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Discussion #9 – Equivalent Circuits

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1 Discussion #9 – Equivalent Circuits
Schedule… Date Day Class No. Title Chapters HW Due date Lab Exam 1 Oct Wed 9 Equivalent Circuits 3.6 2 Oct Thu 3 Oct Fri Recitation  HW 4 4 Oct Sat 5 Oct Sun 6 Oct Mon 10 Energy Storage 3.7, 4.1 NO LAB 7 Oct Tue 8 Oct 11 Dynamic Circuits 4.2 – 4.4 ECEN 301 Discussion #9 – Equivalent Circuits

2 Equivalence - Equality
Mosiah 29: 38 38 Therefore they relinquished their desires for a king, and became exceedingly anxious that every man should have an equal chance throughout all the land; yea, and every man expressed a willingness to answer for his own sins. ECEN 301 Discussion #9 – Equivalent Circuits

3 Discussion #9 – Equivalent Circuits
Current Sources All current sources can be modeled as voltage sources (and vice-versa) Many sources are best modeled as voltage sources (batteries, electric outlets etc.) There are some things that are best modeled as current sources: Van de Graaff generator Behaves as a current source because of its very high output voltage coupled with its very high output resistance and so it supplies the same few microamps at any output voltage up to hundreds of thousands of volts ECEN 301 Discussion #9 – Equivalent Circuits

4 Lecture 9 – Equivalent Circuits
Thévenin Equivalent Norton Equivalent ECEN 301 Discussion #9 – Equivalent Circuits

5 Discussion #9 – Equivalent Circuits
Network Analysis Network Analysis Methods: Node voltage method Mesh current method Superposition Equivalent circuits Source transformation Thévenin equivalent Norton equivalent ECEN 301 Discussion #9 – Equivalent Circuits

6 Discussion #9 – Equivalent Circuits
It is always possible to view a complicated circuit in terms of a much simpler equivalent source and equivalent load circuit. va R1 R3 + – R2 R5 R4 i v Load + v – i Source ECEN 301 Discussion #9 – Equivalent Circuits

7 Discussion #9 – Equivalent Circuits
It is always possible to view a complicated circuit in terms of a much simpler equivalent source and equivalent load circuit. i Load + v – i Source R2 R4 + v – va R5 + – R1 R3 ECEN 301 Discussion #9 – Equivalent Circuits

8 Discussion #9 – Equivalent Circuits
Equivalent circuits fall into one of two classes: Thévenin: voltage source vT and series resistor RT Norton: current source iN and parallel resistor RN vT + – RT Load v i iN RN Load + v – i Thévenin Equivalent Norton Equivalent NB: RT = RN ECEN 301 Discussion #9 – Equivalent Circuits

9 Discussion #9 – Equivalent Circuits
Thévenin Theorem: when viewed from the load, any network comprised of independent sources and linear elements (resistors), may be represented by an equivalent circuit. Equivalent circuit consists of an ideal voltage source vT in series with an equivalent resistance RT vT + – RT Load v i A fancy way of saying: “The circuit that includes everything except for the load” “View from load” ECEN 301 Discussion #9 – Equivalent Circuits

10 Discussion #9 – Equivalent Circuits
Norton Theorem: when viewed from the load, any network comprised of independent sources and linear elements (resistors), may be represented by an equivalent circuit. Equivalent circuit consists of an ideal current source iN in parallel with an equivalent resistance RN iN RN Load + v – i A fancy way of saying: “The circuit that includes everything except for the load” “View from load” ECEN 301 Discussion #9 – Equivalent Circuits

11 Thévenin and Norton Resistances
Computation of Thévenin and Norton Resistances: Remove the load (open circuit at load terminal) Zero all independent sources Voltage sources short circuit (v = 0) Current sources open circuit (i = 0) Compute equivalent resistance (with load removed) ECEN 301 Discussion #9 – Equivalent Circuits

12 Thévenin and Norton Resistances
Example1: find the equivalent resistance as seen by the load RL is =0.5A, vs = 10V, R1 = 4Ω, R2 = 6Ω , R3 = 10Ω , R4 = 2Ω , R5 = 2Ω , R6 = 3Ω, R7 = 5Ω R4 R2 R7 vs + – R5 is R6 RL R1 R3 ECEN 301 Discussion #9 – Equivalent Circuits

13 Thévenin and Norton Resistances
Example1: find the equivalent resistance as seen by the load RL is =0.5A, vs = 10V, R1 = 4Ω, R2 = 6Ω , R3 = 10Ω , R4 = 2Ω , R5 = 2Ω , R6 = 3Ω, R7 = 5Ω R4 Remove the load R2 R7 vs + – R5 is R6 R1 R3 ECEN 301 Discussion #9 – Equivalent Circuits

14 Thévenin and Norton Resistances
Example1: find the equivalent resistance as seen by the load RL is =0.5A, vs = 10V, R1 = 4Ω, R2 = 6Ω , R3 = 10Ω , R4 = 2Ω , R5 = 2Ω , R6 = 3Ω, R7 = 5Ω R4 Zero all independent sources short circuit voltage sources Open circuit current sources R2 R7 R5 R6 R1 R3 ECEN 301 Discussion #9 – Equivalent Circuits

15 Thévenin and Norton Resistances
Example1: find the equivalent resistance as seen by the load RL is =0.5A, vs = 10V, R1 = 4Ω, R2 = 6Ω , R3 = 10Ω , R4 = 2Ω , R5 = 2Ω , R6 = 3Ω, R7 = 5Ω R4 Compute equivalent resistance R2 R7 R5 R6 R1 R3 ECEN 301 Discussion #9 – Equivalent Circuits

16 Thévenin and Norton Resistances
Example1: find the equivalent resistance as seen by the load RL is =0.5A, vs = 10V, R1 = 4Ω, R2 = 6Ω , R3 = 10Ω , R4 = 2Ω , R5 = 2Ω , R6 = 3Ω, R7 = 5Ω Compute equivalent resistance R7 REQ2 R6 REQ1 R3 ECEN 301 Discussion #9 – Equivalent Circuits

17 Thévenin and Norton Resistances
Example1: find the equivalent resistance as seen by the load RL is =0.5A, vs = 10V, R1 = 4Ω, R2 = 6Ω , R3 = 10Ω , R4 = 2Ω , R5 = 2Ω , R6 = 3Ω, R7 = 5Ω Compute equivalent resistance R7 REQ2 R6 REQ3 ECEN 301 Discussion #9 – Equivalent Circuits

18 Thévenin and Norton Resistances
Example1: find the equivalent resistance as seen by the load RL is =0.5A, vs = 10V, R1 = 4Ω, R2 = 6Ω , R3 = 10Ω , R4 = 2Ω , R5 = 2Ω , R6 = 3Ω, R7 = 5Ω Compute equivalent resistance R7 REQ4 R6 ECEN 301 Discussion #9 – Equivalent Circuits

19 Thévenin and Norton Resistances
Example1: find the equivalent resistance as seen by the load RL is =0.5A, vs = 10V, R1 = 4Ω, R2 = 6Ω , R3 = 10Ω , R4 = 2Ω , R5 = 2Ω , R6 = 3Ω, R7 = 5Ω R7 Compute equivalent resistance REQ5 ECEN 301 Discussion #9 – Equivalent Circuits

20 Thévenin and Norton Resistances
Example1: find the equivalent resistance as seen by the load RL is =0.5A, vs = 10V, R1 = 4Ω, R2 = 6Ω , R3 = 10Ω , R4 = 2Ω , R5 = 2Ω , R6 = 3Ω, R7 = 5Ω Compute equivalent resistance REQ ECEN 301 Discussion #9 – Equivalent Circuits

21 Discussion #9 – Equivalent Circuits
Thévenin Voltage Thévenin equivalent voltage: equal to the open-circuit voltage (voc) present at the load terminals (load removed) RT i RT Load + + v – i = 0 vT + – vT + – voc = vT – Remove load ECEN 301 Discussion #9 – Equivalent Circuits

22 Discussion #9 – Equivalent Circuits
Thévenin Voltage Computing Thévenin voltage: Remove the load (open circuit at load terminals) Define the open-circuit voltage (voc) across the load terminals Chose a network analysis method to find voc node, mesh, superposition, etc. Thévenin voltage vT = voc ECEN 301 Discussion #9 – Equivalent Circuits

23 Discussion #9 – Equivalent Circuits
Thévenin Voltage Example2: find the Thévenin voltage vs = 10V, R1 = 4Ω, R2 = 6Ω , R3 = 10Ω R2 R1 RL R3 vs + – iL ECEN 301 Discussion #9 – Equivalent Circuits

24 Discussion #9 – Equivalent Circuits
Thévenin Voltage Example2: find the Thévenin voltage vs = 10V, R1 = 4Ω, R2 = 6Ω , R3 = 10Ω Remove the load Define voc +R1– + R3 – + voc – vs + – + R2 – ECEN 301 Discussion #9 – Equivalent Circuits

25 Discussion #9 – Equivalent Circuits
Thévenin Voltage Example2: find the Thévenin voltage vs = 10V, R1 = 4Ω, R2 = 6Ω , R3 = 10Ω i3 = 0 Choose a network analysis method Voltage divider +R1– + R3 – + voc – vs + – + R2 – i ECEN 301 Discussion #9 – Equivalent Circuits

26 Discussion #9 – Equivalent Circuits
Thévenin Voltage Example2: find the Thévenin voltage vs = 10V, R1 = 4Ω, R2 = 6Ω , R3 = 10Ω i3 = 0 vT = voc +R1– + R3 – + voc – vs + – + R2 – i ECEN 301 Discussion #9 – Equivalent Circuits

27 Thévenin Equivalent Circuit
Computing Thévenin Equivalent Circuit: Compute the Thévenin resistance RT Compute the Thévenin voltage vT vT + – RT Load v i ECEN 301 Discussion #9 – Equivalent Circuits

28 Thévenin Equivalent Circuit
Example3: find iL by finding the Thévenin equivalent circuit vs = 10V, R1 = 4Ω, R2 = 6Ω, R3 = 10Ω, RL = 10Ω R1 R3 iL vs + – RL R2 ECEN 301 Discussion #9 – Equivalent Circuits

29 Thévenin Equivalent Circuit
Example3: find iL by finding the Thévenin equivalent circuit vs = 10V, R1 = 4Ω, R2 = 6Ω, R3 = 10Ω, RL = 10Ω Compute RT Remove RL +R1– + R3 – vs + – + R2 – ECEN 301 Discussion #9 – Equivalent Circuits

30 Thévenin Equivalent Circuit
Example3: find iL by finding the Thévenin equivalent circuit vs = 10V, R1 = 4Ω, R2 = 6Ω, R3 = 10Ω, RL = 10Ω Compute RT Remove RL Zero sources +R1– + R3 – + R2 – ECEN 301 Discussion #9 – Equivalent Circuits

31 Thévenin Equivalent Circuit
Example3: find iL by finding the Thévenin equivalent circuit vs = 10V, R1 = 4Ω, R2 = 6Ω, R3 = 10Ω, RL = 10Ω Compute RT Remove RL Zero sources Compute RT = REQ REQ ECEN 301 Discussion #9 – Equivalent Circuits

32 Thévenin Equivalent Circuit
Example3: find iL by finding the Thévenin equivalent circuit vs = 10V, R1 = 4Ω, R2 = 6Ω, R3 = 10Ω, RL = 10Ω Compute RT Compute vT (previously computed) R2 R1 RL R3 vs + – iL ECEN 301 Discussion #9 – Equivalent Circuits

33 Thévenin Equivalent Circuit
Example3: find iL by finding the Thévenin equivalent circuit vs = 10V, R1 = 4Ω, R2 = 6Ω, R3 = 10Ω, RL = 10Ω R2 R1 RL R3 vs + – RT iL iL vT + – RL NB: iL is the same in both circuits ECEN 301 Discussion #9 – Equivalent Circuits

34 Thévenin Equivalent Circuit
Example3: find iL by finding the Thévenin equivalent circuit vs = 10V, R1 = 4Ω, R2 = 6Ω, R3 = 10Ω, RL = 10Ω RT iL vT + – RL ECEN 301 Discussion #9 – Equivalent Circuits

35 Discussion #9 – Equivalent Circuits
Norton Current Current equivalent current: equal to the short-circuit current (isc) present at the load terminals (load replaced with short circuit) iN RN Load + v – i iN = isc iN RN Short circuit load ECEN 301 Discussion #9 – Equivalent Circuits

36 Discussion #9 – Equivalent Circuits
Norton Current Computing Norton current: Replace the load with a short circuit Define the short-circuit current (isc) across the load terminals Chose a network analysis method to find isc node, mesh, superposition, etc. Norton current iN = isc ECEN 301 Discussion #9 – Equivalent Circuits

37 Discussion #9 – Equivalent Circuits
Norton Current Example4: find the Norton equivalent current iN vs = 6V, is = 2A, R1 = 6Ω, R2 = 3Ω, R3 = 2Ω, RL = 10Ω vs – + R3 is RL R1 R2 ECEN 301 Discussion #9 – Equivalent Circuits

38 Discussion #9 – Equivalent Circuits
Norton Current Example4: find the Norton equivalent current iN vs = 6V, is = 2A, R1 = 6Ω, R2 = 3Ω, R3 = 2Ω, RL = 10Ω vs Short-circuit the load Define isc – + R3 is R1 R2 isc ECEN 301 Discussion #9 – Equivalent Circuits

39 Discussion #9 – Equivalent Circuits
Norton Current Example4: find the Norton equivalent current iN vs = 6V, is = 2A, R1 = 6Ω, R2 = 3Ω, R3 = 2Ω, RL = 10Ω vs i3 Choose a network analysis method Node voltage Node a Node b – + + R3 – is iv va is independent vb is dependent (actually va and vb are dependent on each other but choose vb) vb = va + vs + R1 – + R2 – i1 isc i2 Node d ECEN 301 Discussion #9 – Equivalent Circuits

40 Discussion #9 – Equivalent Circuits
Norton Current Example4: find the Norton equivalent current iN vs = 6V, is = 2A, R1 = 6Ω, R2 = 3Ω, R3 = 2Ω, RL = 10Ω Choose a network analysis method Node voltage vs i3 Node a Node b – + + R3 – is iv + R1 – + R2 – i1 isc i2 Node d ECEN 301 Discussion #9 – Equivalent Circuits

41 Discussion #9 – Equivalent Circuits
Norton Current Example4: find the Norton equivalent current iN vs = 6V, is = 2A, R1 = 6Ω, R2 = 3Ω, R3 = 2Ω, RL = 10Ω Choose a network analysis method Node voltage vs i3 Node a Node b – + + R3 – is iv + R1 – + R2 – i1 isc i2 Node d ECEN 301 Discussion #9 – Equivalent Circuits

42 Discussion #9 – Equivalent Circuits
Norton Current Example4: find the Norton equivalent current iN vs = 6V, is = 2A, R1 = 6Ω, R2 = 3Ω, R3 = 2Ω, RL = 10Ω Choose a network analysis method Node voltage vs i3 Node a Node b – + + R3 – is iv + R1 – + R2 – i1 isc i2 Node d ECEN 301 Discussion #9 – Equivalent Circuits

43 Discussion #9 – Equivalent Circuits
Norton Current Example4: find the Norton equivalent current iN vs = 6V, is = 2A, R1 = 6Ω, R2 = 3Ω, R3 = 2Ω, RL = 10Ω Choose a network analysis method Node voltage vs i3 Node a Node b – + + R3 – is iv + R1 – + R2 – i1 isc i2 Node d ECEN 301 Discussion #9 – Equivalent Circuits

44 Discussion #9 – Equivalent Circuits
Norton Current Example4: find the Norton equivalent current iN vs = 6V, is = 2A, R1 = 6Ω, R2 = 3Ω, R3 = 2Ω, RL = 10Ω iN = isc vs i3 – + + R3 – is iv + R1 – + R2 – i1 isc i2 ECEN 301 Discussion #9 – Equivalent Circuits

45 Norton Equivalent Circuit
Computing Norton Equivalent Circuit: Compute the Norton resistance RN Compute the Norton current iN iN RN Load + v – i ECEN 301 Discussion #9 – Equivalent Circuits

46 Norton Equivalent Circuit
Example5: find the Norton equivalent circuit vs = 6V, is = 2A, R1 = 6Ω, R2 = 3Ω, R3 = 2Ω, RL = 10Ω vs – + R3 is RL R1 R2 ECEN 301 Discussion #9 – Equivalent Circuits

47 Norton Equivalent Circuit
Example5: find the Norton equivalent circuit vs = 6V, is = 2A, R1 = 6Ω, R2 = 3Ω, R3 = 2Ω, RL = 10Ω vs Compute RN Remove RL – + R3 is R1 R2 ECEN 301 Discussion #9 – Equivalent Circuits

48 Norton Equivalent Circuit
Example5: find the Norton equivalent circuit vs = 6V, is = 2A, R1 = 6Ω, R2 = 3Ω, R3 = 2Ω, RL = 10Ω Compute RN Remove RL Zero sources R3 R1 R2 ECEN 301 Discussion #9 – Equivalent Circuits

49 Norton Equivalent Circuit
Example5: find the Norton equivalent circuit vs = 6V, is = 2A, R1 = 6Ω, R2 = 3Ω, R3 = 2Ω, RL = 10Ω Compute RN Remove RL Zero sources Compute RN = REQ REQ ECEN 301 Discussion #9 – Equivalent Circuits

50 Norton Equivalent Circuit
Example5: find the Norton equivalent circuit vs = 6V, is = 2A, R1 = 6Ω, R2 = 3Ω, R3 = 2Ω, RL = 10Ω vs Compute RN Compute iN (previously computed) – + R3 is RL R1 R2 ECEN 301 Discussion #9 – Equivalent Circuits

51 Norton Equivalent Circuit
Example5: find the Norton equivalent circuit vs = 6V, is = 2A, R1 = 6Ω, R2 = 3Ω, R3 = 2Ω, RL = 10Ω vs – + R3 is RL R1 R2 RL iN RN ECEN 301 Discussion #9 – Equivalent Circuits

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