Schedule… Date Day Class Title Chapters HW Lab Exam No. Due date Due date 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 NO LAB 4.2 – 4.4 8 Oct Wed 11 Dynamic Circuits Discussion #9 – Equivalent Circuits ECEN 301 1
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. Discussion #9 – Equivalent Circuits ECEN 301 2
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 Discussion #9 – Equivalent Circuits ECEN 301 3
Lecture 9 – Equivalent Circuits Thévenin Equivalent Norton Equivalent Discussion #9 – Equivalent Circuits ECEN 301 4
Network Analysis Network Analysis Methods: Node voltage method Mesh current method Superposition Equivalent circuits Source transformation Thévenin equivalent Norton equivalent Discussion #9 – Equivalent Circuits ECEN 301 5
Equivalent Circuits It is always possible to view a complicated circuit in terms of a much simpler equivalent source and equivalent load circuit. i i R 2 R 4 + + + v a v R 5 Load Source v R 1 R 3 – – – Discussion #9 – Equivalent Circuits ECEN 301 6
Equivalent Circuits It is always possible to view a complicated circuit in terms of a much simpler equivalent source and equivalent load circuit. i i R 4 R 2 + + + v a v R 5 Load Source v R 1 R 3 – – – Discussion #9 – Equivalent Circuits ECEN 301 7
Equivalent Circuits Equivalent circuits fall into one of two classes: Thévenin : voltage source v T and series resistor R T Norton : current source i N and parallel resistor R N i i R T + + + v T i N Load v Load R N v – – – Thévenin Equivalent Norton Equivalent NB : R T = R N Discussion #9 – Equivalent Circuits ECEN 301 8
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 v T in series with an equivalent resistance R T i R T A fancy way of saying: + “The circuit that + v T Load v – includes everything except for the load” – “View from load” Discussion #9 – Equivalent Circuits ECEN 301 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 i N in parallel with an equivalent resistance R N i + A fancy way of saying: “The circuit that i N Load R N v includes everything except for the load” – “View from load” Discussion #9 – Equivalent Circuits ECEN 301 10
Thévenin and Norton Resistances Computation of Thévenin and Norton Resistances : 1. Remove the load (open circuit at load terminal) 2. Zero all independent sources Voltage sources short circuit ( v = 0) Current sources open circuit ( i = 0) 3. Compute equivalent resistance (with load removed) Discussion #9 – Equivalent Circuits ECEN 301 11
Thévenin and Norton Resistances Example1 : find the equivalent resistance as seen by the load R L i s =0.5A, v s = 10V, R 1 = 4 Ω , R 2 = 6 Ω , R 3 = 10 Ω , R 4 = 2 Ω , R 5 = 2 Ω , R 6 = 3 Ω , R 7 = 5 Ω R 4 R 2 R 7 R 5 + v s – i s R 6 R L R 1 R 3 Discussion #9 – Equivalent Circuits ECEN 301 12
Thévenin and Norton Resistances Example1 : find the equivalent resistance as seen by the load R L i s =0.5A, v s = 10V, R 1 = 4 Ω , R 2 = 6 Ω , R 3 = 10 Ω , R 4 = 2 Ω , R 5 = 2 Ω , R 6 = 3 Ω , R 7 = 5 Ω 1. Remove the load R 4 R 2 R 7 R 5 + v s – i s R 6 R 1 R 3 Discussion #9 – Equivalent Circuits ECEN 301 13
Thévenin and Norton Resistances Example1 : find the equivalent resistance as seen by the load R L i s =0.5A, v s = 10V, R 1 = 4 Ω , R 2 = 6 Ω , R 3 = 10 Ω , R 4 = 2 Ω , R 5 = 2 Ω , R 6 = 3 Ω , R 7 = 5 Ω 2. Zero all independent sources R 4 • R 2 short circuit voltage sources R 7 • Open circuit current sources R 5 R 6 R 1 R 3 Discussion #9 – Equivalent Circuits ECEN 301 14
Thévenin and Norton Resistances Example1 : find the equivalent resistance as seen by the load R L i s =0.5A, v s = 10V, R 1 = 4 Ω , R 2 = 6 Ω , R 3 = 10 Ω , R 4 = 2 Ω , R 5 = 2 Ω , R 6 = 3 Ω , R 7 = 5 Ω 3. Compute equivalent resistance R 4 R 2 R 7 R 5 R R R EQ R R 4 5 R EQ 1 1 2 2 R R 4 6 4 5 R 6 R 1 ( 2 )( 2 ) 10 R 3 ( 2 ) ( 2 ) 4 4 1 Discussion #9 – Equivalent Circuits ECEN 301 15
Thévenin and Norton Resistances Example1 : find the equivalent resistance as seen by the load R L i s =0.5A, v s = 10V, R 1 = 4 Ω , R 2 = 6 Ω , R 3 = 10 Ω , R 4 = 2 Ω , R 5 = 2 Ω , R 6 = 3 Ω , R 7 = 5 Ω 3. Compute equivalent resistance R 7 R R R EQ2 1 3 EQ R 3 EQ R R 1 3 EQ R 6 ( 10 )( 10 ) R EQ1 R 3 ( 10 ) ( 10 ) 100 20 10 R 1 EQ 5 1 R 2 EQ Discussion #9 – Equivalent Circuits ECEN 301 16
Thévenin and Norton Resistances Example1 : find the equivalent resistance as seen by the load R L i s =0.5A, v s = 10V, R 1 = 4 Ω , R 2 = 6 Ω , R 3 = 10 Ω , R 4 = 2 Ω , R 5 = 2 Ω , R 6 = 3 Ω , R 7 = 5 Ω 3. Compute equivalent resistance R 7 R EQ2 R R R 4 3 2 EQ EQ EQ R 6 5 1 R EQ3 6 1 R 2 EQ 5 R 3 EQ Discussion #9 – Equivalent Circuits ECEN 301 17
Thévenin and Norton Resistances Example1 : find the equivalent resistance as seen by the load R L i s =0.5A, v s = 10V, R 1 = 4 Ω , R 2 = 6 Ω , R 3 = 10 Ω , R 4 = 2 Ω , R 5 = 2 Ω , R 6 = 3 Ω , R 7 = 5 Ω 3. Compute equivalent resistance R 7 R R 4 6 EQ R 5 EQ R R EQ 4 6 R EQ4 R 6 ( 6 )( 3 ) ( 6 ) ( 3 ) 18 9 2 6 R 4 EQ Discussion #9 – Equivalent Circuits ECEN 301 18
Thévenin and Norton Resistances Example1 : find the equivalent resistance as seen by the load R L i s =0.5A, v s = 10V, R 1 = 4 Ω , R 2 = 6 Ω , R 3 = 10 Ω , R 4 = 2 Ω , R 5 = 2 Ω , R 6 = 3 Ω , R 7 = 5 Ω 3. Compute equivalent resistance R 7 R R R 5 7 EQ EQ R EQ5 2 5 7 2 R 5 EQ Discussion #9 – Equivalent Circuits ECEN 301 19
Thévenin and Norton Resistances Example1 : find the equivalent resistance as seen by the load R L i s =0.5A, v s = 10V, R 1 = 4 Ω , R 2 = 6 Ω , R 3 = 10 Ω , R 4 = 2 Ω , R 5 = 2 Ω , R 6 = 3 Ω , R 7 = 5 Ω 3. Compute equivalent resistance 7 R R EQ EQ Discussion #9 – Equivalent Circuits ECEN 301 20
Thévenin Voltage Thévenin equivalent voltage : equal to the open-circuit voltage ( v oc ) present at the load terminals (load removed) i R T R T + + i = 0 + + v T v T Load v v oc = v T – – – – Remove load Discussion #9 – Equivalent Circuits ECEN 301 21
Thévenin Voltage Computing Thévenin voltage : 1. Remove the load (open circuit at load terminals) 2. Define the open-circuit voltage ( v oc ) across the load terminals 3. Chose a network analysis method to find v oc node, mesh, superposition, etc. 4. Thévenin voltage v T = v oc Discussion #9 – Equivalent Circuits ECEN 301 22
Thévenin Voltage Example2 : find the Thévenin voltage v s = 10V, R 1 = 4 Ω , R 2 = 6 Ω , R 3 = 10 Ω R 1 R 3 i L + v s R L – R 2 Discussion #9 – Equivalent Circuits ECEN 301 23
Thévenin Voltage Example2 : find the Thévenin voltage v s = 10V, R 1 = 4 Ω , R 2 = 6 Ω , R 3 = 10 Ω 1. Remove the load +R 1 – + R 3 – 2. Define v oc + + + v s v oc – R 2 – – Discussion #9 – Equivalent Circuits ECEN 301 24
Thévenin Voltage Example2 : find the Thévenin voltage v s = 10V, R 1 = 4 Ω , R 2 = 6 Ω , R 3 = 10 Ω i 3 = 0 3. Choose a network analysis method +R 1 – + R 3 – • Voltage divider + + + v s v oc – R 2 – i – R 2 v v oc s R R 1 2 Discussion #9 – Equivalent Circuits ECEN 301 25
Thévenin Voltage Example2 : find the Thévenin voltage v s = 10V, R 1 = 4 Ω , R 2 = 6 Ω , R 3 = 10 Ω i 3 = 0 4. v T = v oc +R 1 – + R 3 – + + + v s v oc – R 2 R – 2 i v v – T s R R 1 2 Discussion #9 – Equivalent Circuits ECEN 301 26
Thévenin Equivalent Circuit Computing Thévenin Equivalent Circuit : 1. Compute the Thévenin resistance R T 2. Compute the Thévenin voltage v T i R T + + v T Load v – – Discussion #9 – Equivalent Circuits ECEN 301 27
Thévenin Equivalent Circuit Example3 : find i L by finding the Thévenin equivalent circuit v s = 10V, R 1 = 4 Ω , R 2 = 6 Ω , R 3 = 10 Ω , R L = 10 Ω R 1 R 3 i L + v s R L – R 2 Discussion #9 – Equivalent Circuits ECEN 301 28
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