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lecture21 - EE 205 Coifman Set your phasors on stun it's...

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n a m f i o C 5 0 2 E E 21-1 Set your phasors on stun... it’s time for phasor circuit analysis In other words, finding the sinusoidal steady state response without touching differential equations. How do the following translate into the phasor domain: Connection constraints (Kirchhoff’s laws) Device constraints (element equations) If a circuit is being driven by sinusoidal inputs with frequency ω , what will the following elements do to this frequency: a capacitor an inductor an Op Amp Homework set #8, due 5/21/08 8-1, 8-2, 8-3, 8-6, 8-10, 8-12, 8-18 , 8-22, 8-26, 8-29, 8-30
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EE 205 Coifman 21-2 Connection constraints, consider KCL at a node with N inputs: i t i t i t N 1 2 0 ( ) + ( ) + + ( ) = ... I t I t I t N N 1 1 2 2 0 cos cos ... cos ω φ ω φ ω φ + ( ) + + ( ) + + + ( ) = Using duality, extend to KVL KVL: The algebraic sum of phasor voltages around a loop is zero KCL: The algebraic sum of phasor currents at a node is zero
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EE 205 Coifman 21-3 Device constraints in phasor phorm Resistor: v t Ri t R R ( ) = ( ) j Im Re I R φ
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EE 205 Coifman 21-4 Inductor: v t L di t dt L L ( ) = ( ) j Im Re I L φ
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EE 205 Coifman 21-5 Capacitor: i t C dv t dt C C ( ) = ( ) j Im Re I C φ
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