Voltage Conversion Factors

Date: 01/10/2001 at 07:02:27
From: Bobby Coleman
Subject: Trigonometry conversions

When I try to convert rms voltage to peak voltage, then peak voltage 
to average voltage, I get one answer, but when I convert the peak 
voltage to rms voltage, then rms voltage to average voltage, I get a 
different answer, but close to the first. Do you know the exact 
factors to use to change these values?

So far, I only have the following:

     peak to rms:     multiply peak by .707
     peak to average: multiply peak by .637
     rms to peak:     multiply rms  by 1.414
     rms to average:  multiply rms  by .9
     average to rms:  multiply avg  by 1.111
     average to peak: multiply avg  by 1.567

Thanks for any help.

Date: 01/10/2001 at 11:57:52
From: Doctor TWE
Subject: Re: Trigonometry conversions

Hi Bobby - thanks for writing to Dr. Math.

For sine waves, the exact formulas for converting among peak, 
peak-to-peak, rms (root-mean-square) and average values are as 
follows:

     Vp   = Vpp/2      = sqrt(2)*Vrms  = pi*Vav/2
     Vpp  = 2*Vp       = sqrt(8)*Vrms = pi*Vav
     Vrms = Vp/sqrt(2) = Vpp/sqrt(8)  = pi*Vav/sqrt(8)
     Vav  = 2*Vp/pi    = Vpp/pi        = sqrt(8)*Vrms/pi

where Vp      = Peak voltage
      Vpp     = Peak-to-peak voltage
      Vrms    = rms voltage (also called "effective voltage")
      Vav     = average voltage
      pi      = the constant pi (approx. 3.14159...)
      sqrt(2) = the square root of 2 (approx. 1.41421...)
      sqrt(8) = the square root of 2 (approx. 2.82843...) = 2*sqrt(2)

These constants were determined using calculus. For more information 
on where these constants came from, see the following:

   Why 0.707? Teaching R.M.S. Values of AC Voltage and Current
   - L. B. Cebik
   http://www.cebik.com/edu4.html   

I hope this helps. If you have any more questions, write back.

- Doctor TWE, The Math Forum
  http://mathforum.org/dr.math/