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SUBMITTED BY :- Vishal Shanker Polowalia

M.TECH - Sem

BRACH :- R! " MICR#$AVE

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1)

Smith chart:-

The Smith chart, invented by Phillip H. Smith (19051987), is a graphical aid rn!gra! designed "r electrical and electrnics engineers speciali#ing in radi

"re$%ency (&') engineering t assist in slving prble!s ith trans!issin lines and

!atching circ%its.

t is pltted n the c!ple*re"lectin ce""icientplane in t di!ensinsand is scaled

in nr!alised i!pedance,nr!alised ad!ittancer bth, %sing di""erent clrs t

disting%ish beteen the!.

These are "ten +nn as the , - and - !ith charts respectively. /r!alised

scaling alls the !ith chart t be %sed "r prble!s invlving any characteristicr

syste! i!pedance hich is represented by the center pint " the chart.

The !st c!!nly %sed nr!ali#atin i!pedance is 50 h!s. &e"lectin ce""icients

can be read directly "r! the chart as they are %nit less para!eters.

s i!pedances and ad!ittances change ith "re$%ency, prble!s %sing the !ith

chart can nly be slved !an%ally %sing ne "re$%encyat a ti!e, the res%lt beingrepresented by a pint.

This is "ten ade$%ate "r narr bandapplicatins (typically %p t ab%t 5 t

10 bandidth) b%t "r ider bandidths it is %s%ally necessary t apply !ith chart

techni$%es at !re than ne "re$%ency acrss the perating "re$%ency band. Prvided

the "re$%encies are s%""iciently clse, the res%lting !ith chart pints !ay be 2ined by

straight lines t create a lc%s.

lc%s " pints n a !ith chart cvering a range " "re$%encies can be %sed t

vis%ally represent3

h capacitiver h ind%ctivea lad is acrss the "re$%ency range

h di""ic%lt !atching is li+ely t be at vari%s "re$%encies

h ell !atched a partic%lar c!pnent is

http://en.wikipedia.org/wiki/Complex_numberhttp://en.wikipedia.org/wiki/Reflection_coefficienthttp://en.wikipedia.org/wiki/Dimensionhttp://en.wikipedia.org/wiki/Electrical_impedancehttp://en.wikipedia.org/wiki/Admittancehttp://en.wikipedia.org/wiki/Characteristic_impedancehttp://en.wikipedia.org/wiki/Ohmhttp://en.wikipedia.org/wiki/Frequencyhttp://en.wikipedia.org/wiki/Frequencyhttp://en.wikipedia.org/wiki/Point_(geometry)http://en.wikipedia.org/wiki/Frequency_rangehttp://en.wikipedia.org/wiki/Bandwidth_(signal_processing)http://en.wikipedia.org/wiki/Locus_(mathematics)http://en.wikipedia.org/wiki/Capacitancehttp://en.wikipedia.org/wiki/Inductancehttp://en.wikipedia.org/wiki/Reflection_coefficienthttp://en.wikipedia.org/wiki/Dimensionhttp://en.wikipedia.org/wiki/Electrical_impedancehttp://en.wikipedia.org/wiki/Admittancehttp://en.wikipedia.org/wiki/Characteristic_impedancehttp://en.wikipedia.org/wiki/Ohmhttp://en.wikipedia.org/wiki/Frequencyhttp://en.wikipedia.org/wiki/Point_(geometry)http://en.wikipedia.org/wiki/Frequency_rangehttp://en.wikipedia.org/wiki/Bandwidth_(signal_processing)http://en.wikipedia.org/wiki/Locus_(mathematics)http://en.wikipedia.org/wiki/Capacitancehttp://en.wikipedia.org/wiki/Inductancehttp://en.wikipedia.org/wiki/Complex_number

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.

In %he Smi%h &har%' a resonant frequencyshows () as a &ir&le. The lar*er %he

&ir&le' %he s%ron*er %he &o()lin*. Three %+)es o, &o()lin* are e,ine

e)enin* on %he ran*e o, beta / si0e o, %he &ir&le' ass(min* %he &ir&le is in %hee%(ne shor% )osi%ion1:

The &o()lin* &oe,,i&ien% is %hen e,ine as

= Q0 /Qext

Q0 (nloae Q1: Q ,a&%or o, %he (n)er%(r2e s+s%em' i. e.' %he s%analone &a3i%+4

Q5 loae Q1: Q ,a&%or o, %he &a3i%+ when &onne&%e %o *enera%or anmeas(remen% &ir&(i%s4Qe6% e6%ernal Q1: Q ,a&%or %ha% es&ri2es %he e*enera%ion o, Q0 (e%o %he *enera%or an ia*nos%i&

im)ean&es.

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7 Uner&ri%i&al &o()lin* 0 < < 11: The rai(s o, resonan&e &ir&le is smaller%han 8.9. Hen&e %he &en%re o, %he &har% lies o(%sie %he &ir&le.

7 Cri%i&al &o()lin* = 11: The rai(s o, %he resonan&e &ir&le is e6a&%l+ 8.9.Hen&e %he &ir&le

%o(&hes %he &en%re o, %he &har%.;

7 #3er&ri%i&al &o()lin* 1 < < 1: The rai(s o, %he resonan&e &ir&le is lar*er%han 8.9. Hen&e

%he &en%re o, %he &har% lies insie %he &ir&le.

In )ra&%i&e' %he &ir&le ma+ 2e ro%a%e aro(n %he ori*in (e %o %he %ransmission lines

2e%ween %he resonan%

&ir&(i% an %he meas(remen% e3i&e.

Adding impedances in series and parallel (shunt)

A l(m)e elemen% wi%h 3aria2le im)ean&e &onne&%e in series is an e6am)le o, a

sim)le &ir&(i%. The &orres)onin* si*na%(re o, s(&h a &ir&(i% ,or a 3aria2le

in(&%an&e an a 3aria2le &a)a&i%or is a &ir&le. De)enin* on %he %+)e o,

im)ean&e' %his &ir&le is )asse %hro(*h &lo&kwise in(&%an&e1 or an%i&lo&kwise

I, a l(m)e elemen% is ae in )arallel' %he si%(a%ion is %he same as ,or an elemen%&onne&%e in series mirrore 2+ ;

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Impedence matching

In the case " a c!ple* s%rce i!pedance Zand lad i!pedance Z4, !a*i!%! per trans"er is

btained hen

here the asteris+ indicates the c!ple* cn2%gate" the variable. here Zrepresents thecharacteristic

i!pedance" a trans!issin line, !ini!%! re"lectin is btained hen

%rce and lad circ%it i!pedance.

http://en.wikipedia.org/wiki/Complex_conjugatehttp://en.wikipedia.org/wiki/Complex_conjugatehttp://en.wikipedia.org/wiki/Characteristic_impedancehttp://en.wikipedia.org/wiki/Characteristic_impedancehttp://en.wikipedia.org/wiki/Characteristic_impedancehttp://en.wikipedia.org/wiki/Transmission_linehttp://en.wikipedia.org/wiki/Complex_conjugatehttp://en.wikipedia.org/wiki/Characteristic_impedancehttp://en.wikipedia.org/wiki/Characteristic_impedancehttp://en.wikipedia.org/wiki/Transmission_line

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Reflection-less matching

!pedance !atching t !ini!i#e re"lectins is achieved by !a+ing the lad i!pedance

e$%al t the s%rce i!pedance. " the s%rce i!pedance, lad i!pedance and

trans!issin line characteristic i!pedanceare p%rely resistive, then re"lectin6less

!atching is the sa!e as !a*i!%! per trans"er !atching

Complex conjugate matching

!ple* cn2%gate !atching is %sed hen !a*i!%! per trans"er is re$%ired. This is

di""erent "r! re"lectin6less !atching nly hen the s%rce r lad have a reactive

c!pnent.

(here indicates the c!ple* cn2%gate).

" the s%rce has a reactive c!pnent, b%t the lad is p%rely resistive then

!atching can be achieved by adding a reactance " the ppsite sign t the lad.

This si!ple !atching netr+ cnsisting " a single ele!ent ill %s%ally nly

achieve a per"ect !atch at a single "re$%ency.

2)

Quality factor

The2anwi%h' ' or f; %o f9' o, a am)e os&illa%or is shown on a *ra)h o, ener*+ 3ers(s

,re=(en&+. The > ,a&%or o, %he am)e os&illa%or' or ,il%er' is . The hi*her %he >' %he

narrower an ?shar)er? %he )eak is.

In )h+si&s an en*ineerin* %he quality factor or Q factor is a imensionless)arame%er %ha%

es&ri2es how (ner-am)ean os&illa%ororresona%oris'@;as well as &hara&%eri0es a resona%or?s2anwi%h rela%i3e %o i%s &en%er ,re=(en&+.@9 Hi*her Q ini&a%es a lower ra%e o, ener*+ loss

rela%i3e %o %he s%ore ener*+ o, %he resona%or4 %he os&illa%ions ie o(% more slowl+. A )en(l(m

s(s)ene ,rom a hi*h-=(ali%+ 2earin*' os&illa%in* in air' has a hi*h Q' while a )en(l(m

immerse in oil has a low one. Resona%ors wi%h hi*h =(ali%+ ,a&%ors ha3e low am)in*so %ha%%he+ rin* lon*er

A &a3i%+ &an 2e es&ri2e 2+ a )arallel RLC &ir&(i% where %he resonan&e &oni%ionis

*i3en when:

http://en.wikipedia.org/wiki/Characteristic_impedancehttp://en.wikipedia.org/wiki/Complex_conjugatehttp://en.wikipedia.org/wiki/Electrical_loadhttp://en.wikipedia.org/wiki/Electrical_elementhttp://en.wikipedia.org/wiki/Bandwidth_(signal_processing)http://en.wikipedia.org/wiki/Physicshttp://en.wikipedia.org/wiki/Engineeringhttp://en.wikipedia.org/wiki/Dimensionless_quantityhttp://en.wikipedia.org/wiki/Dampinghttp://en.wikipedia.org/wiki/Harmonic_oscillatorhttp://en.wikipedia.org/wiki/Resonatorhttp://en.wikipedia.org/wiki/Resonatorhttp://en.wikipedia.org/wiki/Resonatorhttp://en.wikipedia.org/wiki/Q_factor#cite_note-1http://en.wikipedia.org/wiki/Q_factor#cite_note-1http://en.wikipedia.org/wiki/Bandwidth_(signal_processing)http://en.wikipedia.org/wiki/Q_factor#cite_note-2http://en.wikipedia.org/wiki/Q_factor#cite_note-2http://en.wikipedia.org/wiki/Dampinghttp://en.wikipedia.org/wiki/Dampinghttp://en.wikipedia.org/wiki/Characteristic_impedancehttp://en.wikipedia.org/wiki/Complex_conjugatehttp://en.wikipedia.org/wiki/Electrical_loadhttp://en.wikipedia.org/wiki/Electrical_elementhttp://en.wikipedia.org/wiki/Bandwidth_(signal_processing)http://en.wikipedia.org/wiki/Physicshttp://en.wikipedia.org/wiki/Engineeringhttp://en.wikipedia.org/wiki/Dimensionless_quantityhttp://en.wikipedia.org/wiki/Dampinghttp://en.wikipedia.org/wiki/Harmonic_oscillatorhttp://en.wikipedia.org/wiki/Resonatorhttp://en.wikipedia.org/wiki/Q_factor#cite_note-1http://en.wikipedia.org/wiki/Bandwidth_(signal_processing)http://en.wikipedia.org/wiki/Q_factor#cite_note-2http://en.wikipedia.org/wiki/Damping

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L =1 /C

In *eneral' %he =(ali%+ ,a&%or Q o, a resonan% &ir&(i% is e,ine as %he ra%io o, %hes%ore ener*+

o3er %he ener*+ issi)a%e in one &+&le P:

!or a &a3i%+' %hree i,,eren% =(ali%+ ,a&%ors are e,ine:7 Q0 (nloae Q1: Q ,a&%or o, %he (n)er%(r2e s+s%em' i. e.' %he s%an alone&a3i%+4

7 Q5 loae Q1: Q ,a&%or o, %he &a3i%+ when &onne&%e %o *enera%or anmeas(remen% &ir&(i%s4

7 Qe6% e6%ernal Q1: Q ,a&%or %ha% es&ri2es %he e*enera%ion o, Q0 (e %o %he*enera%or an ia*nos%i&

im)ean&es.

All %hese Q ,a&%ors are &onne&%e 3ia a sim)le rela%ion:

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Q factor of RLC circuit =

Impedance is at a minimum at resonance in a series resonant circuit

BW = fc/Q

Where fc= resonant frquenc

Q = qua!it factor

RLC circuits[edit]

In an ieal series R5C &ir&(i%' an in a %(ne raio ,re=(en&+ re&ei3erTR!1 %he Q,a&%or is:

"

where ' an are %he resis%an&e' in(&%an&ean &a)a&i%an&eo, %he %(ne &ir&(i%'

res)e&%i3el+. The lar*er %he series resis%an&e' %he lower %he &ir&(i% >.

!or a )arallel R5C &ir&(i%' %he > ,a&%or is %he in3erse o, %he series &ase: @;

Consier a &ir&(i% where R' 5 an C are all in )arallel. The lower %he )arallel resis%an&e' %he more

e,,e&% i% will ha3e in am)in* %he &ir&(i% an %h(s %he lower %he >. This is (se,(l in ,il%er esi*n

%o e%ermine %he 2anwi%h.

In a )arallel 5C &ir&(i% where %he main loss is %he resis%an&e o, %he in(&%or' R' in series wi%h %hein(&%an&e' 5' Qis as in %he series &ir&(i%. This is a &ommon &ir&(ms%an&e ,or resona%ors' where

limi%in* %he resis%an&e o, %he in(&%or %o im)ro3e > an narrow %he 2anwi%h is %he esireres(l%.

Individual reactive cmpnents

The > o, an ini3i(al rea&%i3e &om)onen% e)ens on %he ,re=(en&+ a% whi&h i% is e3al(a%e'

whi&h is %+)i&all+ %he resonan% ,re=(en&+ o, %he &ir&(i% %ha% i% is (se in. The > o, an in(&%or

http://en.wikipedia.org/w/index.php?title=Q_factor&action=edit&section=7http://en.wikipedia.org/wiki/RLC_circuithttp://en.wikipedia.org/wiki/Tuned_radio_frequency_receiverhttp://en.wikipedia.org/wiki/Electrical_resistancehttp://en.wikipedia.org/wiki/Inductancehttp://en.wikipedia.org/wiki/Capacitancehttp://en.wikipedia.org/wiki/Q_factor#cite_note-14http://en.wikipedia.org/w/index.php?title=Q_factor&action=edit&section=7http://en.wikipedia.org/wiki/RLC_circuithttp://en.wikipedia.org/wiki/Tuned_radio_frequency_receiverhttp://en.wikipedia.org/wiki/Electrical_resistancehttp://en.wikipedia.org/wiki/Inductancehttp://en.wikipedia.org/wiki/Capacitancehttp://en.wikipedia.org/wiki/Q_factor#cite_note-14

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wi%h a series loss resis%an&e is %he > o, a resonan% &ir&(i% (sin* %ha% in(&%or in&l(in* i%s series

loss1 an a )er,e&% &a)a&i%or.@;

$here:

is the resonance frequenc in ra#ians $er secon#"

is the in#uctance"

is the in#ucti%e reactance" an#

is the series resistance of the in#uctor&

The > o, a &a)a&i%or wi%h a series loss resis%an&e is %he same as %he > o, a resonan% &ir&(i% (sin*

%ha% &a)a&i%or wi%h a )er,e&% in(&%or:@;

$here:

is the resonance frequenc in ra#ians $er secon#"

is the ca$acitance"

is the ca$aciti%e reactance" an#

is the series resistance of the ca$acitor&

In *eneral' %he > o, a resona%or in3ol3in* a series &om2ina%ion o, a &a)a&i%or an an in(&%or &an

2e e%ermine ,rom %he > 3al(es o, %he &om)onen%s' whe%her %heir losses &ome ,rom seriesresis%an&e or o%herwise:

http://en.wikipedia.org/wiki/Q_factor#cite_note-dipaolo-16http://en.wikipedia.org/wiki/Electrical_reactance#Inductive_reactancehttp://en.wikipedia.org/wiki/Q_factor#cite_note-dipaolo-16http://en.wikipedia.org/wiki/Electrical_reactance#Capacitive_reactancehttp://en.wikipedia.org/wiki/Q_factor#cite_note-dipaolo-16http://en.wikipedia.org/wiki/Electrical_reactance#Inductive_reactancehttp://en.wikipedia.org/wiki/Q_factor#cite_note-dipaolo-16http://en.wikipedia.org/wiki/Electrical_reactance#Capacitive_reactance