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What is Normalized Phase Noise?

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Trivial question: What is "Normalized Phase Noise" for PLLs?

For example, in https://www.ti.com/lsds/ti/clock-and-timing/rf-plls-and-synthesizers-products.page , this number is in dBc/Hz and ranges between -226 and -231.

Even more confusing here: **broken link removed** where they write: "Normalized Phase Noise (dBc/rtHz) (dBc/Hz)". Wtf? Hz or rtHz? Makes a big difference ...

Usually phase noise is denoted in dBc/Hz at different offset frequencies. Does "Normalized Phase Noise" mean that the frequency domain shape is just normalized to one over the operation bandwidth? In other words, the integral over the actual phase noise curve equals the normalized phase noise times the bandwidth?

If this is the case, is there a direct way to deduce jitter from this number?

Using the relation SNR = 20*log(1/(2*pi*fc*sigma) and sigma = sqrt(10^(A/10))/2/pi/fc

I arrive at the nice equation:

PN = -SNR - 10log(2B)

(where A is just PN + 10*log(2B) with PN the normalized phase noise in dBc/Hz and 2B the operation bandwidth (factor of 2 because phase noise curve is double sided)

which tells me for example that if I want an SNR of 50dB (due to phase noise) and a bandwidth of 400 MHz I would need a PLL with -139 dBc/Hz?

But this does not match the available numbers (in the range of -230dBc)
 

Thank you!

However, this seems like a completely useless metric to me because it just gives a hint about one single point at the phase noise figure L(f).

Suppose I need 100fs RMS jitter at 2 GHz (i.e., integrated L(f)), how would this normalized phase noise metric help me to find the right product?
 

exp said:
However, this seems like a completely useless metric to me because it just gives a hint about one single point at the phase noise figure L(f).
Click to expand...
No.
In your case, Normalized In-Band 1/f Noise is not defined.
There is no option other than ignoring 1/f Noise.
So worst case value of Lout inside PLL_BW should be estimated via Lnorm.

Again see Figure 14 at page-30 of http://cds.linear.com/docs/en/datasheet/6948f.pdf

exp said:
Suppose I need 100fs RMS jitter at 2 GHz (i.e., integrated L(f)), how would this normalized phase noise metric help me to find the right product?
Click to expand...
Again, there is no option other than ignoring 1/f Noise.
So you have to estimate RMS_Jitter value roughly by the following.

Lout = Lnorm + 10*log10(fpfd) + 20*log10(frf/fpfd)

RMS_Jitter = sqrt(2 * 10**(Lout/10) * PLL_BW) / (2*pi*frf)

frf = 2GHz
fpfd = ?
PLL_BW = ?
 
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    exp

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This is really helpful and great, thanks!

To make sure: PLL_BW is not the loop BW of the PLL or so but the actual signal bandwidth of the receiver? And fpfd is the frequency at the phase detector which is supposed to be the reference clock?

What I am still slightly confused: This formula assumes a constant frequency spectrum for Lout .... However, L(f) consists to first order of multiple log-line segments (e.g. 1-300 Hz, 300 Hz-10kHz, 10 kHz - 30 Mhz ...). To my understanding, Lout just estimates the middle "flat" piece. Is it really reasonable to neglect the rest? What errror can be typically expected?
 

I fully understand your confusion. dBc/Hz was the standard for decades, then some yuppie clueless engineers decided to start using other nomenclatures, and now confusion reigns. just chalk it up to their arrogance of not standing on the shoulders of giants.
 

exp said:
PLL_BW is not the loop BW of the PLL or so
but the actual signal bandwidth of the receiver?
Click to expand...
No.
It has to be loop BW in close loop state of PLL.

exp said:
And fpfd is the frequency at the phase detector which is supposed to be the reference clock?
Click to expand...
If there is no reference divider, fpfd=fref.
See Figure 13 at page-25 of http://cds.linear.com/docs/en/datasheet/6948f.pdf

exp said:
This formula assumes a constant frequency spectrum for Lout ....
Click to expand...
Yes.
It assumes constant Lout over PLL_BW.

exp said:
However, L(f) consists to first order of multiple log-line segments (e.g. 1-300 Hz, 300 Hz-10kHz, 10 kHz - 30 Mhz ...).
Click to expand...
See "LTC6948-4 Phase Noise(fRF=6236MHz)" at page-1 of http://cds.linear.com/docs/en/datasheet/6948f.pdf

exp said:
To my understanding, Lout just estimates the middle "flat" piece.
Is it really reasonable to neglect the rest?
What errror can be typically expected?
Click to expand...
It should be reasonable estimation as far as 1/f noise is not very large.

Again see "LTC6948-4 Phase Noise(fRF=6236MHz)" at page-1 of http://cds.linear.com/docs/en/datasheet/6948f.pdf

See page-9 of http://cds.linear.com/docs/en/datasheet/6948f.pdf

See Figure 8 at page-20 http://www.st.com/web/en/resource/technical/document/datasheet/DM00108283.pdf
 

Ok, great, thanks again!

Let me me show the concrete example where I see the inconsistency:

1zAbZ.jpg


Different noise levels are annotated, along with the loop bandwidth (~450kHz). I know the output frequency is frf=2100 MHz. The PLL is the ADF4153. I am very confident that the reference clock is fpfd=737.28 MHz. According to the datasheet, the input reference can be divided by integers between 1,...,15 (4 bit).

Based on different methods (e.g. https://www.jitterlabs.com/support/calculators/ or the MATLAB script https://www.mathworks.com/matlabcentral/fileexchange/22038-phase-noise-to-jitter/content/Pn2Jitter.m) I can obtain the jitter by integration:

f_Hz = [ 0 100 1000 10e3 100e3 1e6 10e6 30e6 1e9 ];
g_dBc1Hz = [ -77.44 -77.44 -81.42 -87.04 -111.83 -138.26 -159 -169 -200 ];
Jitter = Pn2Jitter(f_Hz, g_dBc1Hz, 2.1e9) = 778fs RMS


But then, using the normalized phase noise along with the calculations you suggest:

Lnorm = -220; % from the datasheet of ADF4153
frf = 2.1e9;
fpfd = 737.28e6/15; % 15 is maximum division according to datasheet
BW_PLL = 450e3; % from the plot

Lout = Lnorm + 10*log10(fpfd) + 20*log10(frf/fpfd);
sigma = sqrt(2 * 10^(Lout/10) * BW_PLL) / (2*pi*frf) = 215.36fs RMS

This is far off from the calculations above ...
 
Last edited:

exp said:
Let me me show the concrete example where I see the inconsistency:
Click to expand...
exp said:
f_Hz = [ 0 100 1000 10e3 100e3 1e6 10e6 30e6 1e9 ];
g_dBc1Hz = [ -77.44 -77.44 -81.42 -87.04 -111.83 -138.26 -159 -169 -200 ];
Jitter = Pn2Jitter(f_Hz, g_dBc1Hz, 2.1e9) = 778fs RMS
But then, using the normalized phase noise along with the calculations you suggest:
.....................................
.....................................
sigma = sqrt(2 * 10^(Lout/10) * BW_PLL) / (2*pi*frf) = 215.36fs RMS
This is far off from the calculations above ...
Click to expand...
Code: 
inv_db10 = @(x) 10.^(x/10);
frf = 2100e6; % [Hz]
Loop_BW = 7e3; % [Hz]
Lout = g_dBc1Hz(3);
RMS_Jitter = sqrt(2 * inv_db10(Lout) * Loop_BW) / (2*pi*frf) / 1e-15;
This code gives followings.
Lout = -81.42[dBc/Hz]
RMS_Jitter = 761.49[fsec]
This value is fairly close to result of "Pn2Jitter(f_Hz, g_dBc1Hz, 2.1e9)".

Do you surely read datasheet of ADF4153 ?
https://www.analog.com/media/en/technical-documentation/data-sheets/ADF4153.pdf

exp said:
I am very confident that the reference clock is fpfd=737.28 MHz.
Click to expand...
It can never be.
Surely read datasheet of ADF4153.
Frequency range of REFIN is guranteeded from 10MHz~250MHz.

exp said:
fpfd = 737.28e6/15; % 15 is maximum division according to datasheet
Click to expand...
This means fpfd=49.152MHz.
It can never be.
Surely read datasheet of ADF4153.
Maximum fpfd of ADF4153 is 32MHz.

exp said:
Different noise levels are annotated,
along with the loop bandwidth (~450kHz).
Click to expand...
It can never be.
Loop_BW of https://snag.gy/1zAbZ.jpg is less than 7kHz.

And line of LoopBW is located at 0.5kHz in https://snag.gy/1zAbZ.jpg
Why ?
How do you get this https://snag.gy/1zAbZ.jpg ?

exp said:
I know the output frequency is frf=2100 MHz.
The PLL is the ADF4153.
Click to expand...
Show me true and correct values of the followings.
frf ?
fpfd ?
Loop_BW ?
Charge Pump Current ?

At least, fpfd can never be 737.28e6/15=49.152MHz.
And Loop_BW can also never be 450kHz.

Attached figure is a result of the following code
Code: 
db10 = @(x) 10 * log10(x);
db20 = @(x) 20 * log10(x);
inv_db10 = @(x) 10.^(x/10);
inv_db20 = @(x) 10.^(x/20);

Lnorm = -220; % [dBc/Hz], Normalized Phase Noise Floor
L1_f = -114; % [dBc/Hz], Normalized 1/f Noise, Measured at 10kHz offset, Normalized to 1GHz

frf_meas = 1000e6; %[Hz]
foffset_meas = 10e3;  %[Hz]

frf = 2.1e9; %[Hz]
fpfd = 0.2e6; %[Hz]

% plot the results (except at DC)
semilogx(f_Hz(2:end), g_dBc1Hz(2:end), 'r', 'Linewidth', 2)

Lout_1 = ( Lnorm + db10(fpfd) + db20(frf/fpfd) ) * ones( size( f_Hz(2:end) ) );
semilogx(f_Hz(2:end), Lout_1, 'g', 'Linewidth', 2)

Lout_2 = L1_f + db10(foffset_meas./f_Hz(2:end)) + db20(frf/frf_meas);
semilogx(f_Hz(2:end), Lout_2, 'c', 'Linewidth', 2)

Lout_3 = db10( inv_db10(Lout_1) + inv_db10(Lout_2) );
semilogx(f_Hz(2:end), Lout_3, 'y', 'Linewidth', 2)
Here fpfd = 200kHz
Again How do you get this https://snag.gy/1zAbZ.jpg ?
Show me true and correct conditions of https://snag.gy/1zAbZ.jpg
 

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