What is the derivation process for calculating the effective value of trapezoidal wave current?

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What is the derivation process for calculating the effective value of trapezoidal wave current? [Copy link]

 

What is the derivation process of trapezoidal wave current effective value calculation? It is the calculation of the effective value of the current in the CCM mode of the transformer.

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The calculation of the effective value of any waveform is the same: square the instantaneous value, integrate, average, and take the square root.

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The picture is reproduced from "Circuit Analysis", edited by Zeng Hui, Wuhan University of Technology Press, page 148.

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As long as we write out the function i(t) of current changing with time , we can calculate the effective value of the current.

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It is actually easier to calculate the effective value of trapezoidal wave current than sine wave. The top of the trapezoidal wave is a straight line, which is a linear function. The integration of a linear function is simpler than that of a sine function, and the integration result is a quadratic function.