ECE 201, Section 4Lecture 9Prof. Peter BermelJanuary 30, 2012Loop Analysis• Applying KVL around each loop:ܴସܫଵ+ܫଷ+ܴଶܫଵ−ܫଶ+ܴଵܫଵ= ܸ௦ܴଶܫଶ−ܫଵ−ݒଵ= ܴܫଵܴସܫଷ+ܫଵ+ܴହܫଷ= ܴܫଵܫଶ= −ܫ௦1/30/2012 ECE 201-4, Prof. BermelR4R2RnI1IsBR5I1AVsI3+-+ -I2R1Loop Analysis• Combining KVL + constraints:ܴଵ+ܴଶ+ܴସܫଵ+ܴସܫଷ= ܸ௦−ܴଶܫ௦ܴଶ+ܴܫଵ+ݒଵ= −ܴଶܫ௦ܴସ−ܴܫଵ+ ܴସ+ܴହܫଷ= 01/30/2012 ECE 201-4, Prof. BermelR4R2RnI1IsBR5I1AVsI3+-+ -I2R1Loop Analysis• Rearranging as a matrix equation:ܴଵଶସܴସ0ܴଶ+ܴ0 1ܴସ−ܴܴସ+ܴହ0ܫଵܫଷݒଵ=ܸ௦−ܴଶܫ௦−ܴଶܫ௦01/30/2012 ECE 201-4, Prof. BermelLoop Analysis• Power delivered at each circuit element:– Resistors: can use P=I2R– Voltage sources: can use P=IV– Current sources: use P=IV• Note that powers should sum to zero, due to energy conservation1/30/2012 ECE 201-4, Prof. BermelMATLAB Code1/30/2012 ECE 201-4, Prof. BermelCalling MATLAB Code1/30/2012 ECE 201-4, Prof. BermelLinearity Theorem• For linear resistive circuits, output voltages and currents are a linear combination of independent sources, i.e.:ܸ=ߙܸ+ߚܫேୀଵܫ=ߙܸ+ߚܫேୀଵ1/30/2012 ECE 201-4, Prof. BermelLinearity Example: 3-Loop Circuit1/30/2012 ECE 201-4, Prof. BermelR4R2RnI1IsBR5I1AVsI3+-+ -I2R1Linearity Example: 3-Loop Circuit1/30/2012 ECE 201-4, Prof. BermelR4R2RnI1IsBR5I1AVsI3+-+ -I2R1Linearity Example: 3-Loop Circuit1/30/2012 ECE 201-4, Prof. BermelR4R2RnI1IsBR5I1AVsI3+-+ -I2R1Superposition Property• Superposition property: total output of linear circuit is sum of contributions from each independent source• Special case of linearity property• Applies to current and voltage but not power (in DC circuits)1/30/2012 ECE 201-4, Prof. BermelProportionality Property• Proportionality property: multiplying independent source amplitude by α changes output by factor of α• Again, applies to current and voltage but not power (in DC circuits)• Will lead to some interesting tricks next time!1/30/2012 ECE 201-4, Prof. BermelHomework• HW #6 solution posting this morning• HW #8 due today by 4 pm at EE 325B• HW #9 due Wednesday: DeCarlo & Lin, Chapter 3:– Problem 37– Problem 42– Problem 521/30/2012 ECE 201-4, Prof.
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