Waveform RMS and Average Values

Sine Wave
Full Wave Rectified
Half Wave Rectified
AC Superposed on DC
Periodic Half Sinusoids
Square Wave
Sawtooth Wave
Trapezoidal Wave

The standard formula for calculating the RMS (Root Mean Square) values for a waveform, I(t), is:

Equation for Determining the RMS Value of a Waveform

Equation for Determining the RMS Value of a Waveform

The tables below show equations for calculating the typical waveform RMS and average values.

Current Wave Shape

Configuration

IRMS

IAVG

Diagram for a Sine Wave RMS Calculation

Diagram for a Sine Wave RMS Calculation

Sine Wave

RMS Value for a Sine Wave

0

Current Wave Shape

Configuration

IRMS

IAVG

Diagram for a (Full Wave) Rectified Sine Wave RMS Calculation

Diagram for a (Full Wave) Rectified Sine Wave RMS Calculation

Full Wave Rectified Sine Wave

RMS Value for a (Full Wave) Rectified Sine Wave

0.637Ipk

Current Wave Shape

Configuration

IRMS

IAVG

Diagram for a Half Wave Rectified Sine Wave RMS Calculation

Diagram for a Half Wave Rectified Sine Wave RMS Calculation

Half Wave Rectified Sine Wave

RMS Value for a Half Wave Rectified Sine Wave

0.318Ipk

Current Wave Shape

Configuration

IRMS

IAVG

Diagram for a Sine Wave With a DC Offset RMS Calculation

Diagram for a Sine Wave With a DC Offset RMS Calculation

Direct Current with Superposed Sine Wave

RMS Value for a Sine Wave With a DC Offset

Idc

Current Wave Shape

Configuration

IRMS

IAVG

Diagram for a Repetitive Half Sinusoid Waveform RMS Calculation

Diagram for a Repetitive Half Sinusoid Waveform RMS Calculation

Half-Sinusoids of Duration T and Frequency f

RMS Value for a Repetitive Half Sinusoid Waveform

(2fIpkT)/

p

Current Wave Shape

Configuration

IRMS

IAVG

Diagram for a Repetitive Square Wave RMS Calculation

Diagram for a Repetitive Square Wave RMS Calculation

Square Waves of Duration T and Frequency f

RMS Value for a Repetitive Square Wave

fIpkT

Current Wave Shape

Configuration

IRMS

IAVG

Diagram for a Repetitive Sawtooth Waveform RMS Calculation

Diagram for a Repetitive Sawtooth Waveform RMS Calculation

Sawtooth Waveform of Duration T and Frequency f

RMS Value for a Repetitive Sawtooth Waveform

0.5fIpkT

Current Wave Shape

Configuration

IRMS

IAVG

Diagram for a Repetitive Trapezoidal Waveform RMS Calculation

Diagram for a Repetitive Trapezoidal Waveform RMS Calculation

Trapezoidal Waveform of Frequency f

RMS Value for a Repetitive Trapezoidal Waveform

fIpk(

d+T)


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