Characteristics of a Sine Wave

Electrical sin wave form graph is a showing the variation of voltage or current. The horizontal axis shows the passing of time, progressing from left to right. The vertical axis shows the quantity measured ( voltage, ampere or Power ). There are six must important characteristics of sine wave.

RMS value 

Root mean squared ( RMS ) value is the value of the equivalent direct voltage ( DC ) which would provide the same energy to a circuit as the sine wave measured. That is, if an AC sine wave has a RMS value of 230 volts, it will provide the same energy to a circuit as a DC supply of 230 volts.

RMS value Equation 

V _{RMS =} V <sub>Peek X 0.707

Example
Peek value or Max value = 326 V

V RMS = V Peek X 0.707</sub>

 V <sub>RMS = 326 X 0.707

V RMS = 230.48 V</sub>

Average Value or mean value 
This is normally taken to mean the average value of only half a cycle of the sine wave.

Mean value Equation 

V _mean = V _Peek  X 0.637

<sub>Example
Peek value or Max value = 326 V

V mean = V Peek  X 0.637
V mean =  326 X 0.637</sub>
V _{mean = 207.66 v}


Peak to Peak value

Peak to peak (pk-pk) is the difference between the maximum positive and the maximum negative amplitudes of a waveform. 

Peek to Peek value  

V_{PP =} V _Peek + V _Peek 

_Example

_{Peek value or Max value = 326 V}

_{VPP = V Peek + V Peek} 

V_{PP = 326+ 326}

_{VPP = 652 v}

Instantaneous Value 
Instantaneous value of an alternating voltage is the value of voltage at one particular instant time. The value may be zero if the particular instant is the time in the cycle at which the polarity of the voltage is changing. It may also be the same as the peak value, if the selected instant is the time in the cycle at which the voltage stops increasing and starts decreasing. There are actually an infinite number of instantaneous values between zero and the peak value.

Instantaneous value Equation

v (t) = V_Max sin (w t )

w = 2 x p  x f  or  w = 2 x p / T

v (t) = V_Max sin (2*p*f *t )

Amplitude 

Amplitude is the difference between the maximum positive and the X axis of a waveform. It is equal to peek value.

Periodic Time

periodic time is that amount of time that elapses from the start of a occurrences until the commencement of the next identical happening.

T = 1/f 

T = Periodic time

f  = Frequency 

Frequency 

Frequency is the number of occurrences of a repeating event per unit time.

F =1/T

f  = Frequency

T = Periodic time