ECE 201, Section 4Lecture 10Prof. Peter BermelFebruary 1, 2012HW #5• Received 100 assignments• Scores: µ=88, σ=142/1/2012 ECE 201-4, Prof. BermelExam #1: Thursday, Feb. 9• Contents: – Lectures 1-11 (first class until Friday)– Book chapters 1-3 and 5• Seating will be assigned probably early next week2/1/2012 ECE 201-4, Prof. BermelKey Properties• Linearity theorem – voltages and currents are a linear function of all independent sources• Superposition theorem• Proportionality property2/1/2012 ECE 201-4, Prof. BermelExample 1: Predicting OutputsV1(V) V2(V) I1 (A) Iout(A)8 0 0 40 6 0 120 0 3 214 2 6 ??2/1/2012 ECE 201-4, Prof. BermelLinear ResistiveCircuitV1+-+-V2IoutI1Example 1: SolutionV1(V) V2(V) I1 (A) Iout(A)8 0 0 40 6 0 120 0 3 214 2 6 4/2+12/3+2*21=482/1/2012 ECE 201-4, Prof. BermelLinear ResistiveCircuitV1+-+-V2IoutI1Example 2: Predicting OutputsV1(V) V2(V) I1 (A) Iout(A)6 12 9 123 6 4 92 8 4 86 2 4 ??Linear ResistiveCircuitV1+-+-V2IoutI1Hand Calculation Technique• Can write down the following equations from the results above3ߙଵ+ 6ߙଶ+ 4ߚଵ= 96ߙଵ+ 12ߙଶ+ 9ߚଵ= 12If we multiply the first equation by -2 and add, we readily obtain β1=-6. This yields:ߙଵ+ 2ߙଶ= 11ߙଵ+ 4ߙଶ= 16This readily gives us α2=2.5, α1=62/1/2012 ECE 201-4, Prof. BermelMATLAB Technique2/1/2012 ECE 201-4, Prof. BermelMATLAB code2/1/2012 ECE 201-4, Prof. BermelExample 2: SolutionV1(V) V2(V) I1 (A) Iout(A)6 12 9 123 6 4 92 8 4 86 2 4 172/1/2012 ECE 201-4, Prof. BermelLinear ResistiveCircuitV1+-+-V2IoutI1Example 3• What are the coefficients α and β in:ݒ= ߙܸ௦+ ߚܫ௦2/1/2012 ECE 201-4, Prof. BermelVs+-Is30 Ω10 Ω15 Ω5 Ω60 Ω+-voExample 3: Solution2/1/2012 ECE 201-4, Prof. BermelVs+-Is30 Ω10 Ω15 Ω5 Ω60 Ω+-voܸ௦− ܸ30=ܸ60+ܸ− ܸ10ܫ௦+ܸ− ܸ10=ܸ20A BExample 3: Solution2/1/2012 ECE 201-4, Prof. BermelVs+-Is30 Ω10 Ω15 Ω5 Ω60 Ω+-vo3/20 −1/10−1/10 3/20ܸܸ=ܸ௦/30ܫ௦ܸܸ=0.4ܸ௦+ 8ܫ௦4ܸ௦/15 − 12ܫ௦A BExample 3: Solution2/1/2012 ECE 201-4, Prof. BermelVs+-Is30 Ω10 Ω15 Ω5 Ω60 Ω+-voݒ= ܸ௦/15 − 3ܫ௦A BExample 4: Ladder Networks• Current and voltage everywhere for this 4-loop network? What about N loops?2/1/2012 ECE 201-4, Prof. BermelI1Vs+-R2R2R2RRRRRExample 4: Solution• Assume 1V across resistor at end• 2V across first loop• 4V across second loop• 16 V across fourth loop• 2NV with N loops• Actual voltages: Vs*2M-N2/1/2012 ECE 201-4, Prof. BermelI1Vs+-R2R2R2RRRRRHomework• HW #5-8 solution posted today• HW #9 due today by 4 pm at EE 325B• HW #10 due Friday: DeCarlo & Lin, Chapter 5:– Problem 1– Problem 21(a) – note the typo: you should get ݒ௨௧= ܽଵݒ௦ଵ+ ܽଶݒ௦ଶ– Problem 262/1/2012 ECE 201-4, Prof.
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