Thévenin's Theorem (5.3, 8.8)
Dr. Holbert
March 8, 2006
ECE201 Lect-13
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Thevenin’s Theorem
• Any circuit with sources (dependent and/or
independent) and resistors can be replaced
by an equivalent circuit containing a single
voltage source and a single resistor.
• Thevenin’s theorem implies that we can
replace arbitrarily complicated networks
with simple networks for purposes of
analysis.
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Implications
• We use Thevenin’s theorem to justify the
concept of input and output resistance for
amplifier circuits.
• We model transducers as equivalent sources
and resistances.
• We model stereo speakers as an equivalent
resistance.
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Independent Sources (Thevenin)
RTh
Voc
Circuit with
independent sources
+
–
Thevenin equivalent
circuit
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No Independent Sources
RTh
Circuit without
independent sources
Thevenin equivalent
circuit
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Example: CE Amplifier
+10V
Vin
+
–
1kW
+
2kW
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Vo
–
6
Small Signal Equivalent
Ib
Vin
+
–
1kW
50W
100Ib
2kW
+
Vo
–
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Thevenin Equivalent @ Output
Ib
Vin
+
–
1kW
2kW
50W
100Ib
+
Vo
RTh
+
Voc
+
–
Vo
–
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Computing Thevenin Equivalent
• Basic steps to determining Thevenin
equivalent are
– Find voc
– Find RTh (= voc / isc)
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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, VOC.
Norton: Compute the short circuit current, ISC.
For case 3(b) both VOC=0 and ISC=0 [so skip step 2]
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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 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
RTh (or ZTh) = VTest/Itest
(c) If there are both independent and dependent sources,
then compute RTh (or ZTh) from VOC/ISC.
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Thevenin/Norton Analysis
4. Thevenin: Replace circuit with VOC in series with RTh, ZTh.
Norton: Replace circuit with ISC 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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Class Examples
• Learning Extension E5.3
• Learning Extension E5.5
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Thevenin AC Steady State
• Thevenin’s theorem also applies to AC
steady state analysis.
• An arbitrary linear circuit can be replaced
by an equivalent source and impedance.
• The determination of source and impedance
values is essentially the same as for resistor
circuits.
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Independent Source(s)
ZTh
Voc
Circuit with one or
more independent
sources
+
–
Thevenin equivalent
circuit
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No Independent Sources
ZTh
Circuit without
independent sources
Thevenin equivalent
circuit
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Class Example
• Learning Extension E8.14(b)
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