Dear Sir:

I would like to have a better understanding of the definition of "single sideband phase noise to carrier ratio per Hz."

I have attached a *.pdf file from a HP Product Note. Please look at page 5 of this product note.

On page 5, Figure 2.2, there is a graph which is intended to define the term "single sideband phase noise to carrier ratio per Hz" by graphical means through a spectrum analyzer display. This graph has been utilized in other Agilent/HP seminars to define the term. The graphical method is the best means to define this term.

However, there is a problem.

If you look at the first plot, the vertical axis is labelled, "A". I read in other HP literature that this "A" denotes amplitude. However, the question remains is which "amplitude" is being referenced - power? voltage? etc.). I don't want to make any assumptions about what the "A" denotes, can you please explicitly tell me what the "A" is intended to denote.

I have a second question and this question references the definition of "single sideband phase noise to carrier ratio per Hz" as defined on page 5. Page 5 defines "single sideband phase noise to carrier ration per Hz" as:

(power density in one phase modulation sideband) / (total signal power)

In an Agilent document entitled, "Phase Noise Measurement Methods and Techniques", by Kay Gheen (2012):

A nearly identical graph is utilized on page 9 and "single sideband phase noise" is defined as:

(Area of 1 Hz bandwidth) / (Total area under the curve)

I have enclosed a link to the *.pdf file:

http://www.home.agilent.com/upload/cmc_upload/All/PhaseNoise_webcast_19Jul12.pdf

My question references the graphical definition of "total signal power" and/or the "total area under the curve".

If you look at the horizontal axis, one can see that this axis can possibly extend to a near infinite number. In other words, there is no boundary to the "total area under the curve."

Let's say I had to teach a class to students and I wanted to define the single sideband phase noise using a spectrum analyzer display and I wanted to define what single sideband phase noise is using Agilent's graphical definition set forth on page 5 of its product note. I want to know where to mark the boundary limits of "area under the curve" so that my graphical definition is consistent with NIST's defintion of single sideband phase noise.

Can you please show me how to mark, or interpret the graph, so that the graphical definition on page 5 of the Agilent product note is consistent with the definition set forth by NIST?

By the way, in the process of writing this message, I had posted a link to Kay Gheen's *.pdf file and while searching for this link to post to you, I had discovered that this *.pdf file was associated with an Agilent webcast. I have not seen this webcast yet. I just found out about it now. If my answer is found in the webcast, you will know why I did not know the answer to my question.

In any case, can someone please answer my question. I would like to validate the graphical definition of "the single sideband phase noise to carrier ratio."

I would like to have a better understanding of the definition of "single sideband phase noise to carrier ratio per Hz."

I have attached a *.pdf file from a HP Product Note. Please look at page 5 of this product note.

On page 5, Figure 2.2, there is a graph which is intended to define the term "single sideband phase noise to carrier ratio per Hz" by graphical means through a spectrum analyzer display. This graph has been utilized in other Agilent/HP seminars to define the term. The graphical method is the best means to define this term.

However, there is a problem.

If you look at the first plot, the vertical axis is labelled, "A". I read in other HP literature that this "A" denotes amplitude. However, the question remains is which "amplitude" is being referenced - power? voltage? etc.). I don't want to make any assumptions about what the "A" denotes, can you please explicitly tell me what the "A" is intended to denote.

I have a second question and this question references the definition of "single sideband phase noise to carrier ratio per Hz" as defined on page 5. Page 5 defines "single sideband phase noise to carrier ration per Hz" as:

(power density in one phase modulation sideband) / (total signal power)

In an Agilent document entitled, "Phase Noise Measurement Methods and Techniques", by Kay Gheen (2012):

A nearly identical graph is utilized on page 9 and "single sideband phase noise" is defined as:

(Area of 1 Hz bandwidth) / (Total area under the curve)

I have enclosed a link to the *.pdf file:

http://www.home.agilent.com/upload/cmc_upload/All/PhaseNoise_webcast_19Jul12.pdf

My question references the graphical definition of "total signal power" and/or the "total area under the curve".

If you look at the horizontal axis, one can see that this axis can possibly extend to a near infinite number. In other words, there is no boundary to the "total area under the curve."

Let's say I had to teach a class to students and I wanted to define the single sideband phase noise using a spectrum analyzer display and I wanted to define what single sideband phase noise is using Agilent's graphical definition set forth on page 5 of its product note. I want to know where to mark the boundary limits of "area under the curve" so that my graphical definition is consistent with NIST's defintion of single sideband phase noise.

Can you please show me how to mark, or interpret the graph, so that the graphical definition on page 5 of the Agilent product note is consistent with the definition set forth by NIST?

By the way, in the process of writing this message, I had posted a link to Kay Gheen's *.pdf file and while searching for this link to post to you, I had discovered that this *.pdf file was associated with an Agilent webcast. I have not seen this webcast yet. I just found out about it now. If my answer is found in the webcast, you will know why I did not know the answer to my question.

In any case, can someone please answer my question. I would like to validate the graphical definition of "the single sideband phase noise to carrier ratio."

I will try to answer your two questions.

The first one was about the HP product note. You will notice that in the text, the plot to which you are referring is referenced as the spectrum of the phase fluctuations, as seen on a spectrum analyzer. Juxtaposed to that plot is one of the sidebands, showing sigma^2 RMS on the y-axis. The purpose of these plots are to give you a qualitative idea of what the display would look like for the phase noise of an oscillator on an ideal spectrum analyzer. The purpose is not to specify exactly what units are on the y-axis. In general, it is safe to assume that the "A" refers to amplitude; it is common for spectrum analyzers to display power on the y-axis. Since power is generally proportional to the square of the voltage, and since you could associate the plot in 2.1b to be a subset of the data in 2.1a, you could then make the assumption that you are on a power scale in plot 2.1a. However, I want to emphasize again that these plots are for qualitative purposes and the exact units of the y-axis are not important for the purposes of the product note.

With regards to your question about the definition of SSB phase noise, I will try to interpret it as best I can. I believe that there may be some confusion as to how to interpret the NIST definition graphically. Let's take a look at some more resources. On page 3 of Agilent's phase noise selection guide (http://cp.literature.agilent.com/litweb/pdf/5990-5729EN.pdf), it states the NIST definition of SSB phase noise: "the ratio of the power density at an offset frequency from the carrier to the total power of the carrier signal." The power density can be calculated graphically as the area under the curve within some band (we would normally normalize to 1 Hz bandwidth) at some offset frequency from the carrier. It seems to me that the real confusion comes from the "total power of the carrier signal." In theory, the total power of the carrier signal would be calculated graphically by integrating the power across all frequencies (negative infinity to infinity), as you suggest. However, as you know, there are limitations due to distortions and noise in the analyzer, possible distortion and other noise (including thermal noise) of the input signal, and interfering signals. If we were to integrate all of this, we would end up with a reading that was much larger than the real power of the carrier signal. In most cases, we can estimate the power of the carrier signal on a spectrum analyzer by using the default RBW and placing a marker on the carrier signal; however, a more accurate method would be to perform a band/interval power calculation. The question once again becomes, what are the limits of integration (bandwidth of our band/interval calculation)? This can be a difficult question and vary depending upon all of the real world limitations that I mentioned. That is why we normally stick to the method of measuring the carrier signal power and allowing that to represent the total signal power. In fact, this is a good assumption and the error is usually not significant. Refer to slide 10 of Kay Gheen's presentation for more information.

Also, there is a GREAT article written by Agilent's Bob Nelson which discusses phase noise measurements and explains the details in a format that is very easy to understand. It is highly recommended as reference material: http://mwrf.com/test-amp-measurement-analyzers/demystify-integrated-phase-deviation-results-phase-noise-measurements

If I did not interpret your questions correctly, please let me know.

Best Regards,

Scott