ECE 201 Section 4 Lecture 9 Prof Peter Bermel January 30 2012 Loop Analysis Applying KVL around each loop 1 30 2012 ECE 201 4 Prof Bermel R2 R1 A I1 Vs R4 I2 RnI1 I3 Is B R5 Loop Analysis Combining KVL constraints 0 R2 R1 A I1 Vs 1 30 2012 ECE 201 4 Prof Bermel R4 I2 RnI1 I3 Is B R5 Loop Analysis Rearranging as a matrix equation 0 0 1 0 0 1 30 2012 ECE 201 4 Prof Bermel Loop 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 conservation 1 30 2012 ECE 201 4 Prof Bermel MATLAB Code 1 30 2012 ECE 201 4 Prof Bermel Calling MATLAB Code 1 30 2012 ECE 201 4 Prof Bermel Linearity Theorem For linear resistive circuits output voltages and currents are a linear combination of independent sources i e 1 30 2012 ECE 201 4 Prof Bermel Linearity Example 3 Loop Circuit R2 R1 A I1 Vs 1 30 2012 ECE 201 4 Prof Bermel R4 I2 RnI1 I3 Is B R5 Linearity Example 3 Loop Circuit R2 R1 A I1 Vs 1 30 2012 ECE 201 4 Prof Bermel R4 I2 RnI1 I3 Is B R5 Linearity Example 3 Loop Circuit R2 R1 A I1 Vs 1 30 2012 ECE 201 4 Prof Bermel R4 I2 RnI1 I3 Is B R5 Superposition 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 Bermel Proportionality Property Proportionality property multiplying independent source amplitude by changes output by factor of 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 Bermel Homework 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 52 1 30 2012 ECE 201 4 Prof Bermel
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