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Measurements >> Phase Noise and Jitter Measurements >> Rms noise value calculation
https://designers-guide.org/forum/YaBB.pl?num=1297009423

Message started by Pashtet on Feb 6^th, 2011, 8:23am

Title: Rms noise value calculation
Post by Pashtet on Feb 6^th, 2011, 8:23am

Hello, friends.
When we measure phase noise of VCO the output curve is in dBc/Hz. But if i want to find rms noise, for example, in 1KHz-1MHz range i get result in degrees or radians.
So my question is the following - what are the mathematical relation between these values, i.e. how i can derive mathematically rms noise in degrees having phase noise curve in dBc/Hz?

Title: Re: Rms noise value calculation
Post by vp1953 on Feb 6^th, 2011, 10:41am

Hi Pashtet,

This is a quick derivation so if I have made any mistakes below, feel free to correct me.

Integrate the phase noise from 1kHz to 1MHz. Now you have the rms peak noise relative to carrier (call it Vnoise, bear in mind that Vnoise is actually a ratio of the noise voltage to the carrier amplitude since the units are in dbc). Convert Vnoise from logarithmic unit dBc to actual ratio - call it Vnoise-converted. Take arcsin(Vnoise-converted) and this should give the phase noise in degrees or radians assuming the output voltage is sinusoidal.

Title: Re: Rms noise value calculation
Post by Pashtet on Feb 7^th, 2011, 10:26am

Hello
As you can see from attached picture the average level of noise in 10K-100K offset is near -83 dBc/Hz. So if we integrate we get -83+10*log10(90K)=-83+49.5=-33.5 dBc. -33.5 dBc results in power(10, -3.35)= 4.5*e-4. asin(4.5*e-4)= 4.5*e-4 rad but on the picture i see 1.49*pi/180 = 2.6*e-2 rad :(
Correct me pls if i'm mistaken

Title: Re: Rms noise value calculation
Post by vp1953 on Feb 7^th, 2011, 2:05pm

Hi Pashtet,

The power ratio is 4.6e-4. This still needs to converted to a voltage ratio before doing the arcsin. So the voltage ratio is sqrt(4.6e-4) which is approx 2.2e-2 somewhat close to your measured 2.6e-2

Title: Re: Rms noise value calculation
Post by Pashtet on Feb 10^th, 2011, 7:38am

Hi vp1953,
thanks for your output.
i agree with you that one should convert dBc into actual ratio treating as voltages, not as powers. But i also think that before doing it we should double the integral power of noise - so the total calculations would be the following:
-84+10log10(90K)=-84+49.5=-34.5 dBc
double the noise -34.5+3 = -31.5 dBc
converting into actual ratio 10**(-31.5/20)=0.0266
taking arcsin(0.0266)=0.0266 rad - that's very close to exact 0.026.

Title: Re: Rms noise value calculation
Post by vp1953 on Feb 10^th, 2011, 3:48pm

Hi Pashtet,

you are absolutely right, it should be doubled.