Formula for ripple factor in filter circuits

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Two formulas for calculating ripple factor in filter circuits are discussed: r = (Vrpp/Vdc) and r = (Vrms/Vdc). The first formula, commonly used in basic electronics, relates peak-to-peak ripple voltage to DC output voltage, while the second uses RMS voltage. Although both formulas are referenced in literature, they are not equivalent due to the nature of the waveforms involved. The peak-to-peak method is generally preferred for its simplicity, as the RMS calculation can be complex with non-sinusoidal waveforms. Understanding the context and definitions is crucial for applying these formulas correctly.
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i have come across two different formulas for ripple factor:
One is r= (Vrpp/Vdc), where Vdc is the dc voltage of the output and Vrpp is the peak to peak ripple voltage. My professor uses this formula and I have also seen it being used in basic electronics by Floyd
Another one is r= Vrms/Vdc from electronics by boylestad. Are these correct?

Is it possible to show that they are equivalent. Please help. Thanks in advance
 
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They are not equivalent but Wikipedia shows them both as being used.

http://en.wikipedia.org/wiki/Ripple_(electrical)

So, it depends on your definition.

Peak to peak is easier to use and RMS would be difficult because the waveform is not sinusoidal.
 
Thanks for the reply.
 

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