22 February, 2007

AC Voltage,Average, RMS values,Form factor,Crest factor

AC Voltage :
A voltage in which the polarity alternates.

Measuremnt of AC magnitde :
AC voltage alternates in polarity and AC current alternates in direction. We know that AC can alternate in a variety of different ways, and by tracing the alternation over time we can plot it as a "waveform." We can measure the rate of alternation by measuring the time it takes for a wave to evolve before it repeats itself (the "period"), and express this as cycles per unit time, or "frequency." In music, frequency is the same as pitch, which is the essential property distinguishing one note from another.

One way to express the intensity, or magnitude (also called the amplitude), of an AC quantity is to measure its peak height on a waveform graph. This is known as the peak or crest value of an AC waveform:


Another way is to measure the total height between opposite peaks. This is known as the peak-to-peak (P-P) value of an AC waveform:


This is the measurement in case of a sinusoidal wave either it may be voltage or current. The measurement definition is same fo the ramining wave shapes also.

Average Value :
One way of expressing the amplitude of different waveshapes in a more equivalent fashion is to mathematically average the values of all the points on a waveform's graph to a single, aggregate number. This amplitude measure is known simply as the average value of the waveform. If we average all the points on the waveform algebraically (that is, to consider their sign, either positive or negative), the average value for most waveforms is technically zero, because all the positive points cancel out all the negative points over a full cycle:
This, of course, will be true for any waveform having equal-area portions above and below the "zero" line of a plot. However, as a practical measure of a waveform's aggregate value, "average" is usually defined as the mathematical mean of all the points' absolute values over a cycle.

Root Mean Square (RMS) Value :
RMS value means , first square all the values, then find the average (mean) of these square values over a complete cycle, and find the square root of this average. That is the RMS value.

The value of an AC voltage is continually changing from zero up to the positive peak, through zero to the negative peak and back to zero again. Clearly for most of the time it is less than the peak voltage, so this is not a good measure of its real effect.

Instead we use the root mean square voltage (VRMS) which is 0.7 of the peak voltage (Vpeak):
VRMS = 0.7 × Vpeak and Vpeak = 1.4 × VRMS
These equations also apply to current. They are only true for sine waves (the most common type of AC) because the 0.7 and 1.4 are different values for other shapes.

The RMS value is the effective value of a varying voltage or current. It is the equivalent steady DC (constant) value which gives the same effect. AC voltmeters and ammeters show the RMS value of the voltage or current.

For pure Sinusoidal : RMS = 0.707 (Peak) , AVG = 0.637 (Peak) , P-P = 2 (Peak).
For pure Square : RMS = Peak , AVG = Peak , P-P = 2 (Peak).
For pure Triangular : RMS = 0.577 (Peak) , AVG = 0.5 (Peak) , P-P = 2 (Peak).

The Crest factor of an AC wave form for instance is given by
Crest factor = Peak Value / RMS Value

The form factor of an AC waveform is the ratio of its peak value divided by its average value
Form factor = Peak Value / Average Value
For more details visit the following sites :
http://www.allaboutcircuits.com/vol_2/chpt_1/3.html
http://www.kpsec.freeuk.com/acdc.htm

1 comment:

Q Tang said...

Very helpful infor. thanks a lot