PART IV. Methods of Analysis I

7/25/2019 PART IV. Methods of Analysis I

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ELECTRIC CIRCUIT ANALYSIS 1ELECTRIC CIRCUIT ANALYSIS 1

PART IV: Methods of Analysis IPART IV: Methods of Analysis I

Engr. Michael C. Pacis

BSEE, MEP-EE,

PhD EEE-Major in Power Systems

(candidate)


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I. N!AL ANALYSIS-provides a general procedure for analysis circuits

usingnode voltageas the circuits variables.-using node voltages instead of element voltagesas circuit variables is convenient and reducesthe

number of equationsone must solvesimultaneously.

-basis of nodal analysis is theKirchoffs Current Law (KCL)


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STEPS T !ETERMINE N!AL

VLTA"ES

1. Select a node as a referen#e node.

he !oltages are re"erenced with res#ect to there"erence node.

-. .

%se &hm's aw to e#ress the *ranch c+rrents

in terms o" the node !oltage.

. Sol!e "or the si&'ltaneo's e('ations too*tain the +nnown !oltages.


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I. N!AL ANALYSIS


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I. N!AL ANALYSIS


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I. N!AL ANALYSIS

1 )

Sol*in+ for #'rrents,

-1


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I. N!AL ANALYSISSol*in+ for #'rrents,

-)

-/

A$$lyin+ %CL at node 1 and )

at node 1

at node )

-0

-


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I. N!AL ANALYSISS'2stit'te e(ns -1, -), -/ to e(ns -0 and - res$e#ti*ely

-3

or in ter&s of #ond'#tan#es,

-5

-6


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I. N!AL ANALYSISor this circ+it, we sol!e E/s. (0) and () or (2) and (3) to o*tain

the node !oltages !1 and !$ +sing any standard method, s+ch as

the s'2stit'tion &ethod, the eli&ination &ethod, Cra&er7s

r'le, or &atri8 in*ersion. or e/+ation (2) and (3), the matri

re#resentation will *e4


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Sa&$le Pro2le&s


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Sa&$le Pro2le&s


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I. Nodal Analysis 9ith Volta+e So'r#es


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5ere,


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I. Nodal Analysis 9ith Volta+e So'r#es6C m+st *e satis"ied at a s+#ernode lie any other

node. 7t the circ+it4

or

(11)


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I. Nodal Analysis 9ith Volta+e So'r#eso a##ly 6irchho""'s !oltage law to the s+#ernode in the

"ig+re, we redraw the circ+it as shown *elow. 8oing aro+nd

the loo# in the clocwise direction gi!es

(1$)

rom E/s. (19), (11), and (1$), we o*tain the node *olta+es.


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Sa&$le Pro2le&s


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Sa&$le Pro2le&s


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II. MES ANALYSIS the basic of mesh analysis is Kirchoffs Voltage Law (KVL)

using mesh currents instead of element currents as

circuit variables is convinient and reduces the numberof equations. Mesh analysis applies only on a planar circuit.


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PLANAR CIRCUIT


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NN;PLANAR CIRCUIT

5owe!er, this circ+it is non$lanar, *eca+se there is no way toredraw it and a!oid the *ranches crossing. Non$lanar #ir#'its

can *e handled +sing nodal analysis.


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II. MES ANALYSIS


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II. MES ANALYSIS

or eam#le, #athsabefa andbcdebare meshes, but path

abcdefais not a mesh. The current through a mesh is knownas mesh current. In mesh analysis, we are interested in

applying KVL to find the mesh c+rrents in a gi!en circ+it.


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STEPS IN !ETERMININ" MES

CURRENTS


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STEPS IN !ETERMININ" MES

CURRENTS


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ILLUSTRATIVE E


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ILLUSTRATIVE E


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ILLUSTRATIVE E


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SAMPLE PR>LEMS


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Sol'tions

Si&$lifyin+:

Pro2le& no.1

-1

Si&$lifyin+:

-)


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Sol'tions

s'2stit'te e( -) to e( -1

>y s'2stit'tion

=ro& -)


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Sol'tions>y Cra&ers R'le

e( -1 and -) in &atri8 for&

Th's,


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SAMPLE PR>LEMS


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Sol'tionsPro2le& no.)

Si&$lifyin+:-1

Si&$lifyin+:-)


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Sol'tions

Si&$lifyin+:-/


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Sol'tions-1

-)

-/

>y Cra&ers R'le


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Sol'tions


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Sol'tions


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MES ANALYSIS ?IT CURRENT

SURCES



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SURCES



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SURCES



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SURCES


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PRPERTIES = A SUPERMES


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SAMPLE PR>LEM


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Sol'tion to Pro2le&Ass'&in+ &esh #'rrents

R

%CL at $t R is not a$$li#a2le 2e#a'se

it is 2et9een ) s'$er&eshes@

he two s+#ermeshes intersect and "orm a larger s+#ermesh as shown.7##lying 6: to the larger s+#ermesh,


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Sol'tion to Pro2le&Si&$lifyin+,-1

-)

-/


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Sol'tion to Pro2le&

-0

Si&$lifyin+,

fro& -), i1i);, s'2stit'te to -1, si&$lifyin+

0i) B 3i/ 0i0 -

fro& -/ &'lti$ly 2y 0 and 2y 'sin+ eli&ination -s'2stra#tion to -

1Di/ 13i0 -3


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Sol'tion to Pro2le&

fro& -0 &'lti$ly 2y )., and 2y 'sin+ eli&ination -s'2stra#tion to -3

9e ha*e, i0

).10/A

fro& e( 0, i/ /.6)5A

fro& e( /, i) ;).A

;1 .


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III. LINEARITY PRPERTY


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III. M"ENITY PRPERTY

requires that if the input also called the excitation ismultiplied by a constant, then the output also called theresponse is multiplied by the same constant.


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III. A!!ITIVITY PRPERTY

re/+ires that the res#onse to a s+m o" in#+ts isthe s+m o" the res#onses to each in#+t a##lied se#arately.


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NN LINEAR E


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NN LINEAR E


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NN LINEAR E


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NN LINEAR E


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NN LINEAR E


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Sa&$le Pro2le&s

Sol'tion to Pro2le& 1


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-1

-)

E/ ($) will *ecome

-/

7dding e/ ($) and ()

-

-0



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S+*s (;) to (1)

-3

Con#l'sion: sho9in+ that 9hen the so'r#e *al'e is do'2led, io

doubles.

Sa&$le Pro2le&s


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Sa&$le Pro2le&s

Sol'tion to Pro2 )


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Sol'tion to Pro2 )

re*ersin+ the sol'tion:

Sol'tion to Pro2 )


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Sol'tion to Pro2 )

ere ore, s . s s o9s a ass'& n+ o + *es s

5ence,

PART IV. Methods of Analysis I

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