a question about phase noise calculation

[lily1981216]

Hi, everyone! I see a formula about phase noise. I don't know the meaning of it and how it is derived? Can anybody give me any explanation? Or, please introduce some books or papers about the formula derivation. And the formula is presented as

 

[WimRFP]

Hello,

Phase noise is often expressed as the noise density, PSD [W/Hz], referenced to the carrier power [W] at a certain frequency offset from the carrier.

Phase noise, Side band noise = (PSD (at offset) ) / (carrier power) [1/Hz]

When you convert this to decibels, you get dBc/Hz.
The "c" denotes that the carrier power is taken as reference.

So when you have a spectrum of a Local Oscillator:
Pcar = 1dBm, noise power at 10 kHz offset = -80dBm with an RBW setting of 300Hz.

Noise power = PSD*BW (assuming flat Power Spectral Density within the BW).

You measured noise power -80 dBm, to find the PSD, you have to subtract 10*log(300) = 24.8 dB. So

PSD = -80dBm - 24.8dBHz = -104.8 dBm/Hz (at 10 kHz from carrier).

Now Phase Noise = -104.8 dBm/Hz – 1 dBm = -105.8dBc/Hz @ 10kHz offset.

This definition doesn't make any difference between amplitude and phase noise as it is just a ratio of powers.

 

[lily1981216]

Hello,

Phase noise is often expressed as the noise density, PSD [W/Hz], referenced to the carrier power [W] at a certain frequency offset from the carrier.

Phase noise, Side band noise = (PSD (at offset) ) / (carrier power) [1/Hz]

When you convert this to decibels, you get dBc/Hz.
The "c" denotes that the carrier power is taken as reference.

So when you have a spectrum of a Local Oscillator:
Pcar = 1dBm, noise power at 10 kHz offset = -80dBm with an RBW setting of 300Hz.

Noise power = PSD*BW (assuming flat Power Spectral Density within the BW).

You measured noise power -80 dBm, to find the PSD, you have to subtract 10*log(300) = 24.8 dB. So

PSD = -80dBm - 24.8dBHz = -104.8 dBm/Hz (at 10 kHz from carrier).

Now Phase Noise = -104.8 dBm/Hz – 1 dBm = -105.8dBc/Hz @ 10kHz offset.

This definition doesn't make any difference between amplitude and phase noise as it is just a ratio of powers.

Hi, WimRFP

Thank you! I know the definition you referd to. Usually the definition is used in some papers and books. But I have seen another formula to caculate the phase noise which is described in the image I uploaded. I think the formula is used to derive the phase noise of a reciever when the carrier power, the output SNR and so on are known. But I don't know what each item of the formula means, for example the blocker power. And could you tell me how the formula is derived or some books introducing it?

 

[WimRFP]

Hello,

I know understand your application. It is when receiving a weak signal, while on the adjacent channel a strong signal is present. Due to the phase noise of the LO, signal from the adjacent channel leaks into the IF where your wanted signal is.

Assume Padj = RF power of signal in adjacent channel, Prf is power in wanted channel

Power that appears into your IF (assuming 0dB insertion loss for the mixer) from adjacent channel:

PIFn = Padj*(phase noise)*BW

Phase noise in W/Hz @offset, BW = bandwidth of IF (Hz).

For good reception you need a certain S/N ratio, so the wanted RF signal must be at least above:

PIF = Prf > (S/N ratio)*PIFn This results in:

Prf > (S/N ratio)*Padj*(phase noise)*BW in dB's:

dBPrf > dBSNR + dBPadj + dBphnoise + 10log(BW)

So:

dBph.noise < dBprf - dBSNR - dBpadj - 10log(BW)

This equals your formula, Sdesired = dBprf, Sblocker = dBpadj.

 

[lily1981216]

Hello,

I know understand your application. It is when receiving a weak signal, while on the adjacent channel a strong signal is present. Due to the phase noise of the LO, signal from the adjacent channel leaks into the IF where your wanted signal is.

Assume Padj = RF power of signal in adjacent channel, Prf is power in wanted channel

Power that appears into your IF (assuming 0dB insertion loss for the mixer) from adjacent channel:

PIFn = Padj*(phase noise)*BW

Phase noise in W/Hz @offset, BW = bandwidth of IF (Hz).

For good reception you need a certain S/N ratio, so the wanted RF signal must be at least above:

PIF = Prf > (S/N ratio)*PIFn This results in:

Prf > (S/N ratio)*Padj*(phase noise)*BW in dB's:

dBPrf > dBSNR + dBPadj + dBphnoise + 10log(BW)

So:

dBph.noise < dBprf - dBSNR - dBpadj - 10log(BW)

This equals your formula, Sdesired = dBprf, Sblocker = dBpadj.

Thank you very much! I'm sorry I'm late for replying to you. Your explanation help me a lot! I have clicked helped. And thanks again!