How to determine the power rating of an output LC filter
As the behavior of cored inductors will vary with the DC operating conditions and the spectral content of the applied voltage, it is difficult to provide a unique &quot;power rating&quot; for inductors. Capacitors are a bit simpler to evaluate in that respect, but the situation is similar.
Inductors: There are two main factors. These are the saturation (1) of the core material and the temperature rise (2). The inductor should also be able to withstand the voltage across it, but this is not usually a problem.
1)
The cores in inductors are used in part to contain the magnetic field created by the coils but mostly to increase the magnetic permeability of the magnetic circuit so that inductors can be made smaller and with less coils. However, as the magnetic field in the core increases, there comes a point where the permeability starts to decrease. This is the onset of saturation. Various materials have differing steepness in the &quot;knee&quot; of this relation, with ferrites tending to have a rather sharp decrease while iron powders display a more gradual decrease in permeability. Of course, reality is more complex as this saturation curve have a dependency on the frequency of the magnetic field so this curve is often measured near DC in datasheets. As a saturated inductor is not an inductor anymore (its inductance drops), this constitutes a first &quot;power limit&quot; because the magnetic field is proportional to the current in the coils.
In your case, low audio frequencies are near enough DC to make saturation a relevant constraint. So, knowing the impedance of your load at, say, 20Hz, compute the peak output current. The saturation current of your inductor shall be above that for good performance. Something like 5A in your case.
2)
The temperature rise factors can be approached as follows. Core materials have maximum allowable temperature and based on questions of reliability and safety, one should determine an allowed temperature rise. Then, depending on the desired efficiency, cooling available and maximum size, this determines a maximum power dissipation. I won't go into the details of estimating temperature rise for a given power dissipation in a given device, but rough estimates can be found in various application notes on heatsinking such as:
$$ \Delta T \approx \left(\frac{1000 P}{A}\right)^{0.83},$$
where delta T is the temperature rise above ambient in Kelvins, P is the dissipated power in Watts and A is the exposed area of the device in cm^2.
The dissipated power is the sum of the windings losses and the core losses. The winding losses are as a first approximation simply
$$ P_{Windings} = R_{Windings} I_{RMS}^2.$$
There are additional losses due to proximity effects and gap losses (if using a gapped inductor) but these can be rather difficult to estimate. However, these losses can be quite substantial in some case as in your case. Again, some estimates are obtained from application notes.
The core losses come are inherent to the core itself and depend on frequency. One first estimates the frequency content of the current in the inductor then uses the loss curves in datasheet to arrive at an estimate. In you case, you could estimate the frequency content of your signal as the carrier and, say, 1kHz, to represent the audio signal. Concretely speaking, most inductors will not really be lossy at the audio frequencies where the bulk of the power is concentrated for typical signal (unless you were to use an iron lamination core inductor intended for mains frequency applications which you should, of course, not do). This leaves the carrier. As those integrated IC use quite high switching frequencies, you will need low-loss core materials in the 0.1-10 MHz frequencies. Something like micrometal type-2 toroids or well built gapped (to prevent saturation) ferrites.
Thus, if you chose a low loss material with appropriate (look at tables) wire gauge for the current, it will be fine, power-wise.
Capacitor: The filter you display includes an RC snubber (which will also need a good low-dissipation capacitor!) that is important to damp the output filter under certain load conditions (such as no loads!). Other wise, the voltage peak might become quite high. If the filter is well-damped, then the voltage on the filter capacitors will essentially remain within the rails. So, use a safety margin and pick a voltage rating accordingly.
Then, the capacitor must tolerate the ripple current that will be applied to it. Audio frequencies should not pose too much of a problem, but the carrier frequency will be shunted through the capacitor. Compute the filter impedance at that frequency to estimate the RMS current through the capacitor and select one accordingly. Also a similar issue to core losses arise in capacitor as dielectric losses. Polyester film can get quite lossy in the MHz frequencies. Polypropylene is a good low-loss dielectric as are some ceramics (e.g.: C0G, NPO). However, for your power levels, a polyester film cap of the correct voltage rating will be sufficient.
Other issues: Not just the power rating is important here. You will want a minimum of linearity in your components as the amplifier topology is pre-filter feedback. You should ideally not use iron powder core materials intended for use in DC/DC converter. Use RF application toroids or gapped ferrite inductors. The physical construction is also important here so that the interwindings capacitance does not shunt the inductor at the frequencies of interest. Using a shielded inductor or laying toroids flat on a ground plane will go a long way to reduce emitted EMI.