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Oscillators generally work very well at lower frequencies. But at higher frequencies, the oscillators tend to become unstable. A frequency multiplier enables one to keep an oscillator in a stable range and simply multiply the signal to a stable higher frequency for use (of which the possibilities of uses are near endless, e.g. frequency references, analog clocking, ... )
Read this little piece to see reasons and circuit examples:
Many methods exist. Here's an easy one. Assuming a sinewave input signal, convert it to a square wave, and pass it through a bandpass filter tuned to the fifth harmonic. Now you have an output sinewave that is five times the frequency of the input signal.
Another method, that is broadband, is the simple Wein Bridge, (the same ring diode circuit used as rectifier).
As for mains frequency (50 Hz) the output is a rectified, pulsating 100 Hz, so it works at higher frequency.
A series capacitor is needed.
As a rule of thumb, on the µwave region, a doubler (rectifier) shoul'd be driven with + 10 dBm and it loose 13 dB.
Of course the Phase Noise of a doubler increase much times more than 20 log(N).
The Output Phase Noise is ≥ Input Phase Noise + 20 log (2) + Loss + NF (of the Ampli often required).
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