nodal analysis
DESCRIPTION
Nodal AnalysisTRANSCRIPT
By Pn Zabidah Binti Haron Jabatan Kejuruteraan
Elektrik, PSA
EE602/ZAB/JUN2012
EE602/ZAB/JUN2012
Kirchoff’s Current Law states that the the branch currents incident at a node must sum to zero.
i2+i3-i1-i4 = 0Note : nodes" (points where elements or branches connect) in an electrical circuit in terms of the branch currents.
EE602/ZAB/JUN2012
Z1Z2
I Z3
V1 + _
IA IB
IC
EE602/ZAB/JUN2012
V
By using Kirchoff’s Current Law IA+IB+IC=0 The equation IA:( V-V1)/Z1
IB=-I Ic=V/Z3
V is Node Voltage V1 is supply voltage
EE602/ZAB/JUN2012
Find the value of I 1 , I2 and Ic
I1
3Ω
4+j4 Ω
I2
+ _
+ _
IA IB
IC
4Ω
20>0ºV 15>0ºV
EE602/ZAB/JUN2012
Using Kirchoff Voltage Law (KVL) :Loop 1 :-(20>0º) + 4 I 1 + (4 + j4)(I 1- I 2 ) = 0
4 I 1 + 4 I 1 + j4 I 1 - 4 I 2 - j4 I 2 = 20>0º
(4 + 4 + j4 ) I 1 + (- 4 - j4 ) I 2 = 20>0º
(8+ j4 ) I 1 + (- 4 - j4 ) I 2 = 20>0º ----- ( 1 )
EE602/ZAB/JUN2012
Loop 2 : +(15>0º) + (4 + j4)(I 2- I 1 ) + 3 I 2= 0 4 I 2 + j4 I 2 - 4 I 1 - j 4 I 1 + 3 I 2 = -(15 >0º ) (4 + j4 + 3 )I 2 +( - 4 - j 4 )I 1 = -(15 >0º ) (7 + j4)I 2 +( - 4 - j 4 )I 1 = -(15 >0º ) (- 4 - j 4 )I 1 (7 + j4)I 2 = -(15 >0º ) -----( 2 )
Apply to matrix equation
8 + j4 -4-j4 I 1 = 20>0º-4-j4 7 + j4 I 2 -(15 >0º )
EE602/ZAB/JUN2012
= 8 + j4 -4-j4
-4-j4 7 + j4
= (8+j4)(7+j4) – (-4-j4)(-4-j4) = 40 + j 28= 48.83 < 34.99 º
1 = 20>0º -4-j4 -(15 >0º ) 7 + j4
= (20>0º)(7+j4) - (-4-j4)(-(15 >0º )) = 80 + j20=82.46< 14.04 º
EE602/ZAB/JUN2012
2 = 8 + j4 20>0º -4-j4 -(15 >0º )
= (8 + j4)(-(15 >0º )) - (-4-j4) (20>0º )= -40 + j20= 44.72 < 153.43º
EE602/ZAB/JUN2012
I1 = 1 /
=(80 + j20) / (40 + j 28)= 1.58 - j0.60 Ampere
I2= 2 /
=(-40 + j20) / (40 + j 28)= -0.44+j 0.81 Ampere
Ic= I1 – I2
= (1.58 - j0.60 ) –(-0.44+j 0.81 )= 2.01-j1.42 Ampere
EE602/ZAB/JUN2012
Find the value of I 1 , I2 and Ic
I1
4Ω
5+j3 Ω
I2
+ _
+ _
IA IB
IC
5Ω
100>0ºV 50>0ºV
EE602/ZAB/JUN2012
The principles of Mesh Analysis is the algebraic sum of the voltage supply and the voltage drop across the load, around a closed path is equal zero.
One of the method to solve the electrical circuits problems.
EE602/ZAB/JUN2012