Using [latex]\sin^2\theta+\cos^2\theta=1[/latex], the harmonic magnitude simplifies to Cn=Vnπ2−2cos⁡(2πnD)C_n=\frac{V}{n\pi}\sqrt{2-2\cos(2\pi nD)} Using the identity [latex]1-\cos(2x)=2\sin^2x[/latex], Cn=2Vnπ|sin⁡(πnD)|C_n=\frac{2V}{n\pi}\left|\sin(\pi nD)\right| Therefore, the magnitude of the [latex]n[/latex]th harmonic is Cn=2Vnπ|sin⁡(πnD)|\boxed{C_n=\frac{2V}{n\pi}\left|\sin(\pi nD)\right|}

Rectangular Waveform with Arbitrary Duty Cycle Before deriving the Fourier series, consider a simple periodic rectangular waveform. This waveform is one of the most important examples in power electronics because many switching waveforms can be...

Before starting with the Fourier series, it is important to understand a few basic properties of periodic waveforms. In power electronics, many important voltage and current waveforms are periodic. Examples include the switching-node voltage of...

Power electronic converters use semiconductor switches to control the flow of electrical energy.