ECE 201, Section 4Lecture 11Prof. Peter BermelFebruary 3, 2012HW #6-7• For HW #6: N=100, µ=81%, σ=21%• For HW #7: N=96, µ=69%, σ=34%2/3/2012Exam #1: Thursday, Feb. 9• Review session on Monday, Feb. 6 at 7 pm (LILY 1105)• Posted 3 sample exams on Blackboard to help you study• Extended TA office hours Thurs. until 7:30 pm• I’ll have office hours 9:30-10:30 am MWF in EE 330 and by appointment2/3/2012Source TransformationsCombining voltage sources:Combining current sources:2/3/2012Va+-+ -Va+Vb+Vc+-+ -Ia-Ib+Ic+ -Ic+ -IbIa+-VbVc+-Source Transformation Theorem• The following 2-terminal networks are equivalent:– Voltage source Vain series with resistor R– Current source Ib=Va/R in parallel with resistor R2/3/2012Va+-R+ -IbR+ -Source Transformation2/3/2012IbR+ V-ܫ = ܸ/ܴ − ܫܸ = ܴ(ܫ+ ܫ)Va+-R+ -ܸ = ܸ+ ܫܴIf ܸ= ܴܫ, ܸ = ܴ(ܫ+ ܫ)Example 1• What current flows through the central 3 Ωresistor?2/3/2012+-12 Ω+-40 V+-+-6 Ω 40 Ω 24 Ω48 V36 V3 Ω30 VExample 1: Solution• Rewrite each of the resistor/voltage source pairs as parallel resistor/current source pairs with currents of 36/12=3A; 30/6=5A; 40/40=1A; 48/24=2A2/3/2012+-12 Ω+-40 V+-+-6 Ω 40 Ω 24 Ω48 V36 V3 Ω30 VExample 1: SolutionCombine parallel current sources and resistors. IL=3+5=8 A; IR=1+2=3 ARL=(1/6+1/12)-1=4 Ω; RR=(1/24+1/40)-1=15 Ω2/3/201212 Ω6 Ω 40 Ω 24 Ω3 Ω5A3A1A2AExample 1: SolutionTransform back into V-R pairs:VL=32 V; VR=45 V2/3/20124 Ω 15 Ω3 Ω8 A 3 AExample 1: SolutionCombine in series:V=13 V; R=22 ΩI=V/R=0.59 A2/3/2012+-45 V+-4 Ω 15 Ω3 Ω32 VEquivalent Networks• Equivalent networks: distinct 2-terminal circuits which exhibit the same current-voltage relationship• Examples:2/3/20122 A+ V-ܫ=ܸ/4−28 V+-4 Ω+ -ܸ=8+4ܫ4 ΩEquivalent Network Examples2/3/2012+-12 Ω+-6 Ω18 V3 Vܫ = ܸ/4 − 212 Ω 6 Ω0.5A1.5Aܸ = 8 + 4ܫCar Battery Problem• What is the minimum value of Vo required to achieve a 50 A starter voltage?2/3/2012+-0.02 Ω+-12 VVo0.02 Ω0.2 Ω50 A?Car Battery Solution• Source transformation yields I=(12+Vo)/0.02; Req=0.01 WV=6+0.5VoI=50=(6+0.5Vo)/0.21 Vo=9 V2/3/2012+-0.02 Ω+-12 VVo0.02 Ω0.2 Ω50 A?Homework• HW #9 solution posted today• HW #10 due today by 4 pm in MSEE 230 (note the changed location for today only!)• HW #11 due Monday: DeCarlo & Lin, Chapter 5:– Problem 41– Problem 432/3/2012Last Lecture on Exam #1Monday begins Exam #2
View Full Document