Why do we need multiple stages of multiplication? Can one stage be used (filter+amp)?

As i read from many articles, the classical approach to multiple frequency is using such scheme:
1. fed signal to nonlinear device (diode/fet/etc)
2. filter out second harmonic
3. amplify harmonic
and so on.... For example, for x8 multiplication there is 3 nonlinear elements and 3 band pass filters, and some amplifiers.

Also there is triplers depending on how original oscillation wave is clipped.

In case of frequency comb generator, or if oscillator+amp itself produces some harmonics at x8 frequency, why we can't just put a band pass filter and two amplification stages (before and after band-pass)?

Is it do something with phase noise, etc? Can comb generator be practically used as an oscillator at certain frequency (band-passed and amplified)?

Thanks!

Frequency multiplication while it follows your general procedure, is often a complex design.

If you only need to use second, third, or fourth harmonic, the you need to carefully consider the filtering structure. Using "a non-linear" device certainly generates a comb of harmonics but their relative power varies with the components used, the signal source as well as the load.

Using varactor multipiers often looks attractive from the point of efficiency but their design is tricky and their behavior strongly depends on the frequency and matching. Not all diodes work well.

Recently using "active" frequency multipliers became common. It is now easy to find suitable microwave and mm-wave amplifiers, and the only remaining problem is a good filtering.
What is difficult is to operate such multiplier chain over a wide band. Then in many cases filtering is not possible. Using wideband amplifiers also causes thermal noise to affect the load (mixers,etc.)

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The phase noise is mostly generated in the primary (reference) oscillator. Then it is scaled according the the equation

PNext = 20 log N xPNref +3 [dBc/Hz], where N is the ratio of output to reference frequency.

PN contribution of amplifiers exists but is usually 20-30 dB below that of the scaled reference PN.

Using mutipliers directly as oscillators is possible but not often used (harmonic synchronization). Phase-locked oscillators locked to a reference harmonic is now preferred.

Thank you!
In case i use active device, there is Gain vs Frequency qurve (in datasheet).
For example, if gain is good at 1Ghz and very poor at 5Ghz, can this device be used to multiply 1Ghz up to 5Ghz (5th harmonic)?
After band-pass filter use other active device with good 5Ghz gain to amplify. Or both devices should have good gain at 5Ghz?
I do not see any reason that good-gain-1GHz active device can "absorb" or "smooth" harmonics, but maybe i am wrong..

Everything depends on spectrum purity and efficiency of your frequency multiplier. If you use an amplifier with a low gain at output frequency, you get a low output power. If it is an amplifier, it also has its linearity; some devices are good multipliers if overdriven; but a hard overdrive can burn them.

Designing frequency multipliers is an art; usually there are choices and the art consists in selecting the best option.

yes you can use X8 and bandpass filter it out. However, depending on your spurious requirements, that may not be possible. You bandpass filter would have to pass 8xFin, but reject 7XFin and 9xFin by a lot of dB. And if Fin tunes over some frequency band, the rejection becomes even harder to meet. So, if your only option is a 20 pole bandpass filter.....you have to abandon that approach and go back to X2..filter..X2....filter...X2...filter, where the filters are easier to make.