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Transistor Switch and PWM

A transistor switch can connect and disconnect a load very quickly. If the switch is periodically on and off, the load sees an average voltage.

For an ideal switch with supply voltage \(U_{\rm dc}\):

\[ \begin{align*} \overline{u}_{\rm L} = \frac{1}{T}\int_0^T u_{\rm L}(t)\,{\rm d}t = \frac{T_{\rm on}}{T}U_{\rm dc}. \end{align*} \]

The duty cycle is

\[ \begin{align*} d=\frac{T_{\rm on}}{T}. \end{align*} \]

Thus

\[ \begin{align*} \boxed{ \overline{u}_{\rm L}=dU_{\rm dc} } \end{align*} \]