Sinusoidal Waveforms
Md Shahabul AlamDept. of EEESinusoidal WaveformsOverview of the
ContentsGeneration of Sinusoidal WaveformsInstantaneous
VoltageSinusoidal Waveform ConstructionAngular Velocity of a
Sinusoidal WaveformPhase Difference and Phase ShiftPhase
Relationship of a Sinusoidal WaveformPhase Difference of a
Sinusoidal WaveformThe Cosine Waveform
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 WaveformElectricity and Magnetism
Instantaneous Voltage
What it is and how it is represented ?Voltage at any instant of
time and phaseInstantaneous value = Maximum value x sin
Where, Vmax is the maximum voltage induced in the coil and =t,
is the angle of coil rotation.Sinusoidal Waveform Construction
Coil Angle
()04590135180225270315360e=Vmax.sin070.7110070.710-70.71-100-70.71-0Angular
Velocity of a Sinusoidal Waveformthe 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, . 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: Vm=169.8sin(377t)
volts. Calculate the RMS voltage of the waveform, its frequency and
the instantaneous value of the voltage after a time of
6mS.Sinusoidal Waveform
All the things are quantified in this waveformPhase Difference
and Phase Shiftnot 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 0o by some value when compared to
another sine waveThe phase difference or phase shift as it is also
called of a Sinusoidal Waveform is the angle (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
).Represented in degrees, radians and time shift.Phase Difference
and Phase ShiftPhase Difference Equation
Where:Am-is the amplitude of the waveform.t-is the angular
frequency of the waveform in radian/sec. (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
Phase Difference and Phase ShiftTwo Sinusoidal Waveforms
in-phase
Phase Difference of a Sinusoidal Waveform-out of phase
V leads I by 30 or I lags by V 30In 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.
