What is Form Factor? Form Factor Formula & its Derivation

What is Form Factor?

The ratio of the root mean square value to the average value of an alternating quantity  is called Form Factor. The Form Factor is very important parameter for knowing the perfectness of the waveform. Any periodic waveform has varying magnitude with time. The waveform attains maximum or peak value at a point of time. The direct current has its maximum amplitude at all the times i,e. it has constant magnitude  and the magnitude does not change with time. Contrary to this, the instantaneous value of AC varies with time and attains maximum or peak value and again the magnitude decrease. Before understanding what is the Form Factor, let us understand about the crest factor of AC and its RMS  and average value.

Crest Factor

The crest factor of an AC current or voltage waveform is the ratio of its peak value to root mean square(RMS) value.The crest factor of an AC voltage or current can be found by measuring its peak value and root mean square value.The root mean square value of an AC current is equal to the heating effect of the AC current that is equal to the heating effect of  the DC current. The root mean square value of an perfect sinusoidal AC voltage or current has certain relationship with its peak or maximum value.
The RMS value of an AC voltage is as given below.

Mathematical derivation of AC RMS Value

Mathematical Derivation of Crest Factor 

What is form factor of AC waveform?

The magnitude of the alternating current varies with time both in postive and negative half of the complete cycle. Form Factor shows how distorted is the  waveform.The rms value of AC  is equal to the direct current which when passed through the resistor for a given period of time will produce the same heating effect as produced by alternating current when passed through the same resistor for the same time. The rms value of the ac waveform, as derived above, is equal to Vp/√2. Where, Vp is the peak value.

The average value of AC  is equal to the stady current which transfer the same amount of charge in a given time as transfered by an AC across the same circuit in the same circuit. The derivation of average value of AC is as given below.

Form Factor Formula

Mathematically, we can express the form factor as;

Form Factor Formula Derivation

The form factor of the ac waveform is equal to the ratio of rms value to average value.

Form Factor of various waveform

The form factor of various AC waveshapes are as given below.