RMS Jitter From Phase Noise

Dear Grant,

I've tried to answer your questions as best I can below.

Shawn

> To get RMS Jitter, in radians, from Phase Noise you must integrate the Phase

> Noise.  What are the units of integrated Phase Noise and how do they cancel.

> The equation I am currently using for this is A = Phase Noise (L(f)) + 10*

> log10(frequency2- frequency1) and to generate the RMS Jitter value in radians

> I am using sqrt(2*10^(A/10)).

If one is given the phase noise characteristic, as defined by L(f) in dBc/Hz, then over specific frequency range [f2,f1], the rms jitter in radians and in units of time are found as follows:

1. Integrate the function L(f) between f2 and f1

2. The rms jitter expressed in radians is (2*[Integral(L(f) between f2 and f1]))^0.50

3. The rms jitter expressed in units of time for the carrier frequency fc is [(2*[Integral(L(f) between f2 and f1)])^0.50]/(2pi*fc)

> Additionally, what are the units for 10*log10(frequency2- frequency1) and if L

> (f) is the ratio of Pcarrier and Poffset in dBm, and that has units of dBc/Hz

> , what would be the units if it were converted to a linear value.

The integration of L(f) is done in the linear frequency domain. The units of the integral are radian^2 as seen from [2] above. The units of L(f) are 1/Hz. The units remain the same when converted to a linear value since the quantity still represents a ratio.

> Follow up question. Since L(f) is the ratio of Poffset and Pcarrier(L(f) = Po/

> Pc), it follows that if you increase Pcarrier you decrease L(f), which in turn

> decreases Jitter. If this is true, then one could remove Jitter by increasing

> the power of the carrier. Is this true?

The general answer to your comment is yes - with some caveats. If the random or deterministic noise of concern does not increase proportionally with the carrier amplitude, then increasing the waveform amplitude is a common method used to reduce the magnitude of the jitter over a specific frequency range. However, this method quickly can reach a point of diminishing returns as the added power can make the design non-competitive.

I hope this provides some help!

Dear Grant,

I've tried to answer your questions as best I can below.

Shawn

> To get RMS Jitter, in radians, from Phase Noise you must integrate the Phase

> Noise.  What are the units of integrated Phase Noise and how do they cancel.

> The equation I am currently using for this is A = Phase Noise (L(f)) + 10*

> log10(frequency2- frequency1) and to generate the RMS Jitter value in radians

> I am using sqrt(2*10^(A/10)).

If one is given the phase noise characteristic, as defined by L(f) in dBc/Hz, then over specific frequency range [f2,f1], the rms jitter in radians and in units of time are found as follows:

1. Integrate the function L(f) between f2 and f1

2. The rms jitter expressed in radians is (2*[Integral(L(f) between f2 and f1]))^0.50

3. The rms jitter expressed in units of time for the carrier frequency fc is [(2*[Integral(L(f) between f2 and f1)])^0.50]/(2pi*fc)

> Additionally, what are the units for 10*log10(frequency2- frequency1) and if L

> (f) is the ratio of Pcarrier and Poffset in dBm, and that has units of dBc/Hz

> , what would be the units if it were converted to a linear value.

The integration of L(f) is done in the linear frequency domain. The units of the integral are radian^2 as seen from [2] above. The units of L(f) are 1/Hz. The units remain the same when converted to a linear value since the quantity still represents a ratio.

> Follow up question. Since L(f) is the ratio of Poffset and Pcarrier(L(f) = Po/

> Pc), it follows that if you increase Pcarrier you decrease L(f), which in turn

> decreases Jitter. If this is true, then one could remove Jitter by increasing

> the power of the carrier. Is this true?

The general answer to your comment is yes - with some caveats. If the random or deterministic noise of concern does not increase proportionally with the carrier amplitude, then increasing the waveform amplitude is a common method used to reduce the magnitude of the jitter over a specific frequency range. However, this method quickly can reach a point of diminishing returns as the added power can make the design non-competitive.

I hope this provides some help!