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06.10.2011.  A sinusoids is signal that has the form of the sine or cosine function.  Consider the sinusoidal voltage.

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Presentation on theme: "06.10.2011.  A sinusoids is signal that has the form of the sine or cosine function.  Consider the sinusoidal voltage."— Presentation transcript:

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2  A sinusoids is signal that has the form of the sine or cosine function.  Consider the sinusoidal voltage.

3 as a function of ωt as a function of t  Sinusoids repeat itself every T seconds.  T is called the period of sinusoids.

4 İf write t+T instead of t

5  The frequency f of the sinusoids

6  Consider a more general expression for the sinusoids. Phase (in radian or degrees)

7  Let us consider two sinusoids.

8  A sinusoids can be expressed either in sine or cosine function.  We can transform a sinusoids from sine to cosine or vice versa.

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10  The graphical technique can be also used to add two sinusoids of the same frequency.

11  For example; ?

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13 Solution: Same form

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15  A phasor is a complex number that represents the amplitude and phase of a sinusoid.  Before we completely define phasors and apply them to circuit analysis, we need to be thoroughly familiar with complex numbers,  A complex number z can be written in rectangular form as; imaginary part Real part

16  The complex number z can be written in polar or exponential form as; magnitude phase  z can be expressed in three forms;

17  Relationship between polar and rectangular form;

18  Following operations are important;

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20 İn general; Real part imaginary part Time-domain represantaion Phasor-domain represantaion

21 Sinusoid-Phasor Transformations Time-domain represantaion Phasor-domain represantaion

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26 Solution:

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28 Solution:

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