 Circuits in which the source voltage or current is time-varying (particularly interested in sinusoidally time-varying excitation, or simply, excitation.

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Presentation transcript:

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

 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

A sketch of V m sin t: (a) as a function of t, (b) as a function of t.

 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.

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

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

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

 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.

 Resistor  If the current through a resistor R is

 The phasor form of this voltage is  The phasor representation of the current is  Hence