RF Filters and Power Amplifiers

Hi.

Some time ago a simple but quiet interesting doubt appeared in my head: suppose that we have a simple inverse Class D amplifier (Switched Current Mode Class D) followed by a RLC tank. The waveform generated in current is approximately a square wave. My question is: theoretically, the drain efficiency can be as high as 100%.. so, the square wave gives us a fundamental and a lot of harmonics (in theory an infinite number)... If we are filtering all the harmonics we can reach almost 100% efficiency.. my question is: what happens to all the harmonics that are generated? in theory they draw energy from the power supply, but they are rejected from the Load (antenna).. I know that passives, L - C, have a zero dissipation power behaviour, but still this question about the energy persists in my head..

If anyone can take my doubt away I will be very pleased.

With best regards.

The topology you describe has an inductor in the current path. This holds back sudden current changes. Not a lot of harmonics are generated. Current changes are relatively smooth through the inductor.

The voltage applied to the inductor may be rectangular pulses, but this does not necessarily mirror the current waveform through the inductor.

Ok.. it is true. But what about a DC-DC converter where the voltage output is a square wave and the harmonics all filtered.. what happens to the energy that the harmonics pull from the load?

There is also the capacitor's function, typical filtering action. It charges during the crests. It discharges during troughs.

Going back to the class D amplifier... Suppose the inductor value is too small...

In that case the current spikes are more severe. They are not at the fundamental frequency but the switching frequency. The capacitor must tolerate these spikes going back and forth through it, many times a second. (Perhaps this is the harmonic energy which your question refers to?)

The Ampere waveform can be jagged, even if the voltage waveform changes smoothly.

When high power is coming through the system, the capacitor could have several Amperes going back and forth continually. And if the cap has substantial ESR, then it is liable to overheat.

When I say first harmonic or fundamental is the first sinusoid that will have the same period of the switch. But my question is.. what really happens to the harmonics? In a Class B amplifier, at the plain of the transistor's drain we will have a half rectified sinusoidal waveform which has several harmonics.. they all filtered by the Band Pass filter.. what happens to the energy that they carry?

That energy goes to the ground and that is the idea behind filtering them out.

If there are no dissipative circuit elements (e.g. the transistor can be modeled as an ideal switch, L and C are lossless), all harmonics energy is just recirculated. Similar to the apparent harmonic power in mains supply.

So, this means that energy goes to the ground but is stored again in the source? something like that?

Basically. If you were to do a fourier analysis of the currents through the load and tank, then you would find that for all the harmonics the currents and voltages are 90 degrees out of phase, and therefore don't carry any real power.

That makes a lot of sense! Thank you!