Exam 2 equation sheet mcafee

Exam 2 equation sheet mcafee - EECS 215 Exam 2 Equation...

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1 EECS 215 Exam 2 Equation Sheet – (McAfee) First Order Circuits [ Source-Free ] Source-free RC [ v s (t) = 0 ] Source-free RL [ v s (t) = 0 ] C v C + - R L i L R τ t C RC t C C e v e v t v = = ) 0 ( ) 0 ( ) ( τ t L L tR L L e i e i t i = = ) 0 ( ) 0 ( ) ( First Order Circuits [ Step-Response ] Step response RC [ v s (t) = V S u(t) ] Step Response series RL [ v s (t) = V S u(t) ] v s (t) C v C + - R L i L R v s (t) ( ) RC t S C S C e V v V t v + = ) 0 ( ) ( L tR S L S L e R V i R V t i + = ) 0 ( ) ( Step Response parallel RL [ i s (t) = I S u(t) ] i L i S (t) R L ( ) L tR S L S L e I i I t i + = ) 0 ( ) (
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2 Second Order Circuits [ Source-Free ] Source-free Series RLC [ v s (t)=0 ] (or natural response for series RLC) Source-free Parallel RLC [ v s (t)=0 ] (or natural response for parallel RLC) C R L i L R C v + - Differential Equation: 0 0 2 2 2 2 = + + = + + L L L C C C i dt di RC dt i d LC v dt dv RC dt v d LC Differential Equation: 0 0 2 2 2 2 = + + = + + C C C L L L v dt dv R L dt v d LC i dt di R L dt i d LC Characteristic Equation: 0 1 2 = + + RCs LCs Characteristic Equation: 0 1 2 = + + s R L LCs Source-free Series RLC (continued)
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