Can a frequency multiplier (e.g. doubler) impact signal bandwidth?

Question

My understanding is that if a single tone at frequency F is input to the frequency doubler, one should observe at its output in the spectrum the same tone but now at a frequency 2F.

What happens if this signal is no longer a tone?

To make it simpler and to minimize the impact of possible modulation, 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.

Answer 1

What you'll get is a whole lot of intermodulation distortion, which at its worst will create a wideband noise spectrum and drown out any useful signals.

A frequency doubler in its mathematically purest form is a mixer that gets fed two identical signals and multiplies them. In reality, you'll approximate the multiplication with a non-linear element (i.e. a diode) and a band-pass that removes unwanted frequency components. In effect, you purposefully distort the signal to generate harmonics and filter out the one(s) you want. To get higher-order harmonics, you can use effects such as diode snap-off, as commonly done in the PIN diode multipliers you mentioned.

If you feed a signal into such a frequency multiplier that isn't a pure sinewave, the signal will effectively turn into wideband garbage as it'll get mixed with itself, producing sum and difference frequencies of every combination of any number of points on its entire spectrum. You're essentially mixing two baseband signals together.

In short: A frequency multiplier based on a non-linear element just turns into a very bad mixer when you feed it a signal that isn't a pure sinewave.

Any mixer is also a frequency multiplier, and almost all frequency multipliers are also (bad) mixers. The difference is in the harmonic content and the filtering applied to the output.

A mixer without any filtering at its output actually produces not only the desired sum and difference frequencies, but also the doubled input frequencies. You have to add a bandpass at the output to select only the signal you're interested in.