So if I want to have the best efficiency I need all 3; R, L and C in series?
Tentatively, yes. I also forgot to say series RLC can get by on less amperes, even though the incoming square waves need to be greater voltage amplitude.
My observations come from playing with simulations. Your real-life circuit may show different results.
Series LCR, 100 ohm load. Resonant frequency 50 Hz, shown at bottom right. (This readout only appears if I include the extraneous components.)
LC filter low-pass filter, similar to butterworth type (or 2nd-order bass crossover).
In the second case I think the sinewave distorts more with small changes in L or C or R.
There are numerous variations and configurations, which ought to be examined too.
Also there is the PWM sine wave method, with its own filtering requirements.
If I use a step up transformer to couple to the load then I don't really need a greater amplitude for the topology of RLC in series, right?
A transformer complicates things. It will require another run of simulations to get any idea about what voltage you want to come from the secondary, etc.
My simple experiments consisted of adjusting the square wave amplitude until I obtained 340 V sine peaks at the load. When I changed component values in the butterworth style LC filter, it caused large jumps in output voltage.
If I have a coax cable air core or very low loss core VHF transformer I shouldn't have much efficiency loss from the step up transformer, right?
I guess I am not familiar enough with this type of transformer to answer.
Perhaps it applies to a class E of a different nature than I have been talking about?