m- ju.
a
“ zEntpedance ectance_-Matzhing in.
“x Tmpedance— malehing Fe tha, protess Cia matching —
the Load impedance. to tie. Charatteristic_
_inmpedan cea the Line Pepectania or matching
the Aine_impectane_to_Souree Umpedane ak
__ the Load or Source ~Stcle_v2s peck fvely pice ctles
“Em pedant to Malthing Can be achieved sci ig
ob Half wave Lene wuoh ta tf
“2. One Eighth Wav ve big
_ 3B. Quarter_wavebtag
iL ob. Stab trdnstasbeS
Hal ounel_Quarter_wave transmission {vives ___
_2 The ‘elalionship of He ‘input fmpedane at the
__tnput af the snalf-Wave tyvansmission Line
gS Raia Ini pestanie ta gee Jetting.
te = Ala in the PiMpeclan
—Withh_ gene _kurscon eee
+> A transmigsion tine phat & letminoted wm ‘Some § impedance. Zp that. different. DMZ
——Will_resulk_ in _a_wave ating refletted_trom tp. ~
—_._termtnation back to the Sourte»————___
—— At the input, reflected | Nolkage adds | bey
—Intédent voltage and the vreplected Current sup,
- Checause Hae _wave is Iravellingin Met Oppsite nage
— from tie @nefdenk—_Cursenk
: ie The vesulk to that the Iopubinapedanta. —0f tha lig
1 cliffors from te _characterishieimpedanea ond toy 4
ten of engl Lie gen by
7 Ze - Yo Zrt Zo tanh ve _@®
Zo+ Zr lant vd.
Where = tip.
ls)
a eee (Ba) =o.
-» tan po is TnfPniky ake tanbl as. tepousn we
beth BNR Dash toys Bia os ee
Ro | Zotan bl BLA awe
ba “tanby.)
aaal Toot ee) ——
ft danb’ — —Janbl
a “tan pL = 08 th Pa a _clisstpdlionleas iis Xo taRoy o.
= = Be oes ; te
cs
a Thus Quarter we ie aie a ee
ane Sor fmpedane Watching O¢ Doad Xp wih
input impedane a= Ro®
ZR
Ro J -ZR ®
Main lune
a
x 1 a
= fz
Yo
—~___vesistive Lead suchas Qutenna- ee _
4 A_shortcfreuthed~ Quarter wart-Lane Ca
i ee Bo ae
hie orfnner—tondutchor fate ie
Th fh user to nate h_Gares—tor ce
SEL brine woth Xe- ; gab
ts used in Tnapedanta— ope
eee ene wees
es
OLE —2xaitly Pee Shell te Tel ge
He Aignal (2), then Hae Lere_Coay met
—— Called as “Halt wave Line
Lk To caleulate te Aim eb us tonsil,
ages Ba. (Zr) Rolanbs) + >
Re Ze tan Bs a
a= >/ en ran a
| Re 2
eae ae ee eee eae r
a= “EZ Ro (Zp+e)- 2 Ro ze
ae Roto. __fe
se Sto 262Z¢, hal_nare Liu 1s also Called ast
2 | One te ome transformer: a Ps
{ “i
One Eighth wavelsire os Avg lines _
Saf the Leng of AS Tension tied wou.
—eamalle rL¢ than thre D2n0 can be Callad as Ny bin
a —%s= Ro (Xe+jfotants)
eae
— Bate dyg 5 bss am AZ si My
—_| 3 oe a =
pre Benner Neg a
SS Ro. (Za+i Ro) — _#
_
Roe
z a ot
Ethie Ng Mane ts Used | e Obicin_magadiade matt. peliverw~
sh ~~ Stub Matching: i
eg Sa
4 The press achieving impedance Matehing stag.
“stub ts_caled stub waatehin
+_Sbtub ip a Section nf transmission. Ly i
ye _be_connetted tis parallel wth te Lransihission line
4 The stub may be Short Cereuited_ar Open Ureuited
ab ik Open ends
a shot_cfreuited stab is_prefemed_as ik & practically
__—@asierte achieve a yeltable perfect Short fret valher
than a perfect open Creuihs
—— «The Values of _cli-stante“d and Hie longi tof the.
_— Slub_will dulp t athieve —peifet_matching»
—— Tyra a Slub Matehtng
——. Sfogle shunt slab ___
d-_Suigts Sovies Stub
5: Double stub
A Tot ple shib_ek -
SL
—@
Sis es the load. ue
= (fe AL first Vmin Y= G05
git SB «At divs} Vinax.% = Go|
4g Tn betwen these hoe peink -
—_ _____there __pnvsk- be a_poial= nthe Line, 9
t J} wilh Y= Go. aA —— t > tonductane ~
a Bo» susuplane, >
— th 4 lok ak point Si, the tonductanme of Ho Line ib Go
TAR Si, Meee Goejpicis Ss
—+-A_Stub haste be tonnetted ak potnk 514 Suey
~——thal_ib_susuphane is chosen to _be_equss
Oud oppose tp thak af thine [
—! te Ye pe plein oc ie —-
—k Sime, Dene anol stub are Connected du Parallel,
— the betel admiltane is_ Given as
|
dS
Soh Np tay = TY pain Yebube bin! —
—%* Thus,.hen_stub ts Connected ve parallel —
__| AviHa th ine ak te pail Where Lonductanle—
—— Sh the re is Ge oz =Ro, Aud thenfae—
——_impedane match tng is athieved at le Load—
—+k-A__ghort_cprete ed Stub “eo _ Preferred B——
—-—O¥er_ a @ pen _CPracched Shib, because F-——
Jess _vaoltaliay, doss anol easy Liptag—
Sp tk date oy oo BPeo Shot OP eens heel ——
| 8 Engle Stub. a =
Se - .
| | Single sti
rT Foe Mighsiftatpadeapenaa ale tobe
. aoa eg ben
pai %, “Ub Should be ai_smroolh Mine or should be
terminated by the Charatterishe i impeclanu Ro.
AE i nal a Ne
it So, ia many prattieal cases
__—mallehing— _Baction &bould be Gabekted bah on
a dk lee.
te Some _Pmpedane matehing “Sectfons Lo
transformer, Quarke wave Dene, Hall wave Liu tle
i Another Way af inpectane. “uate hing. Bs
__.Open_ar__Clased Slub. Lie of “Aultccbla’ Length, ab
__ @_dlesfgnated Aistante from the Loads. —_____
The btub will be wed as_a Stunked Reattane
—__acrrss tha Line
Tho Wd tune fe Legh. i “he tne aud tha
_ toad to ‘Vesenante with an_antivesonanty2sistante_
—_ €qnal_ te Ro- —k——————— SS
Ae Know, dhe Broax- & Rain Walaa i
toms SwWR o— 409 he ae
8 fmm thts, tbe. Tah laa ade fia
\-
—
yh soli Sob matimion _vlloge
So ae
Gs Beis. ak se ea Voltage
\ i ‘Ro. i
a Ab. bere Sotmedtal! powk AL ees Vad
Wins the veal partie, the Ynpuk— ee
ey haveatintemedteds yakue ote
ie Deo ffordeneas, the tpul— arn’ oe ae
Se 4 cating pink iets) —
Dole way the. “pink AC Where Gel i
8 Bhai —ShubMe_having 1 Enpul Sus caplertia th a
eae ns be —Connecked “aeose oe =
“the ae Odnilt ame ak - thes pk Hens —_ |
| iene
Se eee ee
| da,
Se
Eerie 7 ps _ aS
a oe yr
: clascmte 5
SF
4 y So, When_a Stub is used, the Length of the
eT Stub op the Location ak iDhech the stub fy el
e bcd re to be Aelermined,
va » Dnitially, Standing _wave Ratio S ond ba
aT Votkage minimum nearesh t, -
Meagurecl a
A wellage—tiat ram ts measured vatber than
Vethoge waximum, Sthie 4 fh position usually Cac -
-[L_ be _debermined, more_accuratals, .
le Tp tbe _LocaMion of the stub ‘s-ftxel afi 2
~ respect to _an ortgtral_vollage wOntnum, no
a Knowledge YF the Load tmpedane fo needed,
© ik Stowe stub % connected ix Shunt_vwitr the Lene
_ itis mast convenient to work wit adnd ante.
_—# The input admf?ttanc Ys, Lisckuig tioard He
__ dead from cung point_on the Lene, may he writou.
Mey OA - eee
/
Bays e eal Ree arse y ®.-
ate, Ro Ganedi@aaks
wl As we kono, b= Gro, and alo Charging te
——Teachang ular “Cod trates gives ~
' =Ik] cos (g-2b5)- jl15i0 C4265)
_ | Ie) Cos C=2B2) 4 jk] Stn (P= 2b),
~blt geops = &- —“
ae 4
a
SONs- Gs sibs (|_|) 80 Ukisie |g,
Tale] tose td ltl $wa__|_—____________. { fia Tae Caste Sag caf tos6) 3 us shoe
ee oh We Ges) +] inh Sint 058) Sieh Sig
bye ie PRO nish hie
: woe =
-\ Zr ier ee + alk) oss ay
re + Sebsiop- + STeP Sing cose IP Seo
diy = j= ll? Dood £etete} — dite) stag
Se Ewterenteye2ikl@sp
A ti Mage oh = UI? = 2 sey Sin i- a
= a
i \ENsI 2)kl (os p , CG
| Nis UZ: Gis +B: = a :
Go 2! Gib 3 —_
Ye Gs 4) 8. amit
Go Ge. i
“4 When the Stub & plaud a Beng ocabiis Srp
-—_Lrnpedanca numa
oS olen a tat case —~
12 @s sor Tete tain? = 2k)
That is
| 21k) Cos@ = ~ a)el®
| t -
| CaSO = aie
! BAet,
Cos p = ~ Ik]
t B= Ws‘ (=1K))
Sine .
ed Ne oe
Forth range of FHL
—®
eps! (- 9) = = x4 co! 6
for He range & [Ot]
—_ We Can wrik
= Be = WS = Ik)
= — w+ CoS CKD)
As we know
= 2 eee Q- abs, =~ x4 litlk)
= Abs, = =b=7 + Co¥' Ik)
ApS = dte sts! tk)
Ve, = bax Wo tk) \
| iateanna
———
Beary : oe
=) tn Col! Ik)
| 7 =
| ge A - Ws!
ra. fora -to8'1K)]
Sis b46 ~ cel)
+ ab
= & Wy L hax tod! Lil} pow SE el
ee
aE 00
_ | # as we Know, 6 = >-abs, b S= istic)
4-1K)
iz fejel = j—Kiz> 2
— elk p+ le? 21k) Cos (0-2 Ba
Heat Rs Se a
EL we can hie Be Os
i Paik? = tee
=e) Ct=1k1)
ald
Ges 7 aan - itlkl = S
aa gee =
a i Ik]
ol
~e yall ikl” a
ee te Us. ate tos (26.52) = HON ge
ee Cos C)-2 p32) == 21k]
ae
“tes t§-abs) = =1
l SO eee a
2b So = b+%*
r
Sos dan
. ey a
fet ere
a - 3. g;
—|_Sas hin 3 82 Ran cod
: 2b cana
at ef fose—ctucy ——
| = G+ 6 <4 A+ 08k)
1A =: Cod! kp |
j_____- 2B OSes = Chength of Ha stub)
gr Ty athe Imagionry Panto Yo vail -be Bs.
Gro. Go .
a7 -
Be = ~ alk) Sinks
“T “Ge L+lkI? 4 2)k\ eos 0
eS ee
Cy Ak 4 2S. 1 We know
(os (b> 2bs,), =~1)
je |Cos 6. = =
| from -
| Stn? + tos 1
BPn? p= | - Coste.
Lo 2 Sine = i
e. oT mn elngite+
a a a ere
atl avi a
Go ae ele 1 Be lis
Se ot Be “aie afc 2 a MLE
eS
ey ear
pe = Bs ot ithe Line. =
i —c8etng et Susceptane) —— |
Te achive Tnapedante— rating —
_ Betub = Gio 2b
| We need
~ Gab Susuphone)
: © SRokan bs |
Lo
ge Fora ebat ckE Stub of Length Ae
Vee = 2 Bee
TT .. °F Rell
_ 3 Bse =: -SGo
tan pl. ane
~\Bsc| = Go 7 _
Tan ble es
4 Hse] sht teeny -to_Bslub 8 wfith_—Chaak
Jes Ss
“fg construeet —Lo_solve_proble
/_—hansmission Abts oud. madéhing clevias._
(Tee ole ve te alispley_Vvtous falas Sl ee
_ —admattiouts..—inpedanie, Stability, Nolsefigne ete a
hts 3 Specall_ Polar dfagram _Contatning constant i
ie esistane circles , Lonstane_veathante Civeles,
“Circles ef Constant swe.
co co b, °
C_ Smith—chark is He most salut “Gra ° 7
Dex Sol — phical tool
oy Smith Chak tsa graphical meas
Zs = Rol Itik) 1b-2bs |] oD
Zs = 1+ )k) 1b-2s ®
Ro Terk Labs
+ Nomaltsed frmpediance Zs is a_camplex quantity
and 40,1 could be resented as ——__-
t Ze YatjXe 2 ltd lk) LO-2b3 _@ ~
at Ro T= 1k) LO=2Bs :
~ecthe_qurankity Ie|_Lb-tks fsa complex quantity —-
Oud _eb “Ub be _ geven by a
ia _ =
Nel pbeobs = utiv:
Sethe ; 5 1
Ns Yat xq = 1 (ud) @ +
pe——" [= Cus)
E J oe Pew adv rty ayy av -v
a
ew
Sf l-wevraiv 2 weve aj
U=u)?— C}?4 Uw 24 v2
2 MatiXes wav alav ®
Qew2tv> (ew 2+v™
& Eqwaling +b yea) urd imaginary pals [epee 2 cry
{| see Ya = AW + V¥q = \-U2_y
y
ta eee ie
L UV? Yo-bUre tr aay? = I= Yo 7
s
U2 C1+¥a yt V7 Clara)— 2U%e = )—¥, _&
0g ee You
= 1 ead
TTeemptely a Ividbing He equ @ by letra ha
ud C Ira) Vee 4 Ta) = 2uYa = I-%
Be They) te tgs be
uae ea tate OO
[— We ae :
——« Competing tthe Aquare -by adding fe a
(4¥a.
both the Sictes,
~~~ 4—2 _ oe
u Vo Yo. +V = l-Yo 4 (Ya
V¥a Lt Ya ita | ETH
Us Xo ne Se es
19%) ia a
2s (ita) 14%e.) + Yo"
esa os eee a
ca
(ess)
+ Equ(_teprsents__‘the equation _of a_ciccle
(qac} + y? ae
% =< ‘Yadius.= _! and.i G'= Ya
1+7%@. 14%
C> Center _shigk fromthe Gnégin -
——~Badius of tha_cerele eel
Ae
Se lt el gf
a ite oe
i rr i
Consiant_Reattante Circles,
ee cles:
aT Paes ea
Oe Ko Law = oy
“Te fF itu aul sav :
E
E Xa l=2utu24v7i- av =o
Ta Divide tx Xa,_we
{= 2uti4+y?— Av -6
Xe
| (u-)* +V* -2v 5
Xa 4
+ Adding | _on both Srdes,
oe
(y-? +y2-2v 40" 2
Xa Xe XG | ¥ from __ equation. _(O) _
j _ iB
| | +Vyo= ;
| 1X 7 K
=] ey jp Yg—f2-—
= ——-
| Th issue View then Conters of E 1
A Canters of alll the S_ceess
nn 7 ae Veal ants of the smith —~
wert danshand.
\\
\
“
|
>
Ss
rs
s
j
a
oe
7 iF Ea ie Las
Sib atalteg ee al Value te eo a ye “The _tanstant_ Scinele Can “be _lrawn 4 whi,
__Nadtus equal te olistane— between he tener
the Smith chart ard Hua Caden. pofok _ :
+—Ye— — \
aba “the constad_S 5 etrele. cole tha Jhortzonbal axis
ak point Ya 2S onthe vight hand side gy
te center _1oKicle- at point Yo = Mo to “thy My -
hant_ side of the Canter- ae
—_
eee
1. 1 Fleing 2p oapedante.
Ee Ds Bang the apt pata of the Sone
is. Measuvenerko-_vallage. staeing. Wine Yate “Paoaduse for Single stub Matching.
Ht i eee es fy
A gtodthenormaltzad. load Ben, CSS
TV pine Mark “tk as_potat P. _-
“Tos Wilh o-as the tnter and OP as radtus) draw
YT a _tonsbant S eProle. ee
Coe3—To —Frinel_the_normadized load admittance (Yin)
Araw_a_tin jetning OP and extend Phe
ct. Same Line til Lt Cuts Me S crrele Mark
“the tatersectian peult_as_¢
75. Mask the ini i ofnk_ag Q’.
6 Draw Q_urit Civcle (Radius — 1) unit Conductor
_ 1. Select Me ‘Snbersection point _of Cale Gini)
_ S) circle wth Unt cércle ncaver tp fhe toad.
8 Mark the paint aa Ry et
—9. Te tfod_the position of the Stub on the 4
———Main line, draw_a Lene jotning oR and.
oxtend the Same A#fne Hi ik tuk the
_Ouber_cercle. }
Io. Mark he peink_as R! _| To. ots Ne pos esttin of the_stub ‘he rom b
eee ee
al Ree YS ot pain oe aud
maxk the -oppostlaValut_of-ub—GS—T
13. Draw_a Loe. jelning or kll Ut cuts He cub -
Circle. .
1 Mark the totersechion Patol OnOuter_Crele og
eh
ls. “the “Vength of the stub Le” i measured by
— mong from shank Cireuil endl Cert extreme viok
—to_peink ste
Examples ~
| Delermine tha Stub J fenglh_Omd the clighma
wal dhe ehh “Poon. the Lead Given Het a _tomplex _
— toad Zu = 50=jJo0 iste be im oi
——15._WransmisSion one us viag_o Shork circuited
Stub.
Belin a
= — leaves wens » = ant . es te
—Charachevistic Lpecanu. = Ze Se
Hea Taped = ee Benito —~
[Beads
NN
JZin = 0-664 ~jp.z3 | cale tro Normalfzed _ mupectanie Zin wile. =
_doll owing _Co.Ortdnalén, on tho Smita
masts: CPotnk PJ). :
“3. Draw sie Constank_S_ Crle,
77 Ganber_of Heard
Radius o Ite cole
aa
Q_= (0:34 job)
— 5 The_clmthane paint @ ik étad clockwise
BG ee
i Unit e2rele— The _-pdinkis R._.
A fia tanh tonipmnans abate tape Impedance
iat ote Cherise
tM ankwe On Jiciiy alt :
Ehhe Ab ‘the paint R, the ‘| to :
yet ib. :
1. Measure the déstane behoon Poth @S RR.
~~ ups scale by moving clockwise, 2 from.
head to. Generator:
~8. This Acgkanw —¥s ta _pasibion a He Stub
| Se el ee i
Note = The Stab must have Xero resistive _
a —___ Component ‘impedance _and.a_Si topkente__.
that asic _Opposile pokardy.
To determine dhe length g Hie_Shorted Stub that-;|
has.om_opposils. reactive tonpanmt to tie unpuk |
— Admittance. the Oulside of Hu Smit chat CR = 5. 1
:
TET => ound Wilh He Sharing —Poink ok»
ved AOE Hey hea Vcoo) ~~
—
anki an admilane —¥ 2 Bf aw) Sieg
_10. “thre _oleshane—hehwee ._ata_peinia AS id
the Lenglh_Leof the stub. —__—
es onase A = 0a _______
OE = 2 A} —
a —
& Thus 4m tee _Srtth Chaxk
[de = arogb AY Te
|g, = 0-088 A
__ Double _etub Matching —___—
Limitatians of Sungle_Stub Makbtng .
—*_Lecating the stub. at_a_deftnite point em the
Dine possible With Openwre Line oracl ____
CEH cult fora Coorxfal tino.
To achieve tmpectante matihing, both the Docdtiou
of the stub_and_the omg, _of He stub are tp ——
be _aidjusted-__ = t—
— 4+ Single stub tsa best sotulien Lora Sigle —
| Ee eae therets a Change va He—-—
peratin, TOGAL MALY. 2 Location _of rr
HE sion as See bs at fo Soo
a
—— Doubk _Slinb + é —
__\» To 6 vertome these Aitticulties, ctouble°s tib ——
so Matching Bs sed a _—
— Th this System, tins Apforent Short otradbed ————~
—}—Stubs reused gor impedante. matzhing -—~
AA The ecaion of the stuhs is arbftreny oud
a Pacing betweon +h shoo stubs 2s made OH
{ ae Inssmate
Ay the firsh stub Isto be suse located very 7
nea head, the spacing ty ‘s_made as.
OL BAe
AG Na Spacing —is__avetded vherauide ce
Nota slates the —
A tae a ubs__eff ectively_in_parallel_at ‘the cana. =
Cop Let the fish Shu chose length AL, pe
“located atthe petnt_a ;
flat tt Aa in
Fale the fnpuk_Wpedanie ab 00 the Dene he
Ct Any petnt_on the béne fi.
Ti) gtvenby
sz =
) 4s = Ze} Zp +] Zo tanbs
———-
a | xo +} 2p fans
B) 2s = ) , Zo: 2. And_Zeat
Ys A Ye
“4 Substituting ll. these expressions into. the
——2xpressfon _ for Zs, we gor Y, a Newalited Senduig nd adenine."
oe
Ye 2 Vy = Normabisad load —adnat Houta"
va 7 glavtiaits erat aul
ae
advert is
“Yu = Ye iten bs — -— e
fo pee opp tetas te
: / so
el Bas malt ug nwlee gel ee
7 Yu_= Ye +) lan bs L-1 bank oI
es yptenbs i
Vy 3 Yt tan be + itanbs Yo tat Be
SS? te ;
Yas yet L+lan2 bs) + 4 yedmaee |
ee ea
payjjletbs Tay plat bs
Le Ak point A, we have = di, Substibuliag ie
: get oo
yy eed ey vee, ea
a TYP tat pda 1+Y,2 Fan’ Bdi
| Sa — Gu +jBi
| :
] henry : Si
#_wWhen'; Stub-1 shaving a susuptane_ 2
HH Bs added __at MS point, the neo
admitant Value will be a
{ ia = Gy +jB,’ ee
1 Where a ! : - =
, a 7 =
Bi = Bit Bs, 3 Gy vemainy_undntt =
_—— ae a toward the Jo, _Admitane of the Line looking
ta tacalion B would be
Te 6. y- > =
—_Yésonated by a stub
Bato Give the clesined nae
| 6 (red Normale
+e . S2of
milloute Ye 21 at Ron He Ling