Phase noise

Mon Aug 30, 2010 10:30 am   

I've seen this formula quoted without explanation by two different sources:

P/N(dbc)= PNF+20logN+10logFr,
where
PNF is technology dependent Phase Noise Floor.
N is the main division rate.
Fr is the reference frequency.

I don't understand the PNF+10logFr terms.

I'm familiar with adding 20logN to reference phase noise to calculate the
"multiplied-up" phase noise at the VCO, assuming perfect phase detector and
divider. The above seems to neglect reference noise and focuses on
imperfect divider/phase detector technology.

What is PNF and why 10logFr?

TIA

Mon Aug 30, 2010 1:30 pm   

On 8/30/2010 5:30 AM, Andrew Holme wrote:

I haven't seen it written like that, but it's reasonable for something
like an app note where you don't want to go into too much depth and you
aren't responsible for the outcome. ;)

PNF seems to be a fudge factor that hides most of the actual physics,
like I_S in the Ebers-Moll equation.

The 10 log Fr term is the reference oscillator jitter. The RMS phase
fluctuations due to additive noise (such as the noise of an oscillator
with good ALC) is

<delta_phi> = sqrt[ P_noise /(2 * P_carrier)],

and the phase noise power is proportional to the square of <delta_phi>.
The noise bandwidth of the oscillator is proportional to the centre
frequency, assuming constant resonator Q, so the reference channel noise
goes as 10 log F_r, at least under the above assumptions.

Cheers

Phil Hobbs



--
Dr Philip C D Hobbs
Principal
ElectroOptical Innovations
55 Orchard Rd
Briarcliff Manor NY 10510
845-480-2058
hobbs at electrooptical dot net
http://electrooptical.net

Tue Aug 31, 2010 2:32 am   

The 20*log(N) is simply the transfer function of (vout/vin) of the
loop.

The other stuff is a function of vin.

Do this, write a simple transfer function for a basic loop with, Kd,
Kv, Fs and 1/N, for gains of the det, vco, filter and divder.

It’ll be clear.

Tue Aug 31, 2010 2:32 am   

The 20*log(N) is simply the transfer function of (vout/vin) of the
loop.

The other stuff is a function of vin.

Do this, write a simple transfer function for a basic loop with, Kd,
Kv, Fs and 1/N, for the gain of det, vco,filter and div..

It’ll be clear.