In this article, we will discuss the form factor and peak factor. Both form factor and peak factor are two important measures related to alternating quantities. The form factor is used for describing the distortion and heating effect of an alternating signal. While, the peak factor is used to get information about the maximum value of the alternating quantity, and thus helps in differentiating the two waveforms.
What is a Form Factor?
In electrical engineering, the waveforms of two different
alternating quantities of the same maximum or peak values and the same frequency may
look different, which means there could be a difference in their configuration.
This difference in the configuration of periodic waveforms where the amplitudes
and frequencies are the same is represented by the form factor (FF).
For an alternating quantity such as alternating current or
voltage, the form factor is defined
as the ratio of the RMS (Root Mean Square) value to the average value of the
alternating quantity. Therefore,
For alternating current, the form factor
is expressed as,
For alternating voltage, the form factor
is expressed as,
The form factor formulae and values of
different types of alternating quantities are given as follows-
(1). The form factor of a sinusoidal
(sine) wave is:
(2). The form factor of a half-wave
rectified sine wave is:
(3). The form factor of a full-wave
rectified sine wave is:
(4). The form factor of a square wave is:
(5). The form factor of a triangular wave
is:
(6). The form factor of a saw-tooth wave
is:
What is a Peak Factor?
The peak
factor gives an idea about the maximum value of an alternating quantity
(current or voltage) that its waveform can provide. The peak factor also helps
in deriving the waveform of a signal from the DC signal.
The peak factor of an alternating
quantity may be defined as under-
The ratio of the maximum or peak value to the
RMS value of an alternating quantity is known as the peak factor of the alternating quantity. It is also known as the crest factor because the peak value is
also called the crest value.
Mathematical, the peak factor or crest
factor can be expressed as,
For an alternating current, the peak
factor is given by,
For an alternating voltage, the peak
factor is given by,
Where Im
and Vm are the maximum or
peak values of the current and voltage respectively, and Irms and Vrms
are the root mean square (RMS) values of the current and voltage respectively.
The peak factor of a sinusoidal
alternating current is:
The peak factor of a sinusoidal
alternating voltage is:
Numerical
Example – The RMS value of a sinusoidal voltage
is 141.4 V and the average value is 127.4 V. If the maximum value of the given
voltage is 200 V. Then, determine the form factor and peak factor of the
voltage waveform.
Solution
– Given data,
`\V_(RMS)=141.4 "V"`
`\V_(av)=127.4 "V"`
`\V_m=200 "V"`
Therefore, the Form factor of the given
voltage waveform is:
`\"FF"=V_(RMS)/V_(av)`
`\⟹"FF"=141.4/127.4=1.11`
The peak factor of the voltage waveform
is:
`\"PF"=V_m/V_(rms)`
`\⟹"PF"=200/141.4=1.414`
Hence, for the given sinusoidal voltage
wave, the form factor is 1.11 and the peak factor is 1.414.
Conclusion
Thus, in the above sections of this
article, we discussed what the form factor and peak factor are. The form factor
is related to the RMS value and average value of the alternating quantity, and
the peak factor is related to the peak and RMS values of the alternating
quantity.
