My understanding is that if a single tone at frequency F is inputted to the frequency doubler, one should observe at its output in the spectrum the same tone but now at a frequency 2F.
However, what happens if this signal is no longer a tone? To make it simpler and to minimize the impact of possible modulation, let's consider this signal now being a wide-band Gaussian noise with a bandwidth B and centered at F. I am wondering when this noise signal encounters the frequency doubler will the doubler make any practical impact on the bandwidth of such a signal.
Practically, can we expect that at the output of the doubler we will now see spectrum of the wideband white noise (with the possible realistic modulation due to the doubler spectrum) centered at 2F and with the same bandwidth B, or with bandwidth 2B, or something else?
Edit (with some additional details about the setup): What is meant here as a frequency doubler/multiplier is a type of PiN diode, such as Cobham DH267. The carrier frequency of the wideband noise signal at the input to the doubler, F, is 6GHz, and bandwidth B of the wideband noise signal is 300 MHz.