Nortans Theorem

1. ECE201 Lect-14 1
Norton's Theorem (5.3, 8.8)
Dr. Holbert
March 20, 2006

2. ECE201 Lect-14 2
Introduction
•Any Thevenin equivalent circuit is in turn
equivalent to a current source in parallel
with a resistor [source transformation].
•A current source in parallel with a resistor is
called a Norton equivalent circuit.
•Finding a Norton equivalent circuit requires
essentially the same process as finding a
Thevenin equivalent circuit.

3. ECE201 Lect-14 3
Independent Sources
Circuit with one or
more independent
sources
R
Th
Norton equivalent
circuit
I
sc

4. ECE201 Lect-14 4
No Independent Sources
Circuit without
independent sources
R
Th
Norton equivalent
circuit

5. ECE201 Lect-14 5
Finding the Norton Equivalent
•Circuits with independent sources:
–Find V
oc
and I
sc
–Compute R
Th
•Circuits without independent sources:
–Apply a test voltage (current) source
–Find resulting current (voltage)
–Compute R
Th

6. ECE201 Lect-14 6
Example: Strain Gauge
•Strain is the amount of deformation of a
body due to an applied force-it is defined as
the fractional change in length.
•Strain can be positive (tensile) or negative
(compressive).
•One type of strain gauge is made of a foil
grid on a thin backing.

7. ECE201 Lect-14 7
A Strain Gauge
•The strain gauge’s resistance varies as a
function of the strain:
DR = GF e R
• e is the strain, R is the nominal resistance,
GF is the Gauge Factor
Backing
Foil

8. ECE201 Lect-14 8
Typical values
•Measured strain values are typically fairly
small-usually less than 10
-3
.
•GF is usually close to 2.
•Typical values for R are 120W, 350W, and
1000W.
•A typical change in resistance is
DR = 2•10
-3
•120W = 0.24W

9. ECE201 Lect-14 9
Measuring Small Changes in R
•To measure such small changes in
resistance, the strain gauge is placed in a
Wheatstone bridge circuit.
•The bridge circuit uses an excitation voltage
source and produces a voltage that depends
on DR.

10. ECE201 Lect-14 10
The Bridge Circuit
R+DR
V
ex
R
R
R
+–
V
out
+
–

11. ECE201 Lect-14 11
Norton Equivalent for Any e
e
e
64
2
+
=
R
V
I
ex
sc
e
e
21
64
4+
+
=
R
R
Th

12. ECE201 Lect-14 12
Thevenin/Norton Analysis
1. Pick a good breaking point in the circuit (cannot split a
dependent source and its control variable).
2. Thevenin: Compute the open circuit voltage, V
OC
.
Norton: Compute the short circuit current, I
SC
.
For case 3(b) both V
OC=0 and I
SC=0 [so skip step 2]

13. ECE201 Lect-14 13
Thevenin/Norton Analysis
3. Compute the Thevenin equivalent resistance, R
Th
(or
impedance, Z
Th).
(a) If there are only independent sources, then short
circuit all the voltage sources and open circuit the current
sources (just like superposition).
(b) If there are only dependent sources, then must use a
test voltage or current source in order to calculate
R
Th
(or Z
Th
) = V
Test
/I
test
(c) If there are both independent and dependent sources,
then compute R
Th
(or Z
Th
) from V
OC
/I
SC
.

14. ECE201 Lect-14 14
Thevenin/Norton Analysis
4. Thevenin: Replace circuit with V
OC
in series with R
Th
, Z
Th
.
Norton: Replace circuit with I
SC
in parallel with R
Th
, Z
Th
.
Note: for 3(b) the equivalent network is merely R
Th
(or Z
Th
),
that is, no voltage (or current) source.
Only steps 2 & 4 differ from Thevenin & Norton!