The slides below show a time domain simulation for an idealized Class-J amplifier based on an example in the book RF Power Amplifiers for Wireless Communications, 2nd ed, by Steve C. Cripps.

This example ran well in QucsStudio in both the Transient and the Harmonic Balance simulators.  It uses a simple output impedance matching network.

Many attempts and using a harmonic tuner instead of the output network ran into various convergence troubles.

Perhaps a better approach is an a priori design of the output matching networks based on load-line analysis, as is done in the Youtube video by Matt Ozalas (Keysight), or in the Excel spreadsheet tool, PA_waves, from Cripps's book.

Follow-on work:  

• Load-line / Waveform design with equations.

• Continuous Class-B to Class-J example.