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SINUSOIDS AND PHASORS . 06.10.2011. 2.2 . Sinusoids. A sinusoids is signal that has the form of the sine or cosine function. Consider the sinusoidal voltage. 2.2 . Sinusoids. as a function of ω t. Sinusoids repeat itself every T seconds. T is called the period of sinusoids.
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SINUSOIDS AND PHASORS 06.10.2011
2.2. Sinusoids • A sinusoids is signal that has the form of the sine or cosine function. • Consider the sinusoidal voltage.
2.2. Sinusoids as a function of ωt • Sinusoids repeat itself every T seconds. • T is called the period of sinusoids. as a function of t
2.2. Sinusoids İf write t+T instead of t
2.2. Sinusoids • The frequency f of the sinusoids
2.2. Sinusoids • Consider a more general expression for the sinusoids. Phase (in radian or degrees)
2.2. Sinusoids • Let us consider two sinusoids. • İn this case, lags by • İf • İf
2.2. Sinusoids • A sinusoids can be expressed either in sine or cosine function. • We can transform a sinusoids from sine to cosine or vice versa.
2.2. Sinusoids • The graphical technique can be also used to add two sinusoids of the same frequency.
2.2. Sinusoids • Forexample; ? -4 5 cos +3 sin
Example 2.2. Calculate the phase angel between and . State which sinusoid is leading. Solution: Same form
2.3. Phasors • 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
2.3. Phasors • The complex number z can be written in polar or exponential form as; magnitude phase • z can be expressed in three forms;
2.3. Phasors • Relationship between polar and rectangular form;
2.3. Phasors • Following operations are important;
2.3. Phasors İn general; imaginary part Real part Time-domain represantaion Phasor-domain represantaion
2.3. Phasors Sinusoid-Phasor Transformations Phasor-domain represantaion Time-domain represantaion
2.3. Phasors Difference Between and V
Example 2.4. Solution:
Example 2.5. Solution: • Here is an important use of phasors for summing sinusoids of the same frequency. • Current is in standart form. Its phasor is;
Example 2.5. • we need to express in cosine form. The rule for converting sine to cosine is to substract. • ifwelet, then