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https://designers-guide.org/forum/YaBB.pl 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 6th, 2011, 8:23am |
Title: Rms noise value calculation Post by Pashtet on Feb 6th, 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 6th, 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 7th, 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 7th, 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 10th, 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 10th, 2011, 3:48pm Hi Pashtet, you are absolutely right, it should be doubled. |
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