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 τ = 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 τ = 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 τ = 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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