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1996 -
2016

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Kirt Blattenberger,

BSEE
- KB3UON

RF Cafe began life in 1996 as "RF Tools" in an AOL screen name web space totaling 2 MB. Its primary purpose was to provide me with ready access to commonly needed formulas and reference material while performing my work as an RF system and circuit design engineer. The Internet was still largely an unknown entity at the time and not much was available in the form of WYSIWYG ...

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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:

There are a number of ways in which the amplitude of a sinewave is referenced, usually as peak voltage (V_{pk}
or V_{p}), peak-to-peak voltage (V_{pp} or V_{p-p} or V_{pkpk} or V_{pk-pk}),
average voltage (V_{av} or V_{avg}), and root-mean-square voltage (V_{rms}). 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.

As
the name implies, V_{rms} 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°).

V_{rms} 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 V_{rms} sinewave applied
across a 1 Ω resistor also produces 1 W of heat. That 1 V_{rms} 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 (V_{rms}) voltage is difficult, it
is done here for you.

**So, **
≈ 0.707 V_{pk}, where
= 0.70710678118654752440084436210485

As the name implies, V_{avg} 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 V_{rms} formula, a full derivation for the V_{avg} formula is given here as well.

**So, **
≈ 0.636 V_{pk,} where
= 0.63661977236758134307553505349006

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