Theme 2 DC Network Analysis and Network Theorems.
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Transcript of Theme 2 DC Network Analysis and Network Theorems.
Theme 2
DC Network Analysis and Network Theorems
Independent Sources
• Ideal Voltage Source- Voltage at Terminals independent of Load
+-
+-
Ideal Voltage Source
• Non-Ideal Voltage Source – – An Ideal voltage source is only theoretical and
does not exist in reality – A practical voltage source can be modelled with a
small resistance in series with an Ideal voltage source
+-
Rs
RL
+
-
VoE
Equation)Divider (Voltage
)( sL
Lo RR
REV
o
Ls
VEThen
,RRWhen
• Ideal Current Source – Current supplied is independent of Load
Ideal Current Source
• Non-Ideal Current Source- Can be modeled with a large resistor in Parallel
Rs RL
IL
I
Equation)Divider (Current
)( Ls
sL RR
RII
L
Ls
IIThen
,RRWhen
Network Theorems
• Kirchoff’s Current Law- The algebraic sum of currents leaving a NODE is zero, at any given instant
i1
i3
i2
i4
04321 iiii
• Convention Used: Currents Entering a Node are POSITIVE, and Currents Leaving a Node are NEGATIVE.
• Kirchoff’s Voltage Law- The algebraic sum of voltage drops around a closed path is zero.
+-
R1 R2
R3
R4
+ - + -
+ -+ -
V1 V2
V3
V4
E
04321 VVVVE
I• Convention
Used: Voltage drop Given a NEGATIVE Sign
• Class Example:– Find Value of I1, I2, I3 , I4 and Direction of I2, and value of R2
R1=5Ω
V3=18V
I3
R2=?
R3=3Ω
R4=4Ω
+ -
V2=24V
+ - V4=20V+ - V1=15V
I1=?
2I4I2=?
• Class Example: Find the Voltage drops across each Resistor.
+-
R
+ -V1
E+ -V2
+ -V
32R
3R
I
• LOOP CURRENT NETWORK ANALYSIS– Formulate circuit equations using a set of current
variables.– The Variables(Unknown Currents) Satisfy KCL.– Thus circuit can be described using independent
KVL equations.• METHOD• Take the shortest KVL loop (Current loops in
Clockwise direction) and write KVL equation.• Where more than one loop Flows in an Element,
the algebraic sum of the currents is used-thus voltage across that element can be found.
+-
R1
R3
R2
EA
I1
+-
+-
EC
EBI2
• Class Example: Write down the KVL Equations using unknown Variables I1 and I2.
0)(
0)(
31222
32111
CB
CA
ERIIRIE
ERIIRIE
23213
23131
21
)(
)(
:I andIfor Solve and Rearrange
IRRIREE
IRIRREE
BC
CA
• Class Example: Find I1 and I2
+-
R1=15Ω
R3=
12Ω
R2=20Ω
EA
=12V
I1
+-
+-
EC=
10V
I2EB=16V
• NODAL VOLTAGE NETWORK ANALYSIS– Formulation of circuit equations where the
variables (Unknown Voltage Nodes) satisfy KVL.– KCL Equations are used to find selected voltage
node values, thus currents through a given element can be found.
• METHOD– Identify independent Nodes, and select one node
as the reference. – Write the KCL Equations and solve
+-
R1
R3
R2
EA
+-
I1
I3
I2
EB
Node M with a Voltage VM
Node O
33
22
11
321
;;
(1) 0
R
VI
R
VEI
R
VEI
III
MMBMA
Solve andSubject theV Make
(1);in Substitute
M
321 R
V
R
VE
R
VE MMBMA
• Class Example: Find I1, I2, I3 and VM
+-
10Ω=R1
6Ω=R3
5Ω=R2
12V EA
+-
I1
I3
I2
8VEB
O
M
VM