Yet another method: Thévenin and Norton
Equivalent Circuits
Norton Equivalent Circuit
Calculation of RT and RN
• RT=RN, same calculation
• Setting all sources to be zero (“killing” the sources)
– Voltage source: short
– Current source: open
Calculation of RT and RN: Cont.
• Calculate equivalent resistance seen by the load.
Calculation of VT
Remove the load and calculate the open circuit voltage
Calculation of IN
short the load and calculate the short circuit voltage
(R1 + R2 )i1 − R2iSC = vS
− R2i1 + (R1 + R2 )iSC = 0
vS − v v
v
=
+
R1
R2 R3
iN = iSC
vS R2
=
R1R3 + R2 R3 + R1R2
Sourse transformation
VTh=INRN
RN=RTh
Summary
Thévenin's Theorem
• Any two-terminal linear circuit can be replaced with a voltage source in
series with a resistance which will produce the same effects at the
terminals.
• VTh is the open-circuit voltage Voc between the two terminals of the circuit that
the Thevenin generator is replacing.
• RTh is the ratio of Voc to the short-circuit current Isc.
In linear circuits, this is equivalent to "killing" the sources and evaluating the
resistance between the terminals. Voltage sources are killed by shorting them;
current sources are killed by opening them.
Detailed Example:
Examples
Let's determine the current flowing through the 6k resistor using the Thévenin
approach. Determining the Thévenin generator that represents the circuit will
facilitate our consideration of different values of resistance in place of the 6k.
-
+
+
-
9 + 9 = I (5 + 12)
I = 18 / 17 = 1.06mA
VOC = 9 − 1.06 × 5 = 3.71V
Double check
RTH=3.53 kΩ
VOC = 12 × 1.06 − 9 = 3.71V
Concept Check
Which of the following circuits is the correct Thévenin generator?
B
A
Answer: B
C
Summary: Norton Therorem
•
•
•
•
Any two-terminal linear circuit can be replaced with a current source in
parallel with a resistance which will produce the same effects at the
terminals.
IN is the short-circuit current Isc of the circuit that the Norton generator is
replacing.
Again, RN is the ratio of Voc to the short-circuit current Isc. Or calculating the
equivalent resistance after “killing” the sources
Note that for a given circuit, RN = RTh.
Example: Norton
Alternatively: ISC=VTH/RTH=3.71/3.53=1.05 mA
17 I1 − 12 I SC = 18
− 12 I1 + 12 I SC = 9
I SC = 1.05mA
Concept Check
Which of the following circuits is the correct Norton generator?
B
C
A
Answer: A
Maximum Power Transfer: Impedance Matching
• Why Thévenin and Norton equivalents? Very easy to
calculate load related quantity. One such an example is
the maximum power transfer to the load.
Rl=RT
Impedance is a
generalized term
of resistance
when capacitors
and inductors
are included.