Is it necessary to filter after each stage of doublers?

i want to ask about doublers put in series. After each doubler stage there is a filter pass for 2f. What if we do not filter in some stages? at very high ghz frequency it is possible to put bandpass or lambda/4 at f at 2f output. But at lower frequencies i do not like the mess with smd filters or giant bandpass hairpins. so what happens when few filters will gone away, and only two final stages have ones?

I think that its to do with the dynamic range of the doubler, if its got 4 V at fundemental freq + 2 V at twice fund + V at four times fund which we want to double again, you can see that the fundemental breaking through and the stage producing even more at twice fundemental. Its best for stability that each stage only has its required input and not a lot of unwanted stuff that could excite oscillations.
Frank

You'll get a lot of unwanted sidebands.

The 2*f interstage filter provides high impedance at desired selected frequency, and provide a short circuit to the unwanted frequencies.
Using this filter has the advantage not only to reject unwanted harmonics (and reducing intermods) but the filter can integrate an interstage matching network which helps increasing multiplier efficiency.

if you are doubling a fixed frequency, you often do not need to filter every time you double. In fact, that is why people sometimes use a X4 or X8 circuit.

But it there is a swept input bandwidth, most systems will want you to bandpass filter at the output of each doubler