ECE201Lect-14
Transcript of ECE201Lect-14
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ECE201 Lect-14 1
Norton's Theorem (5.3, 8.8)
Dr. Holbert
March 20, 2006
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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 requiresessentially the same process as finding a
Thevenin equivalent circuit.
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ECE201 Lect-14 3
Independent Sources
Circuit with one ormore independent
sources
RTh
Norton equivalentcircuit
I sc
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ECE201 Lect-14 4
No Independent Sources
Circuit withoutindependent sources
RTh
Norton equivalentcircuit
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ECE201 Lect-14 5
Finding the Norton Equivalent
• Circuits with independent sources:
– Find V oc
and I sc
– Compute RTh
• Circuits without independent sources:
– Apply a test voltage (current) source – Find resulting current (voltage)
– Compute RTh
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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 foilgrid on a thin backing.
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ECE201 Lect-14 7
A Strain Gauge
• The strain gauge’s resistance varies as a
function of the strain:
D R =
GF e R
• e is the strain, R is the nominal resistance,
GF is the Gauge Factor
Backing
Foil
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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
D R = 2•10-3•120W = 0.24W
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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 D R.
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ECE201 Lect-14 10
The Bridge Circuit
R+D R
V ex
R
R
R
+ – V out
+ –
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ECE201 Lect-14 11
Norton Equivalent for Any e
e
e
64
2
R
V I ex sc
e
e
21
64
4
R RTh
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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
) bothV OC =0 and
I SC =0 [so skip step 2]
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ECE201 Lect-14 13
Thevenin/Norton Analysis
3. Compute the Thevenin equivalent resistance, RTh
(or
impedance, ZTh
).
(a) If there are only independent sources, then short
circuit all the voltage sources and open circuit the currentsources (just like superposition).
(b) If there are only dependent sources, then must use a
test voltage or current source in order to calculate
RTh (or ZTh) = V Test / I test (c) If there are both independent and dependent sources,
then compute RTh (or Z
Th) from V OC / I SC .
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ECE201 Lect-14 14
Thevenin/Norton Analysis
4. Thevenin: Replace circuit with V OC
in series with RTh
, ZTh
.
Norton: Replace circuit with I SC
in parallel with RTh
, ZTh
.
Note: for 3(b) the equivalent network is merely RTh (or ZTh),that is, no voltage (or current) source.
Only steps 2 & 4 differ from Thevenin & Norton!
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ECE201 Lect-14 15
Class Examples
• Learning Extension E5.4
• Learning Extension E8.15(c)