The RMS Value of a Trapezoidal Waveform – Part 2

In a previous article, MasteringElectronicsDesign.com:How to Derive the RMS Value of A Trapezoidal Waveform – Part 1, I showed how to derive the RMS value of a trapezoidal signal with a flat plateau and different rise/fall time values.  In some applications, the trapezoidal signal plateau is not flat, but rather a ramp, as shown in Figure 1.  A typical example is a DC-DC converter, where the transformer winding current might look like the signal in Figure 1.  Of course, in the DC-DC converter example, the amplitude is current and not voltage.  No matter, the calculations are the same.

This waveform is still considered a trapezoidal waveform. Let’s calculate its RMS value.

trapezoidal-waveform-2Figure 1

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How to Derive the RMS Value of Pulse and Square Waveforms

The RMS value of a pulse waveform can be easily calculated starting with the RMS definition. The pulse waveform is shown in Figure 1. The ratio t1/T is the pulse signal duty-cycle. As shown in other articles in this website (MasteringElectronicsDesign.com:How to Derive the RMS Value of a Trapezoidal Waveform and MasteringElectronicsDesign.com:How to Derive the RMS Value of a Triangle Waveform), the RMS definition is an integral over the signal period as in equation (1).

pulse signalFigure 1

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