z, ffi-
ForA:A/+, z;o: o/-e r o -zrffi
z)":,jt-:t! 'a y (1-a;-fi a
z Zoax/+. D Q -t
t
!!t=+-4eoo,
fL: f^^
/l
-lon 4goo = - /.732 ,
- t! - so Z. = aza z+ - G-2'it.d'i.tc.(tttz) t r r l z s t a n9"fr? rg.{@
= ?6.3'iq.st P 8 - / 2 G;ucn , a) 2 0 ' 6 Z o
Z a : Zo cofh >l - 2So /'s9-" Z;, = Zo to.n 1! = 35g / 20'
Ut) , (lL) .
= 3 o o& , o = 2 s ? . 8- j t z . e & ) . 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). nr = - ,'f@ fi )
-
b)
&).
f
,=[@{ e+iuc' -.-+ 2 +j a L =) 2, Q -
we obto;n:
fc
)
G*j,oc -
= O.235r3 xfOo:
R G-
7Ito
a7o-f xlOt (radft,1.
sg.6(a), L =o.tt2 0 . 2 4 6 ( m S f u t ) ,C * r 2 . 4
62
tp4/^), (f F/E).
f.
7-t i i !
it7.G-7e)
€7.G-tx)
P.s- ts
b)
a ) S i n ce ihe lin. is ver Y shor f compa' ed lo a' (t'83)' we.velrrglh , ye AoZ use Eit'(s'fl) and
x 1s-t' 1s/^r, _.[, :74. , : #,:9 s GL). o 't c - s x ro'',(H,/^)lj ^, L-- 4y : LC --+ €,: L C : 4.05. /J€ ffi /o',8 - 0'42(rad/m); f L=?'f:: o'':?!iJr. F : +p= 2rrx - - 2g o (JL), - 'h X,o- -R.ocot Pt' - l9'2 (n)' Xr,: QotanflJ uL/'
'z) B
P.s-/4
fo,
i-p-dancc
/ooJ
Zt: a-)
ll rr lI :
s-l
=
s+l
whore
R"*jXr' ll Z*z-t -t l
,f(rr-qst*-/
1 4+ t |I IttO
,fcr,-,r)'-xt
p, /zo
fL
onJ
tt:
X t/zo.
I +kL
-J-
I
tI I
L
Wh"n -t b)
S:3
-2
vL - +J (to rr- z r]-s)/s
o.nJ r":/9o/zr:2. LL:
*''El'
Y t : P LZ o : + 7 1 . 8 ( g ) .
,:_s 4!
Fo,
a. loss I .t"
lr l"_ || ,'\ '-./
.'
_. et (4
,
Zo- Qo.
(a,-p).ixL.l' _ (cr- t)'* xl (21+Q)*jX, l - T .R r ht ' f' f2ir,) " * X ; 2
ia .,r i - r _t : 0. +
,-;.r)'lr.
S
Ro _ jT: *t
c()pres1)ondt
Z, - 40 +A to (I>),,
Fo"
b)
Ji. "- ,
*-^ c- lni,.t'oruo,,
R.o- ,f4-"-3d
lt-I.
: .5o (llr.
:,tW = +. Min.irl I ' V 4 ' P r V g o + 4 4 J=,1@ (vl;n.S
tr**
:
:2
r-=-
Lott lrtu lin. oF chc",ra eferry4i Fes;r1or-,
zi_R; ffi,*#;,
t -'f,rn
frL'.
zt: P;$;-e!t Ai-izit (Jr)
Z; :5o
lr/av, s et
+n d
Zt-10+J/6CJ\_>,
to +j/o - po't## -*
{h1i
L lo4
.So /..t in1 ane{
:
+ |oot
: So pJ,
-zooot=-(R')2t.
K o : 3 6 . 7 ( - f - ), a/
t:tqnF.l':A7zSI
.I-'- o.tos ,\ .
64
P. g-tt
r,\ L q . ( g - 7 ?| / : /-
. ^ p Rt * i Ro ton B/k ; + 2 X r . _ '-o
r c . - Rr- , /.- -RD
Let
I
x,E,
L'L
+1,r.t
._
z-L
rtr,):
#
x;
:-, I
3
4 €, , vvril< 87. Cr-7il a_s
v(z') ::',:,'r'' ;.:3:':,:7,:i,: 3 i',' : +(zr+R)eif{f
Vo ffag.
.',
/x rvrinimqm
f
wh-n
r+[flri4f , #: er-z7zl
4 :
laf
,
or wh.n oe: 2 (gx o . 3 , \ _ T T: = : * e?o.2ir o-27o+5o.rq6.
D 2,.-po(#)=3oo (ffi) : + 66 +j. zo6
6s i___
p/
o/>/a-;nt
P.g-rs a) lfl:#:
T t
d.nJ t--*n
+zc;t) : \' '
t f ({-
77 I;n
p,
i1
1+ I
--*1"(t w-
,,:t,
:
l'-ttt
So/uin?,
,4,o + ?' Rt b; f,g_
CSL) .
O.27.
e s-!L
U; : o | /o"
Q;uen
2t-Pa 'R,+tl.o
'rL:
*)
F.o,4
F;3. r--s,
F' L,-1a
Va r
-7o ' r , * i .tO
..,/1/!1 t,-.- iro*
'
:-L
3
T/ - V " :
+r
<
.{-o
+
..Q2.
E7-(E-Zs),
l-'i-2&agZ i : 7o o's zo+; zot^o f !' = 2^ oo 2--+ r^2o+i 0.5zoA"f& i /Bl
(v).
z.: {o,
!
-
-3 *:;-a' |;'/ - 2 / 3 L 3i6(r+j+J^,3j)'s
+,
f.t:(*)+:
T, {onf,t:7
- o.s2?/*/8.+'(u)
V: *(ffi)
(^A). /.os4,r-/tr.4"
J;=3 (+#r)= lrVLen
-/Z . + J t * " , f l \ ( - A ) , 4 i-*.ry7/t
T/S is cannec/eJ
lo*he
line,
o
vc/lon+,/!a.ve
#
.eo arnf i;4ud+ 4.a-ve(s towqrd iO. ,o^d p.L, #,W erc ivin3 v+,i+hqi oLp/,'+,tJu V, = 6rAic6 #dil4 C-a,cr se,s a
re$/ec-leJ
7he ref Iec*e.4 wdve 4raveb is
nol re€fec-fed
v
on a.nptlude-V.-:
Lactr hwa,rd
lhe-re bec;a."r.se- Z€-
(6e qenera.lor
CV'and
Zo, ancl Fc=O
Vt : }ft nift (t +t-r) - + e4fl - q 03i /-45o ( 0. --t.33s1-as' (rrd. Sin,;/a,/y.7r= (-C): + e-ifL #r€;# .'.
b)
5=#: s=.
c) ( Po, = ), { A. ( u, tf ) = + ( S) G, k;t) =2. z L x o r (w)= 0.a4 (mw)
zl
(P^)"= f(tm=o f czhoe J- , s o ( t L )F, " : 0 . #"-c,.o2s
66
(nw).
P s-zo a)
I - 2rld (Hr),
f=tscm).
Apcn-
on3comy'olc
coajiauc,
u, {"r fh o " wo rc /e" lA
rouo/u],bo
an a,!4t1|ona/
A/z)
(az'-
and o.4lr-\
o. 167J- /o
1z vat d gi n < ralo r
x--;io.t7f. -
b)
A-
o/.,
on
A_e.a.d
--j+t.r Z, - /s x (-)o.r?s) ".
&).
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 oTTosik side e{ lto cAar}. _-._, y +t $r.74), jo.ozt2 (g. S h o r t - c t r c u i t e dl i n o , I = o . t i 3 , . ! . / . + - o . s 1 3 . .f*arl
{rom {te cy/raoo eompltlc r
/cf/ poiol pr, , rcfalc clockw/tc a6r1 cor,lia;e oo {or an &dite,tal
Drawa sfra,str i::r;:i
i;:li,i,i!,7 ii;i
u2)
*ho ccnler aad iniorsccl at (O-i+.rcjon$cop{uA sidc o{ **e c$er/l * ji.o4t G). v - *,Ojdzt)=
F .g - z t ,r-*(n+4rc)=0.61jo.2.
,{
a) l. Localc 2r-0.6+jo.z on 5.ri+h charl ( Po;.t pt). 2. WiiA cen*ar al O draw a lfleirelc 4treugh p,, inletocliaE O P ea t 1 . 7 7 . - t ' - . ! = 1 . 2 7 .
vL-
anJ
lv). nA).
o
t (nw)
b)
r - #
c)
l, Draw Aca4 2. Move J. Jorh 1. &.ad
oitle'- o.zgcir.l' OP,, inlcrtecJ,hg thopor;phery al Q'. nwavo/tagtAs o.0+6 on lowaed gcncralor'lcalq
line
clocL*itt
by o.1o11 h
O and Pr' , inltrsecltngthc z;- | + jo.sg at pr. 2,. - SOr; - go +jzg.g Cn).
67
o.tl,
(Po;^tpl).
lff-cirele
al Q.
J) Exl..td
iI
/;r* pr'prolo Pt. Lcod f;- o.ls-,io.el. \:' lT l; = o,ots -jo-oog 6).
e) Thoro is no vo/.lag4 77ininu4*'t on lhc/inc-rbuf h -
/.6':z
zr = *
( r o - 1 to) - o.6' jo.2
d) Lacale
zLu0.6- jo.2 on S^,1+1, ( Pt;^t P,). ttVi*h
chari cenlar c;j O draw /1r.o u3h 1,inlcrt APr. ai /.77. 4 S)
f
'1
a- lf l<.;rcjc te*ing /inc S -1.77.
ao.2triztl'
al F;'' i'iac 0Q , ialcrscc*ing |hopcriphcry ryuta'velengths 1z'^.-tg gen
t.) l. Draw
Load Sca{e. 2.lVore r.iockwit fc o.c-Eg (Po;rt 4'). by o./.t^ O and Pr' , inhrtu
.,i) fylcn1
0 Thu.
P.s-23
/ioe dr'Prolo P, . R-cad /;:/.+z-ia.s+. '{;0.02g+-2'o.o/o8G). * !;is a voltag+ ninitaum at ,!'o.oJ6,\.
x/2-2l Firt*
,
An'f,? (
vollz.ga
nr'nirn.tr,rt
a) l. Slarl
Qcc-urs af
t!-
*
- O-t t\.
frorn Pr" and ro{arfc
o. t o r\ Caun{crcjoc.,wht thc loa,d to Pr', fornard 2. Droq fhe lf l-cireto,inlvstciing linc oPo, al Z (S.Z).
3. Ioin ofl', ialorsccling l*e lrlet'relo al Pt.
zr.=o.6ts-jo.lts.
4. 2oad +
Zr-9oL- 3j'75-i2t'7t (n).
6) f=+lf
I'
t,=*"izst.s.'
c) If
Zr= O, *hc f;rsl voltago ninimun would be at - 25 (c^) fro^ *$e shat-cireuil. Zi=\/Z
"2 S^;4t
rh 'kicr,lt
P I-z+
;ng L'nc
f = 2xtos (H'), -\. = /. 5 (,^). + I : ?
. t.77.
C horor*eris/ic
)rnper/n-nce /,'n.,
lront,n,'ssion
2^:r/
- o. 3,/5(^)
of
Tctctrlerz3A'3oo -- /4g
;,,vire '{vwo-r,yire (L).
Co, o /ort/e's air //ne., f,rorn E7' (s'ss ) a-n4 (r-z+), 7
H,
'o= ltl L - +/{: cosh-'(*) -
)t:
/+ g -- 7y6: corl"-, (*) Qiron
P s-zs
D : 2 (c-) -
a(wire
zt = (2s +2>r)/so = 0,9 t j o . - 9 ,
roJ;,r) = 0. 94 (cn)
yr= /-h,
a . ) See con"/rc.e't'ion. P,t Z"-0.grio.E.
P r: Y t = / ' i / lx.
Prt
= Y s+r J ,
: o'
Y r r =l + j l , *
Jz : O./6 L^+ (a.s-o.?I il_\ : o.324)-.
G : bu= /, -rl,=(o.z;*ot2s)^^ll
: O-7TSX.
,9
$':
'l-
t & t I t
F
I
t"_
6g
bgr=-? l.u{-
(o.t7r- o.2s))_ -= o-/acx.
*. 2oad zt=o.6ts-jo.tzs. * Zr-jozt- 33.75-j2t.7g(n).
6) f:#t,=*"i:st.s.' ,'2 S-,4t1 rl) 'kicr.ir, irrg h'ac
c) If
Zr= O, *Ao firsl voltagc niainun would be at Zi- ^/Z ' 2f (c^) fro^ +$e shot-cireuil.
P I-z+
f
= 2xtos (H.),
.\ = /. S('^).+
. t.77.
C horor*er)
ucrrler- i,vire'lvvo-r,vire : /48 (L)' 2o:r,fETTi{
s/ic )rnleJnt',re /,'n.,
lront,n|ssion ,Cor o /otr/er',
air
"o= lT
\,
I : + : o.3'/F(^) #
/,'ne, [.o,-,
7
E7'
k-:e
) an4 (r-z+),
- +/t: cost>-,(*),
/4y = Ac Lorl,-,(*)
Q;ven
P g-zs
D : 2 (c-) -
a(wir.
zr: (zs +;:.r)/so = g , g t j o . S ,
fr:
roJ;rr) = o. 94 (c-).
/-*.
a.) See conslrcaetion, P,t Z":0-5+7o.9.
lx.
P"t
/t=l't/=
Ptt
Y n r =/ + j . 1 , dt = O./ 6 L
Ygt-J,
-0.
[email protected] a I I d,\
-- o.32+)-. Pr", brr=/, -+/,=(o.zstoet)x = o-J7Sx. ber=-?1.*1,:(Osrrs))_ o_2 $': -= O-/2sx.
iJ,
't51
P. g- ze F o , / h-
Z S (' - fI) : /.5.20 ' I fo I Compctred y,:*f,_0.667 P"obi'en, P s-2t V)
Zo-
flor145, [i2.4
ire4
re?u
bi,:-4,: ttThe- /occtfioo*rf
ly'le-hove t
s]u
5 c<1ui#a_nce-s are
: I /.e. 1* and
p-irtlt
4'= o. 4c4 ^.
Q'are-ncLl
^,..,J 2i- O.o 7.4,t,
Ti, e-r e a.re no c6ong,u" in 1$- /acs*'o,rs d,': J,:
t r!J_
G iv.,', '
O,
J;&-nt
aty'$e
s{ubt,
o-,-J 4r': J, : o.324 L.
7s (n) , ,S : 2.4
?
V^in of
o. z ? i (,n) atn cl t. 2 3 g (,-) f.o,-, /oJ. d . j x = ( t 3 s) L so (-). z 3e -A.:2
@. t(,0)
Fi"s i V-,na-t +# hrom
&--
: c.i s4x
luod .
L/se a- Srr','+h cAa.rt. /
t-
"
D"aw a, cen{ered ci"c/e 'throug,A S =2-4 poini.
(4oshea)
2- Loca,{e point Q {or 2, {ro,nY,;^ (po,nl on e x{reme. /e{t ) o- lg 4x (c/ock*'i'e.) 'loworJ 1$< /aa.d. j L= t.31- 6.?S . a) */
a - + r-/5 z"* 1o4.3- jrz.s ./.1:
(jL)
3. Lccxl. 4A. drao,.lr|.o/, o/fosi.t
/2.o.4
o.04+^-
aJ ltainr Q'. chs.rf q-s 6(n a&nithne
4- L(s.'fh" Snrith cha.r* anJ T|nJ +he- inlec-:ecl|on o( ah.l1l-c-ir<(e wi+h tL,e-g=t circle o-+ P,t /B= 't + jOtz. R"cJ 0-/60;- q{ G,
D
Loca.iion qF =4.'b O:or:r*&f-
"effri-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
I t t
I
P. g-Zg
chqr'f ar a.r't irvp<.da.ace. cha-rf . q-sthql )o pro-6/em pg-2g, e.xcept point conrt'ruelion
Llte
,S'-rr.e
Smith
Pscwou/d be.al lhe. exlrerneI'h-
circle
S:/
ryoss
4
r=/
o''.(
5y o ,) Clrc-/e-.
ze>/so = 0.9 +j0.5.
2"= (2s+j
P,t T wo
becomes
/e,ft (mor/<
i b l a 5 a f c t T J c t n: s
Pr' zsr- t+it.
At
---+
P"t
At
cl3 -
(O. t(Z x_ O. ogf).)
: e. o7+
..
zst=/-i/' ---+
(O.lSg,r--O.OCg^)= O.29o)..
dr:
^ci.ieve a. rno-fch \,vi+h - Seriee s{ub h<-uing 35 ^/ Ro , w< n"ed a ncrrna.Jized s{
k '\,
5p,ifh
chor-f
,.ve tn4
*he- re-oui.e-Jsfub
(*5*h
/r=o'347^,
,lt
;/
)
c"fu)ret
5;r
a- slu$
/"->gth
J (m).
;^30i.
7t
./r= o'/si'\.
eb^*s: q Wa rtg u i de.s a nci,Qeso,',alo,'s ,D.q - /'
We- c,se-f7". (q-;+t c r n J ( f - s ? ) - f o . Z r u a n J )--377 1lL) respecfively For ct)r, 7 :1o:/2o"t(r a)
The narrha/rzed
Zrc
w€\ve
/'ft P. Ja nces-ct re y/ o#e.t
q ?a =a t
c
I
o T M = t t o l/'- r T r t t--/'
,
,t xl
4r
'7
!
- kT€
--4,117. f : r., f", /@ Zrr: o,4/7 rlo: lgZ (9), - gol (g). Lre= =hT
z
/t
At f =2.1f., /ryf
:r/,4*.J- o.s?/.
Zr.: o sq|,?o:3J<&). 2rr=#:+23 P o-Z
F.orn
€7 ("t-tg), F = k/ r- c7' : #/ t -1*;'. 1/
(ur/u) I
GL.).
a)
uj
F
=-
(^)
ta
p
( r-G,/tf
:42;:uJ/-(+)' Ir-
(h\'* . (-f ,\' : t \.,(,/ \ f I
n/J)
7;
w h i.6 i,t <1,col.s t'o-f +4e g raph of (u"/"<") ploaad versus (*"-/+) )s a-'uni* lircle .
b)
ie:
2n
'
2npt
(j) ,t/ - (tJ;r
T
v r - (f./tf
zAtr
QA)
I-/t:
i Zre shewn an fh.-/
|roph \ve-
) At I /f" = t-2e,
#e.l
u, /"t:
(, / f")
0.6a, )g/x
= /.62,
u, /ut.: /. (7 .
P 9-3
Fo,
t//a\/9g-ricle.
O",,
TF vtt
A
e-/vvec+: ) txe-
r'n Ft ra. V-
Ult)'
aycra-Jion f-r
(e).
-sqlve
.l'Afllt* dy'
' 1r4,
with be
H"(y,il = fllct)?7
:q.lisli
n/
th*
ite- p
in(;n
+Ae Fo//o,*rh3
h-Hlry):o, 'i con./i+,'o-.slo
foupJoT conJq.h'"5
a - J - e:
p/^/
dH!rv)= o a-{ y-o anJ /:b. fr
lL)
5e/u/ron, H: V) - Bn,"' (ry)
d)
Prop{
b)
fro,-,f7.(7-24),f"- #
=
fic-lJ
expre->siun.s &rr
ko1v,z; t.) = 8, .o, (H
h = T,
#
Fror-, TE, moJs, n=/, (f,)rrre ) Inslo-n/at+?-.,ur;
;
# TE,
rntQa,
cos(a)t-fiz',, F,= ^F@ -f,r) K, (y,Ljr) -- ff s, s in ( ni9 sin (q1q P, sin (#) s;. (*t-f,z). E* (y,z;t)-- #
7s
tt-12,3;,.
P?-t_
P a , r i s ( a ) c + o c l Cb) - s) m i/s- r 1o Pr cb/e^
a.) Phut"
exp.esrions
conpsnert*s
.4r d'e./J
l"(y, z) : Bnc"t {:"rz) tf"L " ,^, - &h< / -(+)' i"
/
!J, (v, z) : .j.*
Bn ;in (!#)
t* (y,.> - iff
Bns in (T)
S u,{ace
cure.f
C n l o w ., p l e fe : 0n upper plare,
f s . 6 5 l t i e s;
f,
:
n= /,2 3''"'
Enxi, -"€
r
a,- x fr @) = i* 8, a jf"". - r x t t C t ) = dr 1-rf "8,€ if"o 1-:
Jrl:
!rat.
o-)
fe modes,
e-if,',
-l
Pq-;
o{
n- i/"".
b) F,-o,nf7 (t-26), hn: # c)
'
P. 7^3
Jst 14r \- Isl *.
n ooa\ n cven.
AS:2x2.'o5:5.3Okm).
fo .
T E rc mo d e :
f.:
*9-= 2a.
:
L"-:2o,:?xQ.o2e Front
{ct.
(q-zc)
qnJ
(q-3t):
(*)'
,^3/
^* #;,
J: b) LJs= Smith chart. )n",*
lrl- #-
(Hz).
:5d/o1 2Jx* l o{ = .925 :
a,OS G?). 12 7L 7 -t,
to1= !:ii i;r*,9
j .,-. bfhrougl>s=2 Fiot.
o.trl+ ,Sh,l+;ry\ 1o*va,J fo*d /.,y #: 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€otffi -*
= ##-t4761)
/ r= (Q-?qt 2o.at)x 511 - t44 + ilio
c-)
1"^r- lo (r- *) 74
- 8.r7 (w),
<9) .
io air-{;((eJ recr\ngu(ar TM,, -uJe u:zrJ zt a-r3u/or {.t.71'/ency Olerali,-tg
Pq'6
\,vaveguicle (re. Ff.?-1s):
E)tr,y)= Eos;.(ff:)s;^(T)
a)
in [7.s (f-ir)ll-ro1sh
Jap+ing 4-o
(?-r+)'
= =ffP)Eusin(T)r",(uu H)r*,y) ), +# (X),;n(T), H|t,,fi : - # u; =- ff H Eocos co'f#)s;"ff)., Ef,t*,y)= #,'#:-#El E4
..,(!), d ,.r,=- #,,# - *r@:,, ,,,,ry)
,.*hu,. in
h,l = (+)'o are
z-direc,+ion
(€-)' ,
f,:1/r^ty'e
deswri6er/
- h).
by the
y''cfor
t/aria.lions ,"t4lz
b) Fro-9.cr- zd,(4)r.,,:fi" - ;fTV, (1 x -c'1Mtt i,,=*-
-) . ) - T= ): :-: ec: -' -
'3 -
P q-l
F,,
r't-(f./f)'
Recfangular waveguide:
E7.(9 - as):
Hz) L
(f.)r,,1,,
t.
Mod"s
:-L=
{f'-f.' Q':/'21Gm), b:3'4a
/;1 t-\s/1nn_ ,m
wi*h lAe -rhorlesl
(cm)'
2
A" ( S (cm) a're:
f
0.6ilr,
a) For b) For
II I I
I
I
L
Mode
TEto
T E,^
T Eot
A kn)
| 4,4
7.20
6.s0
TEt,fTM, 5. ls
A - lo (
T5-
P.q-s
= e)
a:2b,
F(m,n1=/ffi
Modes
7En 7Eot, TEzo 7 8,,, rH,, 7Eo, 7M,t TMaz
? q-q a)
b)
#F(^,n).
b) a: b, F(^,r2 =JT6.
F&rr,n)
I 7E,r,Tt4r, | TEor,TEro |
2
J?
,12 2
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=
hr fhe dominanl TEroaodc. ff t-or f >t2(f)tu.' a>o.o6(m). Thc ncrf h;gher-ordcr aodc is TEo,wlsh Cl,>rf Y. fr, f
- 4.To x lat Ca/) , u. - $.a r { t -(Nzaf -.t xs-
F:
o.ts7(r,) = fS.7 (cm1, mEff.= = 4o.l (rad/m)t + 'n
5?o(fr)-
(zrr\o- mt'-
76
-l-I
I I
Pq-to
Q iven :
a) -r.-f
/
d = 2.Sx lo'2 (m), L =f.st lo'2(t^), f '7. s , toe(Ht).
:#-o.o4(m),
=o.Go,.
4=rlm
^/F, - o.0667 0rr) o 6.67
\S-
(cm),
= (rad/n), F Zn/xr= Q4.2 ' ,l' lot (r'/il, uf "/E c '1 ' l't x lot (m/s)' \= (Zrr)n= ,lo/i :2oott = 629 ULl.
[*
b)X=?-b-o.o233
(m),
=o'g2e ,
Fr'=@
^S - ^'/F, - o.ot+3 (m) = 3.13 (cm,, 2n/^; = f93.2 (rad/m), F'e ' i = u / 6 ' 2 ' 5 7r l a t ( m / s ) , ij = t '4.= t'?s t lot (rn/s),
(Zrr).=
#. b P 9- I t
il
Par*
Llse-E7, (t-tt)
+)
(tL).
G-) Ao.s been cJone in frob)em P. g'6,
a lonq /he
P 9'tz
h-323
*o {in4 th"
av?+d.le
parl h).
Po\^/er I ransmi*fed
wo.ve2etais.
Er{*,Y,2;)=fosin (toonx)s;tt(/oory)cos(2np'or-f z)
Eos;n(4) t;r(f,i M od" d ope rof ian : T M,
co'(2ro'orfz)t4 : 2nf : Zzr/oa (rad/s).
77
-"i
.j
=?J(tl'*(4)' : +/ b) ('.!.),, -
l/,-\7
,
a
-,,
/--..----
##
: i.+ g x ic, (l{").
F : ,4/'-Gi: #[t i
7.
G-zz)
( Zr*,),
-H"I:
?, F€l
/// (raa/ra).
:3zZy/,--r '
37zxo.'i3 -Zoo(!,). 3x/c"
ffi;; P 9 - .:
TE qode
: O.0566(^)=s.ss(.^)
i n C.o25Gn) xo.02t( t' .- ,,tctir - { ;t/.r /^s7.r ar ?
W.:\\/egUide:
Hrr4/.,2;t) - h,s<,tr(#) ror,lfx)ros (at_fz) (d+ -2goz) cL: ry : 8o?r: #,, -':::"n:::)cos --+
b)
TEo, rno-le.
Fro,..n {f - ( 7-< s) :
(f;0"='
? *
=
*
-
#-
Fl.om E7.c?-3s):P:?,F@ f : J74'14 =
Zru= ffi:
7t^
A! : x/C@T
/. 2 x Toto (H,) =t z (gll").
- Z*,ffi:. - /.Y,tta''elo)
' / \q113/'
:/7(&H),
2-a
J#.-Sdd(tL), : c/yuQ@
: 2.24 x ri t 7,o7: 2. 2 4 (co,).
p, = vc)'t ro.v r-.r..=afpn'Ht =+fbfbl+f fb--;o'(ffx) Jx 4Y T )o Jo trrex 4 zr" Jo ui (+,) _ zgo (W). : (zrr).,ab \2'/ 4ztx
78
P 7-/4 Substiluting E7 G-fz),',
9.(7-24)
-r vv,'(-)*,) -h'f''"
a-)
;
: r[a7-n'{, - irlq (rrV, -h)-' i l''"
x
i/r'*n, {,-
'T'o
@7.-h')-'t aJFr@.
Fro- f7.G-ze), @r: ftei"e,
y=d4nif, | 4 .j=T'/z@*r -Qf1.r
wirh
(fQre
%4
=
rr) A/' f - + t (o1(fu),
e")
,o
TEro E '/hz on/y />raf c,-e*fi-\s,
,^tAic/> 6o.t q
rna4e
(f.)rr,o:# Th-r, d4= }ffi
eu{c>t$ fr*/u.n.7
#
--3xroe : ta';'g.1{# G{-). : o.oo?e (ny/d-ooz4(+8D.
: #
P.q-rs (f.)*n= ilffi a') (f),o-
*
'
t' \i"aie = 1x /o1(H): 6 (Qu).
Ncxt higA.t moJe:
b -42id
(f)or # (f.)t,=*i/,.Gf
)
24
tyJro=t
'cm).
is Llsa6 lez b q,J,n;e+h (eH)loz *oa /./f ,1:6.9 P+rerisril/o lanJsi4tz*
o
b ' = 4 5 O a b=0.79a
| 3.+
to
( *(+)
@
@
tL
(Gtlz)
o.a9x12
0.6 l8
o,8.9 ,| |L lo.L 3.t(ard
/o.L 3.rlatl)
e.a (61'tz) xfjiS
P o u : 9 .j ( w ) & r b - o . z e a , a n d t o . Z f t D { o r b - o . S o e .
71
j_
CGHz)
>1.7
b) Fro^t7.G-toD,pa,-I,rgr-2t.3+(*). +
(t
e_=O.Agkn),
/. g x los F(n,-,f),
t{'^^ n ?.:
E
TM:to T€
/f>e.,'r re tonanf
I F (m,n,P)
W::
I
rot
:o.g3
3. /zg
23.5s
TErtt
26.o3
jE', r, TMr,,
28. ss
1t-3tL
T t4yo
3c. og
+ Ea7
T Eert
.3 2. 02
4. goz
- ?9 . 6 0
9.3 40
cx) Since
|
d >a->b., *he
ftiode
is
7€ro,
f.e9uen.,i.r,
f -n* ;n (&Hz)
3.57s 3. no,
T Mtzc
P. q*;z
f(n, x,f ) - too/(7)'. (?S',(gy.
-6r der t4oJet a rtJ
/o-r"./
ryrf
b : O, O6 (m), d = O.QS (n).
/owesf-orc{e.r
t?son46f
r-rode.
r -eFa rtot T/ ;r, 4 - 1. Bo, x rg, ( 11) = l.Yoz' (g.F{z). b) ,:ram E7 (e-/2o): D *tot-:
-
v {,o, ,/'too-bd (a} +41)
P-rf2@ ,ffi W
a.64( a.' +d' )
: 6 '8 6 1 . From E7t.G- /(4) e.nd (g-rrs): W" - *roFo' -t o f,:, H: : o.07z3 x t6tz g7S= o.ozztet), I
w^- fr ob4 (# * r) Hi - 0.o773 (f ;r)-we .
I I I I I
I I
IlI
I
80
II
J_--
P. g - /s
1r:2'5. r - t * l:t l a) )t/t L { a,
n :l(n\ w(oJ
A)
c)
P q-te
(f,,,)g: 3.r 32 (Gtaz).
t
= 5,162.
(€r)'/a\"tot/go
W_ (W)ru: o.oz73(pr)= W^. t
.a|' : :
v
a')
:
4t
r r ( o t:
{Tftotloq
sl= Zla:
- +Jn"/m
4,-*
-,/Va a-
:6.soo
/ q, s oo (21'/+- /a +
t
a--
b)
f*, - &
c)
For
o
n *{o{
(cm).
: 7. j+ (qU") .
copper,
Q,o,
P.9-zo
O.o2gqGn)-2.9q
6-5.to^/o7
G/n).
G
.To., - 6,sool 'rii - 12,443. -
,[ffi"r
a-bd (at+ d')
a) For a.-c! : t.sb - o.o31 f^),
i,o,=+{{ry
b -o.o2 (m).
- t.r7q,toe(L)-s.sqxto1 (Hz)
Qtot- 4o.zz,/VF - ll,O lg. b)
Fo,
Q'rn- l.2o Qrct --r
6'- l.zo2b : /-44 s o. oL - O-o2ss (ft) = 2.g? (crr.).
o gl
W Antenna.s
P. to- t
a.nd Antenna-
A..ays
EV. (/o- /z) a:-rd Qo-/4)
From
a L T- g t,9, r 6) -
4n8t
:
?o-
!1
E, of 4,
Mqximum o
'j aw 7-2-, o
--+
DP,
-
-
4 zAt >?oDP. Z1TZ,
;
€- n/r .
occur at Eo'.
,r?o
11-/F D:1'5,
^ I
- o,/ox /E x /o3 (w|
E o - o : o g z z ( v / - ) - 9 r . z (n v /^). H o : # : O . Z s gQ , . A / m ) . ao
P /o-z
^ -
a)
"_T
U^o,
Uno*-
50.
frIuao
tl
cosgsinede d4
#L"[o{r,n'n = 2.6s (tu/s,). --"r> D=#=lg'95, b)
or l2'7'GD.
L{.^t: + P, :4n -
l. J,'f
Uon- 4?rx2.4, -33-3 ^ t
2-i,Kr' ---*
-a_
Kr-T:
2 P, -i
T-rc.zcstl.
g2
I
.P./o'
of Confinuity:
fq.ra*ion / -Q
j_ (A
)t-
^) Z (z) - Io cos zarz
V-J:'j-_e
.l 7 t-\ -T'
^7o F:=-:Stn27TZ 1c
+
F=+:27 Lt/ovelenS th z, - | Crri..
1
/2)i rz)- zo( , - *t zt)+ f": t:lH 2i'"'.oo P ro-4 w).
^:
*-
#:3oo(n),
a ) pod;oh;on re^sishnu, 6)
j;..t
#-
Pr: f,orr2(*)':
(41../z;on J;polr). tgz
(n).
-W E q . ( i o - 3 o4 ) ,: , f f : 2 . 6 t xt ; 4 l . s } . E r e - ( t o ' 2P? L) ,o . r r ,( e ) * \ , : |r'(d!)'.(#): &-gs.s%. ^'
c) E7.(to-zey:P, =
)
(ro-,o7' 87. 1r;;*!$e;'${i
*
lt'l"-"'-*{*"= tq(^v/n)'
rr (t?)=?f r_j'1: S. o /, /.6,6D. l.17 t rc"
-?:#-3(-).
I
Di p olt bngf h : /-l Cm)+ T * 2, - 73. | (sD. t1
'^+
/.fL
tsowe-r losf , fL:
h .:
f
#-6t/:: (*')8,:7r.t
d;pole.
(zoco'/z)zJz
(AsLx rr= oe?s(F) (*).
g3
.1 i .t -il .:t 'I ! 1
P,lo-e
a.)
Ee
-,i
/fT'( r - #S eir'co'e dz
W
- .m c'jf| Frs) ,
un'i -
fu"-jP"FG),
FG) = s;ne[t-ct!(tt
case hrr, , cos(fhcosl)a t - {(fhcost)', f
In
Ftcl * *(t''s;n
='ry oile6 ptsine)
Ho -
r-ifa g fh sino)i#trttlA
*
c), = ffi h:
sine, r"4-iVa sine.
ri r'siaedad{= $ [nrr,(+),J,
R,= P,/(*il
l:/eo
an4
e'
E, = #
b) P,- *{T"r
P./o- r
gasdJ.
= Zan'(*)''
* xb t ( H ) _ > ^ :
4O (m).<<)-
,,^tilh
qh:rc
?:
-*roll"l^,^r7
ffi
lH+l^or: ItJ^^,- ff: f I;": zntsineJe b) P, : +I""
: 1 , 6 4(7, n ) .
#
/riarrgctlay,
a-) /r,-o'-t P-oLle,n .P;/0-6, tse ha-we ,
+ raloe o-t.o@s1.
cu.rcnf
distribuf,bn.
( fg= +)
^ioo:r.rr(av/^). 7,sI x /o-'(A/d=7st(y,
- # (frq' (i) =s(fhz)-:$rf^'"tl*2;"?ede ! l+'"'GIl
= ryx +ori (#V)':,,t36.s(w)= r.r+ (2w). ,) 2r= Zp,,/ti = o-227 (ft).
r4
-v
P 'to- g
t 4- l ) LF ' P(one paftern {unction {or }f er4o'o,n clipole is , from E7. ( /o- rd,
F^( e) = -s in €.
Mo*. Etu) : {
: F(4)=* _'::': ;':7,"i,,
T; -+ ,\ 6) t -plane
a t € o- ? o "
Be-a,nwi4+h A€: pay'lern
{un.h'on
hr
Or-0,-?oo ho?-wz,ve
4ipo/e-
it, from €7. (ro-sr), cos{(v/?)coseJ ---7^ a
F^rc)b\v.
lVlo"
6
(6,)- I qt Oo=7c".
^ fb. I I P otars, Ooiofs -+
P. lo- to
B"oavvidth
f5(€,'):${ei)=t .
al
0r'- ei- / 27"- S/"- 7gi
A0'=
Ltse E7. (to-27):
F(e) -
cos(fAcos.e)-cos.PA Srn
O
For 2h:/.25A-, - cos(r.zsil -lcos(r.zsncosel | tlffe>l rr?rl-tfl
).
lU;a+h af mainb.a,n Ae{*.rn thc- .first nulls = 2x53./3' =tO6.26".
85
i .i-:
rf
* -_rj -..{
:l
,l
P io-rt
Use 87. (/o- to) for Herlzian dipo/
: E,rc)'t E,@)
-rAo _ _"-j|r'
: -; i ( z h )
#1/'i,r(#_#)
I Ln
tl ^ (be far zor1e,
a-)Ee= t#
n
-/ P- ;
n
I
R-
7op sineA/2 ' (l * la'f 4coseS
= +Prf
,iPrc-lcosdF(il,
where F{e) = sin€ cos($ro, e).
5.14 =)./z , lF@l- ls; n e cos(! cosgl.
:) d=:.,
lf?Sl-ls, ne cosgrreo,il1.
86
p/o-/L
/ior an a.rray c/r'-tf aoce
e/ernenls
o{ i.Jenlica/
sf a.e4
{rom Ff . (/o-g+),
c/ c\pc
Iti : #eo tFc1t)ll*,*1, --fJ
\vhe-rc ( In
lhe H-p/or.
singcos/+f
aF a. d;po/e , e : r/z , F (!,
J=4,9-+'
,\
* lI t,,.-+)ll . oil--i, +i=1, I,q,
r
1z\
Dta=
,-
?, ..t
?::'
; . 4): /
n'
|
,nn . +trl lA@)= l l c o s ( f f c o s (+ t ) l .
I Jatt
P./o- tE
Five
- elemenf
broadsi{e-
|inomia.la-rray.
o) P.otafivc cxcila*ion amplihtdes: f :4:6:4:1. b) 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' ) : For uai{orm
jO.29.. a"?4v , {ro^
llsn(Fcull(''
TtWSi
Eo.(tt-Eil
r.
-E-i'7*3t'
Half -po*c, beo^wid+h {oc S-alct*rr{ llnifonne*A witA 4a tpact'r! = 2(go,-7E.6t.) - 2O.78..
g7
.<
:
P to^ lq
7ne
e/
n< Trna./;zc4 a.rra.y SacaaT at
ra.pzre-J
arrqy
iAe{;u._
1j
iAc^.ili= + I / * zei!+3 J2** z {'3* + e;+{! -, + tl ";,* [z z, eii + {iu) ("i'*+ ;;"*)Jl : + t L c c ,z { + l 3 4 c . o s , l+ I craph
tF V <" fS l r" .!
it shown
befow cntAe./e.Sr . It/r.
-n
-n/t
T
)
1371/z
F o t b r o a J t i d e - , o p r r o f f o n : g : O . , J=, d . o " + = 1 r c o s $ . , f l ' i ( i l 1 = + l z + + c o s ( v c o sd ) + 2 c o s ( 2 j r c a s +)1. T'hrs is 2lot+ed a6aue- om +he rlgh+ . TAe {i.rt siJe,/o,1c,{e.,rel |t 0.//, .b(ugr{//o.lt) = /r.2 (dE) a,awr, {.o* fhe mo,.n_bea.m "" rq d/a-1|on . Th is < o"r,p
F,o*
-Qr. ( to-3?) and
(/o-6d
:
e'jtpl"'t3,7, A,H;)Ay6t)l llol: ry whereA*(U):; !ffi, ,li- $*tino casf; .A, / ,(*\: tyt
t d!z*hL. N2 sin(79V5,
,
D)
7t : i;' tv
-
t
o
sine cosd
I si" (#). s;"(4b) | . IL serq,"'d1 lr G,6tl= NtNz sine
J
sin(f,t3;"(g I
8g
I
-r P to- ta
l.-
h/'
r
a-) /l ertzi^n dipole of J,(z) *- Z@1 , ,
=
/" b)
/eng*h
dt/+
.&.
l/a-/f - uvave 4,'p.o/e- ,uith / . =-f - -' '_=^c .o/,,p -z -J z : * s-t -
f-
c) l l o l {-w o '.te
s;^(rs#l= f+
t-!at,
S J_orr" cos f z dz
rx/4
c//.
-
h = L/4
,B
ctncl J.rz):r(o) 2 - ^ ro)t-
-'^\fT):
dipo/e ,yith A://+
cospz.
?r
p
anJ a( z) =r ( D( t- 4t21/r ) .
r A/4
t": [:;* ( ,- +tzt/x)Jz = ,I^'*r,t - +z/,t)d,: . t l?to- tt
A-
l'{^/f
(m)
t-#='t
- w^\/e
dipole
wir|
Z(z) : J (s)s.r'. ( | f - J(o) cos fz.
srhcts6,1'q/q/ cqrrenf
-lzl)
r
1 1) -
\fT=t)
Frorn E7 (/o- (g) and P.ob/.,n P./o- /6 6) , l.= f rom €V. (to-s€),
vve hono,{ar
ch'strr!>qhbn +r'r
#.
0 = 17/2,
P,n r@7ry-F 1 : + r' @) a)
2-?6(v/m) lE,l=###: l4"l=le,LI: 2.?6x $ = o,v4zu).
b) Fo, rnolched loal, 'P L:
V::
gR,
o'7+i' = ?(w) = /.52 Qnw). /. s a x lo
gx?3.1
I I
s7
=z+,,u,).
P to- rs
(io-sd' pt_: ##r,
,q.
f :/fe(m), c') Para//e/
ha.lf-
tA./awe Jipo/er
;
/rel l{e-rlzian
d ipoles :
P, = /-st4 - (#)'
P./o- rq
64
4:Dr=/,
/.s/4x /c- ': ( w )
Pr: ffiffi{,2,/oj: b) Pora
=##:/h).
Pr:2x(o3(t*r), ^:-f
: /.5/4 D,:
(*,
'"v)
Dz: /.-tO
: / - 2 6 7( m w ) .
.Froq E1s. (/o- /z) ancl (to- t+): 1nU(e,r.il _ 4trR'F", G _: V'D 'Dr
.
ll
1-;' in! () -D-r l' 'c. r, l -:
_
.Dr
r
t q". (/o - 40) an d (/o- 12,)
,r
,h.Q:
r / ^ i :cs(4cosdfz.
t' O.f
I
L
sio)
I
a ) S u ,6 si i i 'q f i n s ( to- 7s\, @ /'n €Z l"re): o./3*f cos( *co'-ldlz
#ecel=
L
st.'d
b) M ox. vo-lue o.FA"(e) for : /O* (H), .f Occ
c) M o-r. yo.lu e o*
>":
:3 (a)
Arq-o./3* = /.ri (m").
Ak) frr .f : 2x /o?(+b),L: /.9 (a),
A " ( g ) : o . / 3 x . / - s z= o . 2 i c * ' ) , wL; ct, i5.--rr,,1 o.lfor ,%on A.e)&r becorts-
f
4re vva.yelergth is shar{er
?o
f =,/o{ft1) a! if :J/ rcPpz).
P./o-zo
/o IogroQ2,: 2o (c B)
A,.t+ennq gain :
-
,f-
GD: /oo'
:f:3':/-/fi- O./ (m).
-
3^loq(Hz)
a) Fo ^/er {en-, ily a.1 ra-ryef1 dT"r
-
(w./*')
FIr: #ffi:o.ot4r Er-/o.o/47x2Y377
b) Power fnlercepi"d c)Scut(ered
e"
ilu
= 3.39
(u/^).
= {urf, = /Sx o. O/4? - O.224 (0.
Ly large/
1)ornrtr 4ensity ay' radq.r e.nf enna
Y,= #-
2.7rrro-'o (w)
Zffi-
Ref /ected po,,ye.raAsor.be4 by anlennct : 4 A"
= 2./exto-h(fi c): 2./rxto-'(#, roo) =zzir' /i" (w)
U P /o-zl
=tz.t (fD.
[art'h
-6,39o (k,-).
rqdi.ts Al.(;lu./" of geosyncAronous
sq./elhles - 3 6, f Ao ( L.,)
Qecs yneh"aus orbit raJiu' = 4,lgo+g4roo :44(so (kn)' . -t/ 6.sso. t Y- s,n'(WiT)=8.561
{-
7o'-{.s6"- gt,*4"
a) Two sqlelllfes cover only 2r(2f)-):.e" < i40: se.lzlfites io eTuqforia( U"u /hr"e p(o-ne, 3x (z{'S = 4 8?o>3 60? Po/or rggioas are naf avared b) L.t
Pr- Poru., fcaasmi(lcd ly
Ae-.aqse '9'
sa-/e/li.t:e-enlennq-
=# fl= Po*., densily wilA;a t'Ae eo.!1€ e Lsin f ,uo of cone,
1f (F{):
ql
:l
$
.i.{
,i J
1 i
P lo-zz
where 9q.te
a) fr.n fq. (/o-so> ' 'p* - ( 4 r r ) ' 'pL ' e-erti lAe /l i'le
sqbsi..7r'1)4s resP
e can{
s Je+rofe
o-,J
e c* i v e ly.
x loj ) --.- Z. /4 x /d" *e/4 x'lO?
Q-:
€arfh
,-),
/ o(e'/to) - 3. i6 , ,/Os;
- 2.go x tdz e",
x"- j#
lo(tr/td - 3. t6 x lot.
e":
r - 3.6s x to7 0n) , --* Pt - 2.1 (@.
Pr- 8 x |dt" (w).
b) F:-om [7 Go-rys, P,- q (ff)'e. xs.t6xto,
A.- fie-:% ',t) :
fr
- I | .9 .fint). | z.ttr to'Li 3.!s'r
2E\
'tr,s
,ot't
\t,
/ - {,5+ * tct2 (w) = /.51 (iw)-
q2
O.g x ld:L
