Paul Jorgenson KE7HR
The synth puts out a more or less square wave which is worked on by the subsequent stages of amplification then filtering. A square wave is the fundamental and all the harmonics. I recall one guy that posted a spectrum plot of the raw output from the Si5351 with evenly spaced spurs out to around 1 GHz. Just what was expected from a square wave.
Most really useful amplifiers have some non-linear properties. Kit built stuff can be quite variable. The harmonic content has to be dealt with to keep from interfering with others. A LPF reduces the harmonics and just leaves the fundamental as a, hopefully, nice sine wave.
The design example that I did and the filters constructed and measured were not dealing with a non-linear waveform - the test gear has a nice signal. A spectrum analyzer will need to be used to see the output from a real amplifier using the filters. It may be quite possible that the amplifier has some "self harmonic suppression" in the way that the signal is being amplified and the LPF has less to do and will therefore have a lower "spike" at the harmonics even though the filter has less suppression at the harmonic frequency. Tradeoffs are everywhere! The large combination of tests reference on the QRP Labs harmonics page attests to how different parts placements and ordering have an effect on the performance.
I am impressed by the constructed filter matching what the software said it should be doing. When you play with parts values in the software, it is easy to see what becomes critical to the filter shape. The software is free, it just takes a bit of time to learn what is going on.