When
plotted as voltage (V) as a function of phase (θ), a square wave looks similar to the figure to the right. The
waveform repeats every 2
π 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 square
wave is as follows:
There are a number of ways in which the amplitude of a square wave 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
Sinewave Voltages and
Triangle Wave Voltages page.
Root-Mean-Square
Voltage (V_{rms})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 square wave, 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
π/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} square wave applied across a 1 Ω resistor
also produces 1 W of heat. That 1 V
_{rms} square wave has a peak voltage of 1 V, and a peak-to-peak
voltage of 2 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, V_{rms} = V_{pk}
Average Voltage (V_{avg})
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
square wave, 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
π/2 radians (90°).
As with the V_{rms} formula, a full derivation for the V_{avg}
formula is given here as well.
So, V
_{avg} = V
_{pk}
* I have no idea why we write "Sinewave," but not "Trianglewave" and
"Squarewave."