SINUSOIDS AND PHASORS

1. SINUSOIDS AND PHASORS 06.10.2011

2. 2.2. Sinusoids • A sinusoids is signal that has the form of the sine or cosine function. • Consider the sinusoidal voltage.

3. 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

4. 2.2. Sinusoids İf write t+T instead of t

5. 2.2. Sinusoids • The frequency f of the sinusoids

6. 2.2. Sinusoids • Consider a more general expression for the sinusoids. Phase (in radian or degrees)

7. 2.2. Sinusoids • Let us consider two sinusoids. • İn this case, lags by • İf • İf

8. 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.

9. 2.2. Sinusoids

10. 2.2. Sinusoids • The graphical technique can be also used to add two sinusoids of the same frequency.

11. 2.2. Sinusoids • Forexample; ? -4 5 cos +3 sin

12. Example 2.1.

13. Example 2.2. Calculate the phase angel between and . State which sinusoid is leading. Solution: Same form

14. Example 2.2.

15. 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

16. 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;

17. 2.3. Phasors • Relationship between polar and rectangular form;

18. 2.3. Phasors • Following operations are important;

19. 2.3. Phasors

20. 2.3. Phasors İn general; imaginary part Real part Time-domain represantaion Phasor-domain represantaion

21. 2.3. Phasors Sinusoid-Phasor Transformations Phasor-domain represantaion Time-domain represantaion

22. 2.3. Phasors Difference Between and V

23. Example 2.3.

24. Example 2.3.

25. Example 2.3.

26. Example 2.4. Solution:

27. Example 2.4.

28. 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;

29. Example 2.5. • we need to express in cosine form. The rule for converting sine to cosine is to substract. • ifwelet, then

30. Example 2.5.