1/19/16 Two sources behave the same with respect to RLoad if I S =
Thevenin equivalent
RLoad = 0
VS
RS
Norton equivalent
RS is called
“output impedance”
should be low in
systems that use
voltage as the signal
Output Current vs. Voltage
i
IS
1
slope =
short circuit
RS
RLoad = ∞
v
open circuit
VS
48
Thevenin Equivalent - Example
What is current through R3 ?
.
•  Find VTHEV of “branch” (2-node component)
–  Compute voltage between A and B without R3
“open circuit”
VTHEV = VS
4K
= 8V
1K+4K
49
© Ste*en 2012 1/19/16 (continued….)
•  Now, to find INORT
–  Short the output, compute current through “short
circuit”
INORT =
10V
= 10mA
1KΩ
•  Use VTHEV to find RTHEV given INORT.
RTHEV =
8V
= 800Ω
10mA
50
(continued….)
•  Use VTHEV to find I through R3 .
I=
8V
≅ 3mA
2K+800Ω
•  Use INORT to find I through R3.
Use the current
divider equation
I = I NORT
RNORT
≅ 3mA
R3 +RNORT
51
© Ste*en 2012 1/19/16 Superposition Theorem
•  The current in a branch equals the sum of the currents
produced by each voltage source or current source, with
the other sources all set to 0.
•  The currents add independently (linearly)
•  Setting a voltage source to 0 V means a short circuit
(piece of wire).
•  Setting a current source to 0 A means an open circuit
(removed).
52
Superposition Theorem - Example
Solve for I1 as the sum of
two currents, I11 and I12
Setting IB to zero (open circuit)
I11 =
VA
R1 + R2
Setting VA to zero (short circuit)
I12 = −
Add the two independent
currents together:
I B R2
R1 + R2
I1 = I11 + I12 =
Current divider,
current going
the other way.
VA − I B R2
R1 + R2
53
© Ste*en 2012 1/19/16 Superposition Theorem - Further Example
Solve for I2 as the sum of
two currents, I21 and I22
Setting IB to zero (open circuit)
I 21 =
VA
R1 + R2
Setting VA to zero (short circuit)
I 22 =
Add the two independent
currents together:
I B R1
R1 + R2
I 2 = I 21 + I 22 =
VA + I B R1
R1 + R2
54
Norton Equiv. by Superposition
Find Norton equivalent INORT from a to b,
and RNORT, using Superposition.
INORT is the current through a short circuit
from a to b.
55
© Ste*en 2012 1/19/16 Break INORT into 2 components:
I NORT = I1 + I 2
I1 from current source with voltage source at 0V (short circuit).
Ignore all resistors, since all current goes through short from a to b.
I1 = −8A
current going
the other way.
I2 from current source with current source at 0 A (open circuit).
Ignore 8Ωresistor since it is parallel to short from a to b.
I A = 60 (6 + (12 × 4) (12 + 4))
I 2 = I A (12 / (12 + 4)) = 5A
I NORT = I1 + I 2 = −8A+5A = 3A
56
To find RNORT :
•  Set all voltage and current sources to 0 and
find total resistance between a and b.
•  This is RNORT (which is the same as RTHEV)
simplify using parallel resistors
(6 ×12) / (6 +12) = 4
simplify further to two 8 ohm resistors in parallel, so
RNORT = RTHEV = 4Ω
57
© Ste*en 2012 1/19/16 Simplify and compute currents
through each resistor
58
Equivalent
simplified
circuits
59
© Ste*en 2012 1/19/16 With total of 2A, compute individual currents
1A
1A
1A
1A
1A
1/3A 2/3A
60
Mesh analysis yield simultaneous linear equations.
61
© Ste*en 2012 1/19/16 Example of a Mesh
62
© Ste*en 2012