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CHAPTER 1

THE MEASUREMENT OF ELECTICAL

Electrical measurement instrument is a tools tat use! To !etermine

electrical "uantities o# DC an! AC suc as $olta%e& current& resistance& 'o(er& (or)

#actors& an! #re"uenc*& (e use electrical measurin% instruments+

+Tere is t(o )in! o# measurement s*stems,

1+ measurement (it analo% s*stem& Analo% s*stems associate! (it

in#ormation an! analo% !ata tat so(in% #rom te a''ointment o# an

electronic scale a''ointment o# an electronic scale+

-+ measurement Di%ital s*stems relate! to in#ormation an! !i%ital !ata+ Te

a''ointment o# a !iscrete !i%ital num.er is numeric an! !iscontinuous

'ulses associate! (it time an! !is'la*e!+



Multimeter is an electrical measure instrument can .e use! to measure some

"uantities& suc as AC an! DC $olta%e& DC an! AC electrical current& te

resistance

Sin%le measurement instrument is a tools tat can .e use to measure! onl*

sin%le "uantities& #or e/am'le to measure! 0ust current or 0ust $olta%e onl*



Tere are se$eral terms an! !e#initions a.out electrical measurements ,

a+ Measure instrument& is a !e$ice to !etermine $alue or ma%nitu!e #rom "uantit*

or $aria.le+

.+ Accurac*& 'ro/imit* %au%es rea! te actual $alues o# te $aria.les measure!+c+ Precision& te measurement results %enerate! #rom te measurement 'rocess& or

te !e%ree to !istin%uis one measurement to anoter+!+ Sensiti$it*& te ratio #rom out'ut si%nal or res'onse measurement tool in'ut

can%es or $aria.les measure!+e+ Resolution& te smallest can%e o# $alue measurement tat can .e a!!resse! .*

te measure instrument+

#+ Error& te rate !e$iation #rom te true $alue $aria.les measure!+

Magnitude and Electrical Symbols

In 'ractical electrical "uantities No( te SI s*stem a$e ma!e a list o#

"uantities& units an! s*m.ols in te #iel! o# electricit* an! ma%netism teinternational #orce+

Ta.le 1+-+ Ma%nitu!e an! Electrical S*m.ols



Ma%nitu!e an! Name an! E"uation

Electromoti$e Force& $olt V

Potential Electrical& $olt V

Resistance& om Ω R 3 24IElectric Car%e& Coulom.& C 5 3 It

Ca'asitance& Fara!& F C 3 542

Electric Fiel!& V/m E 3 24l

Electric #lu/ !ensit*& C m2 D 3 I-

Ma%nitu!e an! Name an! E"uation

Ma%netic Fiel!& A/m 6 H!l 3 nI

Ma%netic Flu/& (e.er Wb E 3! 4!t

Ma%netic #lu/ !ensit*& tesla T 7 3 I-

In!uctance& enr* H M 3 4I

Permea.ilit*& H/m 8 3 74H

CHAPTER -S9STEM AND PRINCIPLE OF ELECTRIC MEASUREMENT

Kind of measurement instrument

Electrical measurement instrument tat usuall* use! #or measure! inclu!in% ,



)in! o#& si%n mar)& 'rinci'le& use!& te outori:ation& an! 'o(er use! can .e

e/am'le .* tis ta.le ,

Ta.el -+ Measurement instrument e/am'le

No )in! Si%n

mar)

;or) 'rinci'le Use! E/am'le Ran%e o# (or) an! ener%* Da*a

Current 2olta%e Fre)uens

1 - < = > ? @ A B 1

1 Circular

core

Electroma%netic

s*tle .et(een te

ma%netic #iel! an!

current

DC A2O1&> / 1

?1

-1

-1

< small

- Mo$ea.le

coil

R

Te com.ination o#

can%er usin% semi

con!uctor #or te

circular core to mo$e

AC A2OF> / 1

=1

111

< 1

= small

< TermoMom

en

Te com.ination o#

can%er usin%

termomomenan!

measure! toolcircular

AC

E#e)ti#

DC

A2;1

<> >/1

1

1&>/1-

1< small

= Iron core

roun!

Electroma%netic tat

(or) at iron core in

te ma%netic #iel!

AC

E#e)ti#

DC

A21

-

</1-

11<

>/1- lar%e

> electro

!inamo

meter

Electroma%netic tat

(or) at te electricit*

core n te ma%netic

#iel!

AC

E#e)ti#

DC

A2MF1

- > 11

< 1

< ar%e

? in!uction

D

An electroma%netic

tat cause o# tecurrent #iel!

AC

E#e)ti#

A2;

;

11

1-

11<

1<

/

1 1-

ar%e

note, A , F , Fre)uensimeter 2 , 2oltmeter

1. Analo%ue rotation coil 'la* measure! Instrument

Electricit* is an im'ortant 'art& 'ermanent ma%net& resistance meter& an! te

coil turn+ Mecanical 'arts inclu!e nee!le 'ointer& scale an! scre(s re%ulator o#



te nee!le+



Tor"ue resultin% #rom te electroma%netic interaction accor!in% to e"uation T 3 7

A I N

;ere ,

T 3 Tor"ue GNm

7 3 ma%netic #lu) !ensit* G;.4m-

A 3 e##ecti$e coil area Gm-

I 3 current to te coil turn GA

N 3 num.er o# turns



2. Measurement o# Iron Pla*

au%e steel s(i$el as a !i##erent anatom* (it s(i$el s'in!le+ A (ire

entan%lement (it te ca$it* o# te tu.e to %enerate an electroma%netic #iel!

GFi%ure -+1<+

Insi!e te ca$it* mounte! #in tu.e steel sa#t an! connecte! (it nee!le

scale meter+ I# te current trou% a (ire entan%lement& arisin% electroma%netic

an! iron #in (ill mo$e to #ollo( te la( o# attraction ma%netic #iel!+

Te amount !e$iation o# te nee!le (it te current

trou% (in!in% s"uare meter scale is not linear .ut non

linear !istance num.ers+ au%e steel s(i$el sim'le sa'e

an! "uite relia.le+



3. Measurement electro!*namic

Electro!e measure tool as t(o t*'es o# (in!in% (ire& tat is (in!in% (ire

mounte! current& an! $olta%e as te coil (in!in% (ire connecte! to te rotar* sa#t

an! te nee!le+

Interaction o# te ma%netic #iel! (in!in% current an!

$olta%e (in!in% 'ro!uces nee!le an%le !e$iation is

'ro'ortional to te 'o(er use! .* loa!

P 3 V · I · cos



Use o# electro!*namic %au%e as a measure o# electrica l'o(er or (attmeter+

Fittin% (it te notation (attmeter terminals 1& -& <& an! >+ Terminals 1< are

connecte! to te (in!in% currents ;attmeter& connecte! in series (it te loa!+

Terminals -> connecte! to te (in!in% $olta%e ;attmeter+ Terminal 1- is cou'le!

to a su''l* $olta%e o# te su''l* $olta%e GFi%ure -+1>+

Installation o# meter terminals soul! not .e con#use!& .ecause te meter

!oes not #unction as a result+ For te measurement o# 'o(er& (ere a lar%e loa!

current trans#ormer CT can .e use! to re!uce te current #lo(in% to (in! (attmeter

current+

Su''ose te tree 'ase motor 'o(er >> ); (it = 2 $olta%e (ill !ra(

currents meses 1 A+ Te a.ilit* o# K;H meter ma/imum #lo( trou% a 1 A&

ten use a CT current trans#ormer (it a ratin% o# 14>A #or te measurement o#

motor 'o(er can .e im'lemente!+

;attmeter 'orta.le (irin% to te loa! GFi%ure -+1?+ Tere are tree selector

s(itc& #or settin% am'era%e& $olta%e re%ulation& an! limits te selection o#

measurement scales+To 'lace te sa#et* selector am'era%e an! $olta%e selector at te i%est

measurin% limit+ Rotatin% !isc measure tool !oes not use te nee!le+ Construction

rotatin% !isc meter as t(o iron core GFi%ure -+1@+ U iron core (in!in%s mounte!

t(o currents in eac le% o# te core& usin% a lar%e (ire section+ EIsa'e! iron core

(it one (in!in% $olta%e& mounte! on an iron core mi!!le le%& te num.er o# turns

te $olta%e more (it #ine (ire cross section+



Fi%ure -+1? ;irin% a sin%le 'ase (attmeter (it loa!

4. Measurement Pla*.ac) Disc

Measurement 'la*.ac) !isc !oesnJt use nee!le to 'ointer te result+ Te

contruction o# tis instrument is te* a$e t(o iron core+ Te 'oint o# iron core

U use t(o airs'rin% current in te all o# inti le%t& usin% te .i% (ires+ Teiron core sa'e is EI (it sin%le airs'rin% $olta%e an .een 'lace at te

center o# iron core le%t& te $ilta%e airs'rin% is more muc #rom te (ires+



Fi%ure -+1@ Te 'rinci'le o# rotatin% !isc

meter

Fi%ure -+1 K;Hmeter



CHAPTER <

KIND OF ELECTRIC MEASUREMENT INSTRUMENT

1+ DC 2olta%e Measurement

2olta%e $oltmeter %au%e as a meters resistance Rm GFi%ure <+1+ Prisoners

meters also so( sensiti$it* meter& calle! IFSD G#ull scale !e#lection current re"uire!

to !ri$e te nee!le meter at #ull scale+ To raise te limit must .e mounte! $oltmeter

measurin% te series resistance o# te R2+

R2 meter series resistance e"uation,

Iam.ar +-- Taanan seri R2 'a!a $oltmeter

R2 meter series resistance e"uation,

R$ 3 ol! series meters

Rm 3 resistance in meters

U 3 $olta%e

Um 3 $olta%e meter

Im 3 #lo( meters

n 3 te multi'lication #actor



2. Measurement o# DC currents

Te measurin% electric currents& am'ermeter (it !isa.ilities to .e a.le to

measure current& resistance in meters Rm limit te a.ilit* o# te limit measure+

Raisin% te limit o# measurement carrie! out .* installin% a 'arallel resistance R '

(it am'ermeter GFi%ure <+-+ R' Inmates (ill ener%i:e! .* I'& te current trou%

te meter Rm #or Im+

Fi%ure <+- resistanc 'arallel am'ermeter

To raise te 'risoners in te *ar!s& in #ront o# te 'rison *ar!s Rm a!!e!

series resistance R$+ So tat te 'risoners in te ne( meter GRm R$ GFi%ure <+<+

Prisoners 'arallel R' remains ener%i:e! I'& (ile te current trou% te GRm R$

o# Le$+

Resistanc 'arallel am'ermeter

Parallel resistance R' e"uation,



R' 3 'arallel resistance

U 3 $olta%e

I 3 current measure!

Im 3 current trou% te meter

I' 3 current trou% te 'arallel resistance

Rm 3 resistance in meters

In 'ractical #or measurin% te (i!t o# te limit ma!e into tree le$els

GFi%ure <+=+ Measurin% limit o# te #irst scale& te s(itc in 'osition 1 use! a

'arallel resistance R'1+ Limit te scale measurin% - 'osition s(itc - is use! 'arallel

resistance R'-+ Limit o# te tir! measure& te 'osition o# te s(itc < is use!

'arallel resistance R'<+

Fi%ure <+= 7or!er measurin% am'ermeter

;it !i##erent meto!s (it te aim o# e/ten!in% te limit measure& use!tree 'arallel resistance R'1& R'-& an! R'< are tree 0ointe! series GFi%ure <+>+

S(itc 'osition 1& te 'risoner GR'1 R'- R'< in 'arallel (it te circuit GR$ Rm+

S(itc 'osition -& 'risoners GR'- R'< in 'arallel (it te circuit GR'1 R$ Rm+



;en te s(itc 'osition <& 'risoners R'< 'arallel (it te circuit GR'1 R'- R$

Rm+

Fi%ure <+> Te a!!ition o# te limit measure m

< + Measurement o# Prisoners

Measurement o# 'risoners can .e !one in t(o (a*s& namel* !irectl*

measure te resistance $alue an! te meto! o# in!irect measurement o# te .ri!%e

GFi%ure <+?+ Measurement o# resistance usin% a multimeter can !irectl*& .* 'lacin%

te selector mo!e selector on te measurement o# resistance+ Measure! resistor

connecte! to .ot ca.le an! meter rea!s resistance $alues on a scale o# meters+

In!irect measurements& usin% a s'ecial meter 'risoners (it te (or)in% 'rinci'les

suc as te ;eatstone .ri!%e+



+

Fi%ure <+? Prisoners T*'es o# Measurement

=+ ;eatstone 7ri!%e

De$elo'ment o# series an! 'arallel resistor circuit %eneratin% 'rinci'le o# te

;eatstone .ri!%e GFi%ure <+@+ DC $olta%e source circuit !ole #our resistors+ R 1

series (it R-& an! R< series (it R=+ Kirco##s $olta%e la( states te amount o#

$olta%e !ro' e"ual to te $olta%e source+

+U 3 U 1 U 2 !an U 3 U 3 U 4



R

U U

Fi%ure <+@ Te series o# .ri!%es ;eatstone

A7 'oint mounte! $oltmeter measures te $olta%e !i##erence& i# te meter so(s

:ero& meanin% tat te $olta%e U1 3 U< calle! .alance! con!ition+ I# U1 U< calle!

un.alance! con!itions an! te meter so(s a certain num.er+

U 1 U <

U AB 3 V & 3

- =

R1 R<

-3

R=

R1& R/ Prisoners (o sou%t

R-& Rn Prisoners $aria.le

R<& R= Prisoner set& constant



Ca'ter =

OSCILLOSCOPE

1+Osilosco'e

Oscillosco'e inclu!in% an electronic measure instrument& use! to $ie(

(a$e#orms& anal*:in% te (a$e& an! oter 'enomena in electronic circuits GFi%ure

=+1+ ;it te oscillosco'e can see te $olta%e am'litu!e an! (a$e .o/es&

tere#ore te a$era%e 'rice& 'ea)& RMS Groot mean s"uare& an! 'rice summit or

'ea) o# te $olta%e 2'' (e can measure+ In a!!ition& also te relationsi' .et(een

#re"uenc* an! 'ase .et(een t(o (a$es can also .e com'are!+



Tere are t(o t*'es o# oscillosco'es,

1+ Analo%ue Oscillosco'es

-+ Di%ital oscillosco'es



<+ Analo% Oscillosco'e

7loc) !ia%ram .asic o# te oscillosco'e consists o# a transmitter o# electrons

GElectron 7eam& 'em.elo) $ertical G9am'li#ier& 'em.elo) ori:ontal Gam'li#ier& time .ase %enerator GS(ee' enerator& 'o(er su''l*& an! a ollo( tu.e

GCRT see Fi%ure =+- ++

Fi%ure =+- 7loc) !ia%ram o# oscillosco'e s*stem

Electron transmitter,

An oscillosco'e is te most im'ortant 'art+ Cato!e in te CRT GCato!e Ra* Tu.e

(ill emit electrons to te CRT screen trou% te electro!es electron emission

intensit* tat is !etermine! te num.er o# electrons emitte! .* te cato!e Fi%ure

=+<+



Fi%ure =+< Te ra!iation o# an electron to a

'os'orescent screen CRT

Materials tat re#lect li%t on te CRT screen can .e o.taine! #rom sul#i!&

o/i!es or silicates o# ca!mium& (ic is acti$ate! trou% a!!itional materials #rom

sil$er& %ol! or co''er+ In %eneral& te color %reen (as cosen #or te !is'la* li%t on

te CRT screen& .ecause te uman e*e is %enerall* sensiti$e to tis color+

2ertical am'li#ier,

Tis am'li#ier can !eli$er $olta%e to 1 2+ Tis am'li#ier must .e a.le to

stren%ten te DC or AC $olta%e (it te same rein#orcement+ Te measurement

si%nal can .e set $ia te POS G'osition+

In'ut9 G2ert+ In'ut,

Tis section is connecte! to te $olta%e !i$i!er& #or !i$i!in% te $olta%e to .e

measure!& (it a ratio o# 1 , 1 or 1 , 1+ GFi%ure =+=+ Tis .utton soul! .e

assiste! .* a si%nal .o/ to com'ensate+



Hori:ontal am'li#ier,

Tis am'li#ier as t(o in'uts& one o# te s(ee' %enerator& 'ro!ucin% a trace

Gs(ee' ori:ontall* trou% te CRT an! oter in'uts to stren%ten te e/ternal

si%nal an! !is'la*e! on te CRT onl* on te ori:ontal a/is+

Hori:ontal a/is scale on te CRT oscillosco'e& use! to measure te time

G'erio! o# te si%nal .ein% measure!& #or e/am'le& - ms4!i$ision+

eneratorTime,

Time %enerator %eneratin% sa(toot si%nal& (ose #re"uenc* can .e set& .*

re%ulatin% te 'erio! trou% te TIME 7ASE+ CRT (ill !is'la* te measure! si%nal

Gin'ut si%nal onl* i# te 'erio! si%nal is e/actl* e"ual to te 'erio! o# tis or te

sa(toot si%nal is a multi'le o# te 'erio!+



Fi%ure =+> Tri%erin% raises sa(toot si%nal

Tri%%erin% an! time .ias,

Sa(toot si%nal (ill .e%in to emer%e i# tere is a tri%%er si%nal GFi%ure =+>+At te time o# te in'ut si%nal 'asses te tri%%er le$el& ten te sa(toot si%nal

.e%an to a''ear

Po(er Su''l*,

Per#ormance o# te 'o(er su''l* is a##ectin% te 'er#ormance o# oter 'arts

o# te oscillosco'e+ Te 'o(er su''l* is not re%ulate! 'ro'erl* (ill cause

measurement errors an! !o not loo) %oo! on a CRT G#ocus& .ri%tness4.ri%tness&sensiti$it*& an! so on+



+1B T(o Cannel Oscillosco'e

O#ten 'eo'le nee! to ta)e measurements o# t(o !i##erent AC si%nals in te

same time+ For e/am'le& cannel1 to measure in'ut si%nal an! cannel- to

measure te out'ut si%nals simultaneousl*& ten t(ocannel oscillosco'e ca'a.leo# !is'la*in% t(o si%nals at te same time in one screen+

Fi%ure =+? 7loc) !ia%ram o# t(ocannel oscillosco'e

7loc) !ia%ram o# t(ocannel oscillosco'e Fi%ure =+? as .eam a %eneratin%

s*stem Gelectron %un+ T(o in'ut si%nals can .e inserte! trou% te cannel1 an!

cannel- Geac am'li#ier9+ Acti$ation o# te secon! am'li#ier9 is selecte!

electronicall*& $ia !i##erent #re"uenc* #or eac cannel+ 7ot te in'ut si%nal (ill %o

trou% an electron%un an! ten alternatel* !is'la*e! on te CRT+

I# te in'ut si%nal as a lo( #re"uenc*& te electronic s(itces (oul! set it ati% #re"uencies+ Con$ersel*& i# te in'ut si%nal as a i% #re"uenc*& ten te

electronic s(itces (oul! set it at a lo(er #re"uenc*+

Dou.le s(ee' !is'la* G!ualtrace o# sin%le electron .eam can .e !one in -

(a*s& tat is co' time sarin% an! time sarin% alternate+ Selection o# cannels

carrie! .* te multi$i.rator electronic s(itces (ic (ill o'erate automaticall*+



+- Di%ital Oscillosco'e

7loc) !ia%ram o# a !i%ital oscillosco'e GFi%ure =+@ all o# te analo% si%nal

!i%iti:ation+ Di%ital oscillosco'e& stora%e oscillosco'e #or e/am'le consist o#,

•

ADC GAnalo%toDi%ital Con$erter• DAC GDi%italtoAnalo% Con$erter

• Electronic Stora%e

Fi%ure =+@ Dia%ram .loc) o# a !i%ital oscillosco'e



Fi%ure =+ Sam'lin% analo% ima%e si%nal .* te ADC

On te oscillosco'e o# tis t*'e& all !ata (ill .e !is'la*e! are store! in te

RAM+ Te analo% si%nal

(ill .e sam'le! Gsam'lin%& an! ten "uanti:e! .* te ADC& (ic is %i$en a

$alue G.inar* in accor!ance (it te ma%nitu!e o# te am'litu!e tersam'lin%

GFi%ure =++ Tis $alue can .e !is'la*e! .ac) !irectl* on a CRT screen or PC

monitor $ia RS-<- connectin% ca.le+

Te !i##erence .et(een analo% an! !i%ital oscillosco'e at te ADC si%nal

'rocessors+ Steerin% te electron .eam on te oscillosco'e is e"ui$alent to steerin%

te electron .eam on analo% oscillosco'e+ Tere is a !i%ital oscillosco'e e"ui''e!

(it matematical so#t(are #or si%nal anal*sis or 'rinter+

Measurements (it Oscillosco'e

Here is an illustration o# te measurement usin% te oscillosco'e inclu!e,

1+ measure te DC $olta%e&

-+ measure te AC $olta%e& 'erio!& an! #re"uenc*&

<+ measure te AC electrical current&

=+ !i##erent 'ase measurement AC $olta%es (it electrical currents& an!

>+ t*ristor #irin% an%le measurements+



1+ Measurin% DC 2olta%e

Prisoners R1 an! R- ser$e as a $olta%e !i$i!er+ roun! oscillosco'e connecte! to a

ne%ati$e DC 'o(er su''l*+ Pro.e cannel1 connecte! (it te en! connection R1

(it R-+ Uni!irectional $olta%e measure! at te DC mo!e+

For e/am'le,

2DC 3 >24!i$+ <!i$ 3 1> 2

Form o# a DC $olta%e is a strai%t tic) lines on te CRT screen+ Measure!

$olta%e is measure! #rom te :ero line to te ori:ontal line DC+

Fi%ure =+B Measure DC $olta%e (it an oscillosco'e

-+ Measurin% AC $olta%e& 'erio! T& an! #re"uenc* F

Trans#ormer is use! to isolate te electrical 'o(er measure! .* te oscillosco'e+ I#

usin% electricit* ten te #re"uenc* is > H:+

For e/am'le,



2' 3 -24!i$ < !i$ 3 ? 2

T 3 -ms4!i$ 1 !i$ 3 - ms

# 3 1 4 T 3 14-ms 3 > H:

Sinusoi!al AC $olta%e (it i% U an! (i!t o# te 'erio! T+ Te amount o#

$olta%e ? 2 an! 'erio! is - millisecon!s an! te #re"uenc* is > H:+

Fi%ure =+1 Measure AC $olta%e (it an oscillosco'e

<+ Measure AC Po(er Flo(

7asicall*& onl* oscillosco'e measure te $olta%e+ to measure te current

in!irectl* (it R 3 1; to measure te $olta%e !ro'+

For e/am'le,



2' 3 > m2 4 !i$ <!i$

3 1> m2 3 &1> 2

Form te si%nal current trou% te resistor R is a sinusoi!alli)e $olta%e+ On te

loa! resistor $olta%e si%nal an! current si%nal (ill se'asa+

Fi%ure =+11 Measure AC current (it an oscillosco'e



=+ Measurin% te 'ase !i##erence (it current 2olta%e AC Po(er+

Pase !i##erence can .e measure! (it a series o# C1 an! R1+ Te $olta%e

o# te su''l* $olta%e U1 re$eal an AC %enerator+ U- $olta%e !i$i!e! .* te $alue o#

resistor R1 re'resentation o# an AC electric current+ Si#t U1 (it U- 'ase o# D/+E/am'le,

U1 $olta%e sinusoi!al si%nal !is'la* G'o(er su''l* $olta%e an! $olta%e U- Gi#

!i$i!e! .* R1& re'resentation o# te AC current+

Pase si#t .et(een $olta%e an! current o# 3 B+



Measurin% te I%nition An%le TRIAC

Triac is an electronic com'onent tat can cut 'o(er sinusoi!al si%nal on te

'ositi$e si!e an! ne%ati$e+

2olta%e re%ulator use! to Triac $olta%e isolation (it 'o(er su''l* $olta%e

an oscillosco'e+Ten te !immer an%le tri%er li%ts so (e can .e set #rom te .ri%test to

.e !im+

For e/am'le,

Fi%ure =+1< Measurin% TRIAC #irin% an%le (it te oscillosco'e



Lissa0ous Meto!

T(o si%nals can .e measure! !i##erent 'ase .* utili:in% te in'ut $ertical

'ase Gcannel9 an! ori:ontal Gcannel+ 7* usin% t(ocannel oscillosco'e

can !is'la* !i##erent 'ase )no(n as Lissa0ous meto!+a+ Di##erent 'ase Q or <?Q

T(o !i##erent si%nals& in tis case te in'ut si%nal an! out'ut si%nal i# com.ine!

(oul! 'ro!uce con#i%uration o# an entirel* !i##erent #orm+ Te in'ut si%nal is

inserte! into cannel 9 G$ertical an! inserte! into te cannel out'ut si%nal

Gori:ontal is !i##erent o# Q& com.ine! to 'ro!uce a si%nal allo*s are strai%t

lines tat #orm an an%le o# =>Q

Fi%ure =+1= Measurin% TRIAC #irin% an%le (it te oscillosco'e

.+ Pase !i##erence o# BQ or -@Q2ertical si%nals in te #orm o# sinusoi!al si%nals+ Si%nals o# !i##erent ori:ontal

'ase o# B Q or -@Q inclu!e!+ Allo* results tat a''ear on te CRT screen is a

line o# s'erical GFi%ure =+1>+



Fi%ure =+1> Te in'ut si%nal !i##erent #rom BQ to te out'ut 'ase

Fi%ure =+1? Lissa0ous ima%es to !etermine #re"uenc*

9 measurements can .e use! to measure te #re"uenc* o# un)no(n+ For

e/am'le te re#erence si%nal inserte! into te oter in'ut si%nal to te ori:ontal

an! $ertical in'ut+

#$ 3 #re"uenc* o# un)no(n

FR 3 #re"uenc* re#erence

N$ 3 num.er o# loo's o# un)no(n #re"uenc*

NR 3 num.er o# loo' re#erence #re"uenc*



Fi%ure =+1? E/am'le Gc+ For e/am'le te re#erence #re"uenc* 3 < )H:& ten #2 3

<+G-4< )H: 3 - )H: