ECE201 Lect-131 Thévenin's Theorem (5.3, 8.8) Dr. Holbert March 8, 2006

ECE201 Lect-132 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.

ECE201 Lect-133 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-134 Independent Sources (Thevenin) Circuit with independent sources R Th V oc Thevenin equivalent circuit +–+–

ECE201 Lect-135 No Independent Sources Circuit without independent sources R Th Thevenin equivalent circuit

ECE201 Lect-136 Example: CE Amplifier 1k  V in 2k  +10V + – VoVo +–+–

ECE201 Lect-137 Small Signal Equivalent 1k  V in 100I b + – VoVo 50  IbIb 2k  +–+–

ECE201 Lect-138 Thevenin Output 1k  V in 100I b + - VoVo 50  IbIb 2k  R Th V oc + – VoVo +–+– +–+–

ECE201 Lect-139 Computing Thevenin Equivalent Basic steps to determining Thevenin equivalent are –Find v oc –Find R Th (= v oc / i sc )

ECE201 Lect-1310 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]

ECE201 Lect-1311 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.

ECE201 Lect-1312 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!

ECE201 Lect-1313 Class Examples Learning Extension E5.3 Learning Extension E5.5

ECE201 Lect-1314 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.

ECE201 Lect-1315 Independent Source(s) Circuit with one or more independent sources V oc Thevenin equivalent circuit Z Th +–+–

ECE201 Lect-1316 No Independent Sources Circuit without independent sources Thevenin equivalent circuit Z Th

ECE201 Lect-1317 Class Example Learning Extension E8.14(b)