EE_10_F07_Lecture 12

EE_10_F07_Lecture 12 - UCLA ELECTRICAL ENGINEERING...

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UCLA ELECTRICAL ENGINEERING DEPARTMENT: EE 10: CIRCUIT ANALYSIS 1 LECTURE 12 L ECTURE 12 LECTURE NOTES: NOV. 26, 2007 OUTLINE SUMMARY OF INITIAL CONDITIONS IN R-C AND R-L CIRCUITS . ............................. 2 STEP AND NATURAL RESPONSE R-C AND R-L CIRCUITS. ............................................ 2 PRINCIPLES AND PROBLEM SOLVING PROCEDURES FOR RC AND RL CIRCUITS ......................................................................................................................................................... 3 RL NATURAL RESPONSE. ........................................................................................................ 3 Time Constant. ......................................................................................................................... 3 τ = L/R. .................................................................................................................................... 3 Conditions Prior to t = 0. ........................................................................................................ 3 Conditions At t = 0 + (an infitesimal time After t = 0) . ............................................................ 3 Current and Voltage at t > 0. .................................................................................................. 3 RC NATURAL RESPONSE . ....................................................................................................... 4 Time Constant. ......................................................................................................................... 4 = RC . .................................................................................................................................... 4 Conditions Prior to t = 0. ........................................................................................................ 4 Conditions At t = 0 + (an infitesimal time After t = 0) . ............................................................ 4 Current and Voltage at t > 0. .................................................................................................. 4 RL STEP RESPONSE . ................................................................................................................. 5 Time Constant. ......................................................................................................................... 5 = L/R S ................................................................................................................................... 5 Conditions Prior to t = 0. ........................................................................................................ 5 Conditions At t = 0 + (an infitesimal time After t = 0) . ............................................................ 5 Current and Voltage at t > 0. .................................................................................................. 5 RC STEP RESPONSE. ................................................................................................................. 6 Time Constant. ......................................................................................................................... 6 = R S C .................................................................................................................................... 6 Conditions Prior to t = 0. ........................................................................................................ 6 Conditions At t = 0 + (an infitesimal time After t = 0) . ............................................................ 6 Current and Voltage at t > 0. .................................................................................................. 6 SOLVING FOR PARALLEL INDUCTOR AND SERIES CAPACITOR CIRCUIT RESPONSE. ................................................................................................................................... 8 EXAMPLE PROBLEM. ............................................................................................................. 10 EXAMPLE PROBLEM. ............................................................................................................. 13 EXAMPLE PROBLEM. ............................................................................................................. 18 1
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UCLA ELECTRICAL ENGINEERING DEPARTMENT: EE 10: CIRCUIT ANALYSIS 1 LECTURE 12 SUMMARY OF INITIAL CONDITIONS IN R-C AND R-L CIRCUITS Determination of initial conditions will be critical for solving all of our circuit problems depending on R-C and R-L circuits. Initial conditions are determined by circuit properties of inductors and capacitors in steady state conditions These steady state conditions prevail over the semi-infinite time preceding the switching event. o For a circuit that has stabilized over a near infinite period, capacitor current will be zero and inductor voltage will be zero since the time derivatives of voltage and current will be zero. o Thus, computation of capacitor voltage proceeds by treating the capacitor as an open circuit. o Also, computation of inductor current proceeds by treating the inductor as a short circuit. Further, we also must compute initial circuit conditions that prevail immediately after the switching event. o We recall that a capacitor stores energy in its electric field. This may not change instantaneously. Thus, capacitor voltage remains continuous through the switching event. o We recall that an inductor stores energy in its magnetic field. This may not change instantaneously. Thus, inductor current remains continuous through the switching event. STEP AND NATURAL RESPONSE R-C AND R-L CIRCUITS We must identify step and natural response circuits: o Step response circuits are those that include the presence of a source after the switching event o Natural response circuits do not include the presence of a source after the switching event 2
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UCLA ELECTRICAL ENGINEERING DEPARTMENT: EE 10: CIRCUIT ANALYSIS 1 LECTURE 12 PRINCIPLES AND PROBLEM SOLVING PROCEDURES FOR RC AND RL CIRCUITS RL NATURAL RESPONSE -v L + i L R L R S I S R Switch Opens At t = 0 Figure 1. RL Natural Response Circuit TIME CONSTANT τ = L/R CONDITIONS PRIOR TO T = 0 i L (t < 0) = I S v L (t < 0) = v R (t < 0) = 0 Note v L (0) will vary with each circuit. (For the particular circuit above v
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EE_10_F07_Lecture 12 - UCLA ELECTRICAL ENGINEERING...

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