Circuits Lecture 8: Thevenin and Norton Theorem (1) 李宏毅 Hung-yi Lee

Textbook Chapter 2.5

Network A two-terminal network is a function represented by i-v characteristics Given a network, computing its i-v characteristics, and then label it with simpler equivalent network v i

Computing i-v characteristics i v  Add a voltage source v  Find i v is a unknown variable Represented by v Obtain the relation of i and v  Add a current source i  Find v i is a unknown variable Represented by i Obtain the relation of i and v v i

Computing i-v characteristics i v Voltage source v Independent Sources x 1, x 2, x 3 …… i is the weighted sum of the voltage (or current) of the sources. The relation of i and v is linear! constant

Computing i-v characteristics The v-i characteristics is linear! v i Case 1: current source Case 2: voltage source Case 3: resistor i=mv Resistor with resistance 1/m Ω m>0, normal resistor m<0, ? Negative resistor

Computing i-v characteristics v i Case 4: resistor +voltage source

Computing i-v characteristics The v-i characteristics is linear! v i Case 1: current source Case 2: voltage source Case 3: resistor Case 4: resistor +voltage source

Thevenin Theorem Two Terminal Network  Two terminal network consists entirely of independent source, resistor and controlled sources.  If controlled sources are present, then the control variables is within the same network. Find v oc and R t directly without drawing i-v characteristics?

Thevenin Theorem - v oc Two Terminal Network Keep two terminals open

Thevenin Theorem - R t (As we have done in Superposition) Textbook P Voltage Source Suppress the independent sources: Current Source Short Open Why?????

Thevenin Theorem - R t (Example) Refer to lecture 7 Suppress the independent sources

Thevenin Theorem - R t Superposition: v Independent Sources in network: x 1, x 2, x 3 …… i Voltage source v

Norton Theorem Two Terminal Network Thevenin Theorem Norton Theorem

Norton Theorem - i sc Two Terminal Network Let two terminals short If we already know v oc, R t =v oc /i sc After we find i sc, If we already know R t, v oc =i sc R t

Thevenin Parameters V oc, R t and i sc are Thevenin parameters v oc : keep the two terminals open R t : suppress the independent sources i sc : let the two terminals short Know any of two can find the last one

Example 2.14

Open circuit Short Circuit Set to Zero Find v oc Find i sc Find R t

Example 2.14 Short Circuit Then “open circuit” or “source set to zero”?

Example 2.14 Source set to zero Find equivalent resistance R t

Example 2.14

Check: Open circuit

Example Find the current and voltage on R L Three-terminal networks? Thevenin Theorem Circuit Analysis Obliterate R L

Example Find the current and voltage on R L Find Thevenin Parameters + - i

Example Find the current and voltage on R L Open circuit Short CircuitSet to Zero Find v oc Find i sc Find R t

Example Find the current and voltage on R L Open circuit Find v oc So easy!

Example Find the current and voltage on R L Short Circuit Find i sc R 1, R 2, R 3, R 4 : (last page)

Example Find the current and voltage on R L Set to Zero Find R t Simple (but hard to figure out) Check by yourself

Example Find the current and voltage on R L + - i

Homework 2.62, 2.64

Homework

Thank you!

Answer 2.62 Rt=5k, isc=vs/8k, voc=5vs/ Rt=-60, isc=is, voc=-60is

Homework Rt=100k,isc=-20m

Homework Rt=-1k/60, voc=2

Acknowledgement 感謝 徐瑞陽 (b02) 糾正錯誤的作業答案 感謝 林楷恩 (b02) 糾正錯誤的作業答案