part iv. methods of analysis i
TRANSCRIPT
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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 ðod, the eli&ination ðod, 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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I. Nodal Analysis 9ith Volta+e So'r#es
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I. Nodal Analysis 9ith Volta+e So'r#es
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I. Nodal Analysis 9ith Volta+e So'r#es
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
MES ANALYSIS ?IT CURRENT
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MES ANALYSIS ?IT CURRENT
SURCES
MES ANALYSIS ?IT CURRENT
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MES ANALYSIS ?IT CURRENT
SURCES
MES ANALYSIS ?IT CURRENT
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MES ANALYSIS ?IT CURRENT
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. 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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III. LINEARITY PRPERTY
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III. LINEARITY PRPERTY
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&$le Pro2le&s
Sol'tion to Pro2le& 1
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Sol'tion to Pro2le& 1
-1
-)
E/ ($) will *ecome
-/
7dding e/ ($) and ()
-
-0
Sol'tion to Pro2le& 1
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Sol'tion to Pro2le& 1
S+*s (;) to (1)
-3
Con#l'sion: sho9in+ that 9hen the so'r#e *al'e is do'2led, io
doubles.
Sa&$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,