Crest factor is defined as the ratio of the peak value (or maximum value) to the RMS value of a waveform. It is denoted by the capital letter ‘C’. It is also known as peak factor. The waveform can be any quantity like current, voltage, etc.
Crest factor Formula
$\text{Crest factor}=\frac{{A_{peak}}}{{A_{rms}}}$
where,
Apeak is the peak or maximum value of the waveform
Arms is the rms value of the waveform
Crest factor of Half wave rectifier
Let the peak value of the rectified output be Vm.
The RMS value of output voltage of single-phase half-wave rectifier is given by
$V_{rms}=\frac{V_{m}}{2}$
As we know the crest factor is given by
$\text{Crest factor}=\frac{{V_{peak}}}{{V_{rms}}}$
Therefore, we get
$\text{Crest factor}=\frac{{V_{m}}}{{\frac{V_{m}}{2}}}$
∴ Crest factor = 2
The crest factor of half wave rectifier is 2
Crest factor of Full wave rectifier
Let the peak value of the rectified output be Vm.
The RMS value of output voltage of single-phase full-wave rectifier is given by
$V_{rms}=\frac{V_{m}}{\sqrt{2}}$
As we know the crest factor is given by
$\text{Crest factor}=\frac{{V_{peak}}}{{V_{rms}}}$
Therefore, we get
$\text{Crest factor}=\frac{{V_{m}}}{{\frac{V_{m}}{\sqrt{2}}}}$
∴ Crest factor = √2 = 1.414213
The crest factor of full wave rectifier is √2
Crest factor of Bridge rectifier
Let the peak value of the rectified output be Vm.
The RMS value of output voltage of bridge rectifier is given by
$V_{rms}=\frac{V_{m}}{\sqrt{2}}$
As we know the crest factor is given by
$\text{Crest factor}=\frac{{V_{peak}}}{{V_{rms}}}$
Therefore, we get
$\text{Crest factor}=\frac{{V_{m}}}{{\frac{V_{m}}{\sqrt{2}}}}$
∴ Crest factor = √2 = 1.414213
The crest factor of full wave rectifier is √2
