Voltage Conversion FactorsDate: 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/ |
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