April 8, 2002
Review - 3
Techniques of Circuit Analysis
Thevenin’s Theorem
Any two-terminal bilateral dc network can be replaced by an equivalent circuit consisting of a
voltage source and a series resistor.
To find the Thevenin voltage VTh and the Thevenin resistance RTh:
1. Mark the terminals of the remaining two-terminal network.
2. Calculate RTh by first setting all sources to zero(voltage sources are replaced by short
circuits and current sources by open circuit) and then finding the result resistance
between the two marked terminals
3. Calculate VTh by first replacing the voltage and current sources and then finding the
open-circuit voltage between the marked terminals.
4. Draw the Thevenin equivalent circuit with the marked terminals
Example: Find the Thevenin circuit of a and b terminals for the following network.
3
a
12
6A
RTh
6
36V
VTh
b
Step 2.
3
12
6
RT
h
RTh = 3 +
( 6)(12)
= 3 + 4 = 7Ω
6 + 12
Step 3:
Use superposition. For the 36 V source we can apply the voltage divider rule
Ece207-c-1
3
12
6
36 V
ETh' =
( 6)(36) 216
=
= 12 V
6 + 12
18
For the 6A source we have can apply the current divider rule
3
12
6A
6
(12)(6) 72
=
= 4A
12 + 6 18
= I 6Ω ( 6) = ( 4)( 6) = 24 V
I 6Ω =
"
ETh
'
ETh = ETh
ETh" = (12)( 24) = 36V
Norton’s Theorem
Any two-terminal bilateral dc network can be replaced by an equivalent circuit consisting of a
current source and a parallel resistor.
The steps to find IN and RN
1. Mark the terminals of the remaining two-terminal network.
2. Calculate RTh by first setting all sources to zero(voltage sources are replaced by short
circuits and current sources by open circuit) and then finding the result resistance
between the two marked terminals
3. Calculate IN by first replacing the voltage and current sources and then finding the shortcircuit current between the marked terminals.
4. Draw the Norton equivalent circuit with the marked terminals
Ece207-c-2
Example: Find the Norton equivalent circuit of a and b terminals for the following network.
a
4
4
6
7V
2
8A
b
Step 2:
4
4
6
RN
2
RN =
( 6 / 2)( 4) 12
=
= 1.714Ω
( 6 / 2) + 4 7
Step 3: Using superposition for the 7V source
IN
4
4
4
6
7V
7V
2
I N' =
7
= 1.75 A
4
For 8A source
I
4
4
6
4
2
8A
2
8A
Ece207-c-3
I N" =
2(8)
= 2.667 A
2+4
I N = I "N − I N' = 2.667 − 1.75 = 0.917
IN
RN
Maximum Power Transfer
RTh
VTh
RL
For maximum Power transfer RTh should be equal to RL
RTh = RL
The maximum power transfer is
p=
2
VTH
4 RL
Superposition:
•
•
•
Activate one source at a time to calculate the voltage and currents of the circuits
( replacing ideal current sources with an open circuit to deactivate, replacing voltage
sources with a short circuit to deactivate)
Sum the resulting voltage and currents to determine the voltage and current that exits
when all independent sources are active.
Depending sources are always active when applying superposition
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