ece201 lect-131 thévenin's theorem (5.3, 8.8) dr. holbert march 8, 2006
TRANSCRIPT
ECE201 Lect-13 1
Thévenin's Theorem (5.3, 8.8)
Dr. Holbert
March 8, 2006
ECE201 Lect-13 2
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.
ECE201 Lect-13 4
Independent Sources (Thevenin)
Circuit with independent sources
RTh
Voc
Thevenin equivalent circuit
+–
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No Independent Sources
Circuit without independent sources
RTh
Thevenin equivalent circuit
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Example: CE Amplifier
1kVin
2k
+10V
+
–Vo
+–
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Small Signal Equivalent
1kVin 100Ib
+
–
Vo
50
Ib
2k+–
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Thevenin Equivalent @ Output
1kVin 100Ib
+
-
Vo
50
Ib
2k
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)
Circuit with one or more independent
sources
Voc
Thevenin equivalent circuit
ZTh
+–
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No Independent Sources
Circuit without independent sources
Thevenin equivalent circuit
ZTh
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Class Example
• Learning Extension E8.14(b)