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 a Trapezoidal Waveform – Part 1

In this article I will show you how to calculate the RMS value of a trapezoidal waveform. This periodic waveform is shown in Figure 1. It has a rise time from 0 to t1 and a fall time from t2 to t3. The plateau is between t1 and t2, and the signal is periodic with the period T. If you know this, then you can derive the RMS value of a triangle, square and pulse waveform as well.  Go to How to Derive the RMS Value of a Triangle Waveform and How to Derive the RMS Value of Pulse and Square Waveforms for further reading.

Figure 1

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