Bridges - Part IV: Half-Bridge with output filter

Which filter? LC! If your inductive load requires a reduced ripple current or voltage, you may add an output LC filter but...this becomes a synchronous buck! Yes, you can use a current-controlled buck to drive the load with the required current and improved EMI/ripple performance. Look at the image below as a reference.

Since you want to drive an averaged current in the load and the additional LC filter is just adding a ripple reduction feature, the well-known half bridge formulas are still valid. $$V_{load,avg} = \frac{V_{sup} T_{on}}{T} = V_{sup} D$$ $$I_{load,avg} = \frac{V_{load,avg}}{R_{load}}$$

Both the voltage across the load and the current in the load are a sinusoid superimposed to a constant value (ideally a constant).

Now, the LC filter must be designed and its components must be chosen following the parameters listed below: