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AC Circuits

AC Circuits. Introduction. Circuits in which the source voltage or current is time-varying (particularly interested in sinusoidally time-varying excitation, or simply, excitation by a sinusoid). Why sinusoids?. Nature itself is characteristically sinusoidal. Name it!

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AC Circuits

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  1. AC Circuits

  2. Introduction • Circuits in which the source voltage or current is time-varying (particularly interested in sinusoidally time-varying excitation, or simply, excitation by a sinusoid)

  3. Why sinusoids? • Nature itself is characteristically sinusoidal. Name it! • Sinusoidal signal is easy to generate and transmit • Fourier analysis, any practical periodic signal can be represented by a sum of sinusoids • A sinusoid is easy to handle mathematically

  4. A sketch of Vmsin t: (a) as a function of t, (b) as a function of t.

  5. More general: • Sinusoids are easily expressed in terms of phasors. • A phasor is a complex number that represents the amplitude and phase of a sinusoid.

  6. A complex number: r is the magnitude of z, and is the phase of z.

  7. The idea of phasor representation is based on Euler’s identity • For v(t): • or • Thus where:

  8. V is the phasor representation of the sinusoid v(t) • A phasor is a complex representation of the magnitude and phase of a sinusoid

  9. The differences between v(t) and V should be emphasized: 1. v(t) is the instantaneous or time domain representation, while V is the frequency or phasor domain representation. 2. v(t) is time dependent, while V is not. 3. v(t) is always real with no complex term, while V is generally complex.

  10. Phasor Relationships for Circuit Elements • Resistor • If the current through a resistor R is

  11. The phasor form of this voltage is • The phasor representation of the current is • Hence

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