# Phase Noise and Multi-carrier Frequency conversion

I have a oscillator with a phase noise mask that was represented in dBc at specific offsets from a carrier.

Two options for a multicarrier signal going into a converter, apply the phase noise mask (dBc/Hz) on the total signal power of a multichannel signal (multi-carrier or multiple subcarriers - however you call it) or the dBc is applied on each individual power of the channels. dBc/Hz is a meaningless value until its changed into dBW/Hz. My question is whether in a mixer with a multi-channel signal, to apply phase noise is it applied against total signal power or each individual channel/subcarrier/carrier power...

Representing the oscillator with phase noise spectrum as one number, but noting that in reality it covers a bandwidth.

$$Oscillator=Ae^{i \theta }$$

Representing the signal with 3 channels or 3 carriers as below, but noting that in reality each channel covers a bandwidth

$$Signal=e^{i x } + e^{i x }+e^{i x }$$

Then the conversion process is just a multiplication (but is it really this simple multiplication for multicarrier?).

$${Signal} \times {Oscillator} =Ae^{i \theta } (e^{i x } + e^{i x }+e^{i x })=Ae^{i (x+ \theta ) } + Ae^{i (x+ \theta )}+Ae^{i (x+ \theta )}$$

This means the same phase noise mask is applied onto each channel or carrier and in this case the phase noise contribution is based on total signal power going into the converter.

It cannot be this simple multiplication because applying the same phase noise mask where it is based on a dBc of total carrier power dramatically increases the EVM from the phase noise in multicarrier situation. Basically 2 carriers gives a 3 dB worse EVM, 4 carriers is 6 dB worse EVM and 8 carriers is 9 dB worse EVM.

But if the phase noise dBc is applied on each individual channel or carrier power then how is that working in real physical world, a signal is multiplied by an LO and that LO has the phase noise thats being imparted onto the signal where that signal is composed of many channels or carriers.