1st Week: "Sinusoids & Phasors"

What is a Sinusoid & Phasor?


Sinusoid
 

Thus far our analysis has been limited for the most part to dc circuits, those circuits excited by constant or time-invariant sources. We have restricted the forcing function to dc sources for the sake of simplicity, for pedagogic reasons, and also for historic reasons. Historically, dc sources were the main means of providing electric power up until the late 1800s. At the end of that century, the battle of direct current versus alternating current began. Both had their advocates among the electrical engineers of the time. Because ac is more efficient and economical to transmit over long distances, ac systems ended up the winner. Thus, it is in keeping

with the historical sequence of events that we considered dc sources first. We now begin the analysis of circuits in which the source voltage or current is time-varying. In this chapter, we are particularly interested in sinusoidally time-varying excitation, or simply, excitation by a sinusoid. 

  

A sinusoid is a signal that has a form of the sine or cosine function.

v(t) = Vm sinωt

Vm=the amplitude of the sinusoid

ω=the angular frequency in radians/s

ωt=the argument of the sinusoid
 

A periodic function is one that satisfies f(t) = f(t+nT), for all t and for all integers n.

Remember,

Conversions, 

sin (ωt±180◦ )= −sinωt

cos (ωt±180◦) = −cosωt

sin (ωt±90◦) = ±cosωt

cos (ωt±90◦) = ∓sinωt

Phasors

Sinusoids are easily expressed in terms of phasors, which are more convenient to work with than sine and cosine functions.

A phasor is a complex number that represents the amplitude and phase of a sinusoid.

A complex number z can be written in rectangular form as,

z = x+jy (rectangular form)

z=r<φ (Polar form)

z=re^jφ (Exponential form) 

Reflection:

• Sinusoids are in phase if the sum of their amplitudes is not equal to zero. Sinusoids are out-of-phase if the sum of  their amplitudes is equal to zero.
• A phasor is a complex number that represents the amplitude and phase of a sinusoid.

Video:

For more information, watch the video below:

That's all. Thank You for visiting my blog.

GOD Bless! :)

By:

AYALA, ARNY  S.   BSECE -3

ECE 311

Professor:

ENGR. JAY S. VILLAN, MEP - EE