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Pulse Width Modulation (PWM)

The most common switching technique, where the duty cycle of the switching pulses is varied relative to a high-frequency carrier signal. The output voltage is approximated by a series of rectangular pulses.
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The statement of the theorem

Let VdcV_{dc} be the DC bus voltage and Vc(t)V_{c}(t) be the high-frequency triangular carrier signal. The switching signal si(t)s_i(t) for phase ii is generated by comparing the modulating signal mi(t)m_i(t) (e.g., sinusoidal reference) with Vc(t)V_{c}(t): si(t)={1if mi(t)>Vc(t)0if mi(t)<Vc(t)undefinedif mi(t)=Vc(t) s_i(t) = \begin{cases} 1 & \text{if } m_i(t) > V_{c}(t) \\ 0 & \text{if } m_i(t) < V_{c}(t) \\ \text{undefined} & \text{if } m_i(t) = V_{c}(t) \end{cases} The output voltage is then approximated by the duty cycle δi=Vdc2TonTsw\delta_i = \frac{V_{dc}}{2} \frac{T_{on}}{T_{sw}}.