Allan Herriman
Guest
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 Posted:
Thu Dec 23, 2004 8:09 am Post subject:
Re: Phase noise units dBc/Hz vs dB-rad^2 /Hz Why are they |
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On 22 Dec 2004 18:43:45 -0800, "Mark" <makolber@yahoo.com> wrote:
| Quote: | Question about measuring phase noise density.
I know the units of dBc/Hz are numerically equal to the units of
dB-rad^2/Hz.
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How do you know this?
| Quote: | I'm trying to understand why this is true.
I know a modulation index (BETA) of 0.1 for example is = 0.1 radians
peak phase deviation and that the first pair of sidebands at this
deviation are (using the narrow band approximation)~= -20*log(BETA/2)=
-26dBc in this example. But 0.1 radians would be -20dB-rad.
So I have a 6 dB error (factor of 2) and the radians SQUARED doesn't
fit in?
So can anyone explain why dBc/Hz and dB-rad^2/Hz are equivalent?
Thanks
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Beta is *peak* angle deviation. You are interested in the RMS angle
deviation, which is (for your sinusoidal example) 1/sqrt(2) of the
amplitude. That's a 3dB error.
SSB phase noise is defined as the average of the power in the upper
and lower sidebands.
For *noise* sidebands, the upper and lower sidebands are not
correlated, so their powers add. Your sinusoidal modulation example
has sidebands that are in phase, so their amplitudes add. This causes
the the other 3dB error.
Regards,
Allan |
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