Electronics World Cover,TOC,and list of posted Popular Electronics articles QST Radio & TV News Radio-Craft Radio-Electronics Short Wave Craft Wireless World About RF Cafe RF Cafe Homepage RF Cafe in Morse Code Google Search of RF Cafe website Sitemap Electronics Equations Mathematics Equations Equations physics Manufacturers & distributors Manufacturers & Services Consultants Engineer Jobs Twitter LinkedIn Advertise on RF Cafe! Engineering Books Crosswords Engineering Humor Kirt's Cogitations Engineering Event Calendar Day in History RF Engineering Quizzes AN/MPN-14 Radar 5CCG Notable Quotes App Notes Bookstore Calculators Education Engineering Organizations Magazines Software,T-Shirts,Coffee Mugs Articles - submitted by RF Cafe visitors Simulators Technical Writings Advertisers Websites RF Cafe Archives Test Notes Slide Rules RF Cascade Workbook RF Stencils for Visio Shapes for Word Thank you for visiting RF Cafe!

RF Cafe Software

RF Cascade Worbook
 RF Cascade Workbook 2005 - RF Cafe
Calculator Workbook
RF Workbench
Smith Chart™ for Visio
Smith Chart™ for Excel
RF & EE Symbols Word
RF Stencils for Visio

Your RF Cafe
Progenitor & Webmaster

Click here to read about RF CafeKirt Blattenberger
BSEE
KB3UON
EIEIO

Carpe Diem!
(Seize the Day!)

5th MOB:
My USAF radar shop

Airplanes and Rockets:
My personal hobby website

Equine Kingdom:
My daughter Sally's horse riding website

Sinewave Voltages - Vpk, Vpk-pk, Vavg, Vrms

A sinewave is defined by the trigonometric sine function. When plotted as voltage (V) as a function of phase (θ), it looks similar to the figure to the right. The waveform repeats every 2p radians (360°), and is symmetrical about the voltage axis (when no DC offset is present). Voltage and current exhibiting cyclic behavior is referred to as alternating; i.e., alternating current (AC). One full cycle is shown here. The basic equation for a sinewave is as follows:

 

     Sinewave equation - RF Cafe

 

There are a number of ways in which the amplitude of a sinewave is referenced, usually as peak voltage (Vpk or Vp), peak-to-peak voltage (Vpp or Vp-p or Vpkpk or Vpk-pk), average voltage (Vav or Vavg), and root-mean-square voltage (Vrms). Peak voltage and peak-to-peak voltage are apparent by looking at the above plot. Root-mean-square and average voltage are not so apparent.

Also see Triangle Wave Voltages and Square Wave Voltages pages.

Root-Mean-Square Voltage (Vrms)

Sinewave voltages : rms, average, peak, peak-peak - RF CafeAs the name implies, Vrms is calculated by taking the square root of the mean average of the square of the voltage in an appropriately chosen interval. In the case of symmetrical waveforms like the sinewave, a quarter cycle faithfully represents all four quarter cycles of the waveform. Therefore, it is acceptable to choose the first quarter cycle, which goes from 0 radians (0°) through p/2 radians (90°).

Vrms is the value indicated by the vast majority of AC voltmeters. It is the value that, when applied across a resistance, produces that same amount of heat that a direct current (DC) voltage of the same magnitude would produce. For example, 1 V applied across a 1 Ω resistor produces 1 W of heat. A 1 Vrms sinewave applied across a 1 Ω resistor also produces 1 W of heat. That 1 Vrms sinewave has a peak voltage of √2 V (≈1.414 V), and a peak-to-peak voltage of 2√2 V  (≈2.828 V).

Since finding a full derivation of the formulas for root-mean-square (Vrms) voltage is difficult, it is done here for you.

 

   RMS voltage formula - RF Cafe 

RMS voltage equation - RF Cafe

 

     So,   Vrms equation - RF Cafe ≈ 0.707 Vpk,   where Square root of 2 (reciprocal) - RF Cafe = 0.70710678118654752440084436210485

 

Average Voltage (Vavg)

As the name implies, Vavg is calculated by taking the average of the voltage in an appropriately chosen interval. In the case of symmetrical waveforms like the sinewave, a quarter cycle faithfully represents all four quarter cycles of the waveform. Therefore, it is acceptable to choose the first quarter cycle, which goes from 0 radians (0°) through p/2 radians (90°).

As with the Vrms formula, a full derivation for the Vavg formula is given here as well.

   Average voltage equation - RF Cafe

 

     So,   Average voltage formula - RF Cafe ≈ 0.636 Vpk,   where 2 over pi - RF Cafe = 0.63661977236758134307553505349006

 

 

 

* I have no idea why we write "Sinewave," but not "Trianglewave" and "Squarewave."

Try Using SEARCH to Find What You Need.  >10,000 Pages Indexed on RF Cafe !

Copyright 1996 - 2016
Webmaster:  Kirt Blattenberger, BSEE - KB3UON
Family Websites:  Airplanes and Rockets | Equine Kingdom

All trademarks, copyrights, patents, and other rights of ownership to images
and text used on the RF Cafe website are hereby acknowledged.