Average Voltage in AC Waveforms – Definition, Formula and Measurement

Introduction

Whether it is a sine wave, square wave, or triangular wave, the average voltage (or average current) of a periodic waveform is equal to the equivalent DC value of that alternating waveform.

The average (or mean) value of a waveform is defined as the area under one complete cycle of the waveform divided by the time period. In other words, it represents the sum of all instantaneous values over one time period (T) divided by that total time.

In electrical engineering, the terms average voltage, mean voltage, and average current are used for both
AC waveforms and DC rectification calculations. The symbols V_AV and I_AV are commonly used to represent average voltage and average current respectively.

Why Average Value in AC is Important

Unlike DC, where voltage and current remain constant with time, the magnitude of AC quantities continuously changes. Therefore, calculating their exact value is more challenging. To represent the magnitude of an alternating signal, different terms are used such as:

• Peak Value
• Peak-to-Peak Value
• RMS (Root Mean Square) Value
• Instantaneous Value
• Average (Mean) Value

Knowing the average voltage and average current is very useful in many circuit analysis applications. In fact, most rectifier-type multimeters measure the average AC voltage first, and then convert that value into an RMS reading for display.

Average Value of an Alternating Waveform

The average value of an alternating waveform can be determined by calculating the mean of all mid-ordinate values over one complete cycle. This is done by adding together each instantaneous value of the waveform and dividing the total by the number of values.

Mathematically, the average voltage is given by:

V_AV = (1 / T) ∫ v(t) dt    (over one complete cycle)

This equation shows that the average voltage is the integral (area) of the instantaneous voltage over one full time period, divided by the total time for one cycle.

Conclusion

The concept of average voltage is essential for understanding the behavior of AC circuits, rectifiers, and signal processing systems. Although AC values vary with time, the average value provides a meaningful DC-equivalent quantity that can be used for analysis and measurement.