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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.
as a function of ωt
 Sinusoids repeat itself
every T seconds.
 T is called the period of
sinusoids.
as a function of t
İf write t+T instead of t
 The frequency f of the sinusoids
 Consider a more general expression for the sinusoids.
Phase (in radian or degrees)
 Let us consider two sinusoids.
 İn this case, 𝑣1 lags 𝑣2 by 𝝋
 İf 𝝋 ≠ 0, 𝑣1 and 𝑣2 are out
of phase
 İf 𝝋 = 0, 𝑣1 and 𝑣2 are in
phase
 A sinusoids can be expressed either in sine or cosine
function.
 We can transform a sinusoids from sine to cosine or
vice versa.
 The graphical technique can be also used to add two
sinusoids of the same frequency.
 For example;
?
-4
5
53.10
+3
sin 𝜔𝑡
cos 𝜔𝑡
Calculate the phase angel between 𝑣1 = −10 cos 𝜔𝑡 +
Solution:
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;
Real part
imaginary part
The complex number z can be written in polar or
exponential form as;
magnitude
phase
z can be expressed in three forms;
Relationship between polar and rectangular form;
Following operations are important;
İn general;
Real
part
imaginary part
Time-domain represantaion
Phasor-domain represantaion
Sinusoid-Phasor Transformations
Time-domain represantaion
Phasor-domain represantaion
Difference Between 𝒗 𝒕 and V
Solution:
Solution:
 Here is an important use of phasors for summing
sinusoids of the same frequency.
Current 𝑖1 𝑡) is in standart form. Its phasor is;
 we need to express 𝑖2 𝑡) in cosine form. The rule for converting
sine to cosine is to substract 900 .
 if we let 𝑖 = 𝑖1 + 𝑖2 , then