1. Md Shahabul Alam Dept. of EEE Sinusoidal Waveforms

2. Overview of the Contents Generation of Sinusoidal Waveforms Instantaneous Voltage Sinusoidal Waveform Construction Angular Velocity of a Sinusoidal Waveform Phase Difference and Phase Shift Phase Relationship of a Sinusoidal Waveform Phase Difference of a Sinusoidal Waveform The Cosine Waveform

3. Generation of Sinusoidal Waveforms Michael Faraday discovered the effect of “Electromagnetic Induction” and this is the basic principal that is used to generate a Sinusoidal Waveform Electricity and Magnetism

4. Instantaneous Voltage What it is and how it is represented ? Voltage at any instant of time and phase Instantaneous value = Maximum value x sin θ Where, V max is the maximum voltage induced in the coil and θ = ω t, is the angle of coil rotation.

5. Sinusoidal Waveform Construction Coil Angle ( θ ) 04590135180225270315360 e = Vmax.sin θ 070.7110070.710-70.71-100-70.71-0

6. Angular Velocity of a Sinusoidal Waveform the velocity at which the generator rotates around its central axis determines the frequency of the sinusoidal waveform and which can also be called its angular velocity, ω. But we should by now also know that the time required to complete one revolution is equal to the periodic time, (T) of the sinusoidal waveform. Problem:A sinusoidal waveform is defined as: V m = 169.8 sin(377t) volts. Calculate the RMS voltage of the waveform, its frequency and the instantaneous value of the voltage after a time of 6mS.

7. Sinusoidal Waveform All the things are quantified in this waveform

8. Phase Difference and Phase Shift not all sinusoidal waveforms will pass exactly through the zero axis point at the same time, but may be “shifted” to the right or to the left of 0 o by some value when compared to another sine wave The phase difference or phase shift as it is also called of a Sinusoidal Waveform is the angle Φ (Greek letter Phi), in degrees or radians that the waveform has shifted from a certain reference point along the horizontal zero axis (the lateral difference between two or more waveforms along a common axis ). Sinusoidal Waveform Represented in degrees, radians and time shift.

9. Phase Difference and Phase Shift Phase Difference Equation Where: A m - is the amplitude of the waveform. ω t - is the angular frequency of the waveform in radian/sec. Φ (phi) - is the phase angle in degrees or radians that the waveform has shifted either left or right from the reference point. Phase Relationship of a Sinusoidal Waveform

10. Phase Difference and Phase Shift Two Sinusoidal Waveforms – “in-phase Phase Difference of a Sinusoidal Waveform-out of phase V leads I by 30 or I lags by V 30

11. In AC power circuits this ability to describe the relationship between a voltage and a current sine wave within the same circuit is very important and forms the bases of AC circuit analysis.