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ECE 231 -5(2)

ECE 231 -5(2) - ECE-231 Section Circuits and Systems I...

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ECE-231 Section Circuits and Systems I Spring 2011 Session 5 Professor Stewart Personick Office: ECEC Room 321 [email protected]

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The concept of Superposition (Applied to the analysis of linear circuits)
Suppose y = 5 z + 10 x This is a linear equation , that relates y to: z and x In this equation: x and z are independent variables, and y is a dependent variable If z = 7 , and x=0, then y = 35 If z = 0 and x = 3 then: y = 30 If z = 7 and x = 3 then (from superposition): y = 35 + 30 =

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Linear circuit with two (2) sources + - V1 = 12 Volts I2 =1 Ampere 10 Ohms Resistor All of the circuits we have been analyzing , including circuits like this one, are linear circuits . The equations that characterize the currents and voltages (KCL, KVL, Ohm’s law) associated with these circuits are linear equations . Example: i1 x 10 Ohms + Vab - 12V = 0 i1 + 1A = 0 This means that there are no terms in those equations like : Vab x i1 or ( Vab) 2 or V1 x i2 Every term in those equations is linearly proportional to either: one of the dependent voltages or currents (like i1 x 10 Ohms) or one of the independent sources (like -1 x V1 = -12V) . i1 node a node b
Linear circuit with two (2) sources + - 12 Volts 1 Ampere 10 Ohms We can solve for the voltages and the currents in a linear circuit, having multiple independent voltage sources and/or current sources, by finding the dependent voltages and currents produced by each source, separately. Then we can add the voltages and currents produced by each source, separately, to find the voltages and currents that are produced by the combination of all of the sources. Note: When we calculate power flows , the equations we use are not linear equations. We cannot add the power flows produced by each source, separately, to find the power flows produced by multiple sources working in combination. For example: (i1a + i1b) x (V1a +V1b) does not equal (i1a x V1a) + (i1b x V1b) i1 node a node b

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Linear circuit with two (2) sources step 1: turn off the current source + - 12 Volts 0 Amperes 10 Ohms We can solve for the voltages and currents in this circuit by finding the voltages and currents produced by each source, separately. Then we can add the voltages and currents produced by each source, separately, to find the voltages and currents that are produced by the combination of both sources. i1 node a node b
Linear circuit with two (2) sources step 1: turn off the current source + - 12 Volts 10 Ohms We can solve for the voltages and currents in this circuit by finding the voltages and currents produced by each source, separately. Then we can add the voltages and currents produced by each source, separately, to find the voltages and currents that are produced by the combination of both sources. i1 node a node b i1 = 0 Vab = 12V

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Linear circuit with two (2) sources step 2: turn off the voltage source + - 0 Volts 1 Ampere 10 Ohms We can solve for the voltages and currents in this circuit by finding the voltages and currents produced by each source, separately.
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ECE 231 -5(2) - ECE-231 Section Circuits and Systems I...

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