EE 42 100 Discussion sections Section Day Time Room GSI Dis 101 M 3 4pm 241 Cory Liu Vincent Dis 102 W 4 5pm 241 Cory Li Li Dis 103 F 9 10am 3108 Etcheverry Liu Vincent Dis F 10104 11am 71 Evans Liu Vincent 3107 Etcheverry Li Li 45 Evans Li Li Dis Dis 105 Th 4 5pm Th 12106 1pm EE 42 100 Spring 2006 Lecture 3a Prof White 1 Lecture Week 3a OUTLINE Superposition Analysis method for circuits with sources and linear elements Th venin and Norton equivalent circuits Maximum Power Transfer EE 42 100 Spring 2006 Lecture 3a Prof White 2 Superposition A linear circuit is constructed only of linear elements linear resistors linear dependent sources and independent sources We ll discuss dependent sources a bit later Principle of Superposition In any linear circuit containing multiple independent sources the current or voltage at any point in the network may be calculated as the algebraic sum of the individual contributions of each source acting alone Procedure 1 Determine contribution due to an independent source Set all other independent sources to 0 2 Repeat for each independent source 3 Sum individual contributions to obtain desired voltage or current EE 42 100 Spring 2006 Lecture 3a Prof White 3 Superposition Example Find Vo 24 V 2 4V 4A 4 Vo EE 42 100 Spring 2006 Lecture 3a Prof White 4 Equivalent Circuit Concept A network of voltage sources current sources and resistors can be replaced by an equivalent circuit which has identical terminal properties I V characteristics without affecting the operation of the rest of the circuit iA network A of sources and resistors iB vA network B of sources and resistors vB iA vA iB vB EE 42 100 Spring 2006 Lecture 3a Prof White 5 Source Combinations Voltage sources in series can be replaced by an equivalent voltage source v1 v2 v2 v1 Current sources in parallel can be replaced by an equivalent current source i1 EE 42 100 Spring 2006 i2 i1 i2 Lecture 3a Prof White 6 Th venin Equivalent Circuit Any linear 2 terminal 1 port network of independent voltage sources independent current sources and linear resistors can be replaced by an equivalent circuit consisting of an independent voltage source in series with a resistor without affecting the operation of the rest of the circuit Th venin equivalent circuit Actual circuit RTh a iL vL RL VTh network of sources and resistors a iL vL RL b b load resistor EE 42 100 Spring 2006 Lecture 3a Prof White 7 Why use such equivalent circuits They may be much easier to use than the actual circuits when doing circuit analysis Example We can reduce the entire telephone network or the entire power system that delivers energy to an AC outlet to a Thevenin equivalent containing just one voltage source Vth and one resistor Rth or one impedance Zth which we ll see a little later EE 42 100 Spring 2006 Lecture 3a Prof White 8 Calculating a Th venin Equivalent 1 Calculate the open circuit voltage voc a network of sources and resistors voc b 2 Calculate the short circuit current isc Note that isc is in the directionaof the open circuit V v Th oc network voltage drop across the terminals a b i of sources and resistors sc b EE 42 100 Spring 2006 Lecture 3a Prof White voc RTh isc 9 Th venin Equivalent Example Find the Thevenin equivalent with respect to the terminals a b EE 42 100 Spring 2006 Lecture 3a Prof White 10 Alternative Method of Calculating RTh For a network containing only independent sources network of and linear resistors independent sources and resistors with each source set to zero 1 Set all independent sources to zero voltage source short circuit current source open circuit Req 2 Find equivalent resistance Req between the terminals by inspection R R eq Or set all independent sources to zero 1 Apply a test voltage source VTEST 2 Calculate ITEST VTEST RTh I TEST EE 42 100 Spring 2006 Lecture 3a Prof White ITEST network of independent sources and resistors with each source set to zero 11 VTEST Th RTh Calculation Example 1 Set all independent sources to 0 EE 42 100 Spring 2006 Lecture 3a Prof White 12 Norton Equivalent Circuit Any linear 2 terminal 1 port network of independent voltage sources independent current sources and linear resistors can be replaced by an equivalent circuit consisting of an independent current source in parallel with a resistor without affecting the operation of the rest of the circuit Norton equivalent circuit a network of sources and resistors iL vL RL iN RN iL vL RL b EE 42 100 Spring 2006 a b Lecture 3a Prof White 13 Finding IN and RN RTh Analogous to calculation of Thevenin Eq Ckt 1 Find open circuit voltage and short circuit current IN isc VTh RTh 2 Or find short circuit current and Norton Thevenin resistance EE 42 100 Spring 2006 Lecture 3a Prof White 14 Finding IN and RN We can derive the Norton equivalent circuit from a Th venin equivalent circuit simply by making a source transformation RTh vTh a a iL vL RL iN RN iL vL RL b b voc vTh RN RTh iN isc isc RTh EE 42 100 Spring 2006 Lecture 3a Prof White 15 Maximum Power Transfer Theorem Th venin equivalent circuit Power absorbed by load resistor RTh VTh 2 iL vL RL VTh RL p i RL RTh RL 2 L dp To find the value of RL for which p is maximum set to 0 dRL 2 dp 2 RTh RL RL 2 RTh RL VTh 0 4 dRL RTh RL RTh RL 2 RTh RL EE 42 100 Spring 2006 RL 2 RTh RL 0 A resistive load receives maximum power from a circuit if the load resistance equals the Th venin resistance of the circuit Example Maximizing power to speakers from music system Lecture 3a Prof White 16 EE 42 100 Spring 2006 Lecture 3a Prof White 17
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