lecture 29 - Phasors

# lecture 29 - Phasors - 1 • Phasors ECE 201 Lecture 29...

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1 Phasors ECE 201: Lecture 29 Borja Peleato

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Phasors A sinusoidal signal (voltage or current) can always be expressed as x(t)=A x *cos(wt+θ) or, equivalently x(t)=Re{X*e jwt } where X=A x *e X is a complex number known as the PHASOR corresponding to x(t) The magnitude of X is the same as the amplitude (maximum value) of x(t) The phase of X is the same as that of x(t), i.e., the real part of X is equal to x(0) Phasors do not depend on time We can go back and forth between phasors and time signals: if x(t)= A x *cos(wt+θ) then X=A x *e x(t) = Re{X*e jwt } 2
Circuit elements We have studied three main circuit elements (op amps have to be dealt with separately): R, L, and C Each characterized in terms of an equation relating its voltage drop with its current: R gave Ohm’s law: V(t)=R*I(t) L gave C gave We can always use these to analyze the circuit, but when all the inputs are sinusoidal, these equations can be significantly simplified 3

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Impedance
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