An advanced question - sampling an oscillator's signal for analysis

[tomato]

Understood. The objective of the delay line approach is to get an estimate of phase noise and phase noise bandwidth for each oscillator. I need to know if the short-term phase noise of the GPSDO (for which I have no specification) is sufficiently smaller than the other oscillators in order to use it as the reference in a two oscillator configuration. While I may not get phase noise close to the carrier for each oscillator, I should get enough information to reasonably conjecture that the GPSDO has (or does not have) sufficiently lower phase noise than the other oscillators to use it as a reference. The reason I am worried about this (at least for short-term stability characterization) is the GPSDO has an OCXO as the base oscillator that is corrected by the GPS signal periodically. Short-term its stability may be no better than the other OCXOs I have.

You're using the phrase "short term" a lot, yet it has different meanings in different contexts.  Short term as it relates to a GPS disciplined oscillator is orders of magnitude longer than short term as it relates to delay line measurements.

I think you may find that none of the phase noise of the OCXO is "short term", as defined by the delay line.  In other words, all the phase noise is close to the carrier and, therefore, not readily measured by the delay line method.

[dnessett]

You're using the phrase "short term" a lot, yet it has different meanings in different contexts.  Short term as it relates to a GPS disciplined oscillator is orders of magnitude longer than short term as it relates to delay line measurements.

I think you may find that none of the phase noise of the OCXO is "short term", as defined by the delay line.  In other words, all the phase noise is close to the carrier and, therefore, not readily measured by the delay line method.

Let me clarify. I am concerned that when measuring the stability of the GSPDO over a few seconds, its phase noise will be that of an OCXO. If so, using it as the reference for short-term (in this context, a few seconds) experiments may not be valid. It may work fine in the medium term (say minutes, but less than an hour) and the long-term (hours), but if the GPSDO over a few seconds displays phase noise equal to that of a OCXO, I will need to figure out how measure the phase noise of another OCXO (and perhaps the Rubidium oscillator) using a different reference than the GPSDO (say, by buying a low phase noise oscillator).

In regards to the delay line measurements, it is not my objective to establish the complete phase noise characterization of each oscillator using this technique. I just want to see if the GPSDO can be used as a reference in each type of experiment (i.e., short-term (seconds), medium-term (minutes) and long-term (hours)). While I may not be able to measure phase noise close the carrier using the delay line approach for any oscillator, if the GPSDO has less phase noise than another oscillator away from the carrier, then I can conjecture it will have less phase noise near the carrier than the other oscillator.

For example, suppose I measure the phase noise for the GPSDO using the delay line technique and come up with -100 dBc @ 10 Hz, -125 dBc @ 100 Hz and -145 dBc @ 1 KHz. I then measure another oscillator using the delay line technique and come up with -90 dBc @ 10 Hz, -110 dBc @100 Hz, and -120 dBc@ 1 KHz. It is then likely that the phase noise of the GPSDO will be better than the other oscillator for Fourier frequencies nearer to the carrier. This will give me confidence that I can use the GPSDO as the reference oscillator in the two oscillator test setup.

[tomato]

In regards to the delay line measurements, it is not my objective to establish the complete phase noise characterization of each oscillator using this technique. I just want to see if the GPSDO can be used as a reference in each type of experiment (i.e., short-term (seconds), medium-term (minutes) and long-term (hours)). While I may not be able to measure phase noise close the carrier using the delay line approach for any oscillator, if the GPSDO has less phase noise than another oscillator away from the carrier, then I can conjecture it will have less phase noise near the carrier than the other oscillator.

For example, suppose I measure the phase noise for the GPSDO using the delay line technique and come up with -100 dBc @ 10 Hz, -125 dBc @ 100 Hz and -145 dBc @ 1 KHz. I then measure another oscillator using the delay line technique and come up with -90 dBc @ 10 Hz, -110 dBc @100 Hz, and -120 dBc@ 1 KHz. It is then likely that the phase noise of the GPSDO will be better than the other oscillator for Fourier frequencies nearer to the carrier. This will give me confidence that I can use the GPSDO as the reference oscillator in the two oscillator test setup.

In the context of delay line measurements, 10 Hz - 10kHz from the carrier is near the carrier.  You will not be able to measure this with a delay line that is a few hundred feet long.

[dnessett]

In the context of delay line measurements, 10 Hz - 10kHz from the carrier is near the carrier.  You will not be able to measure this with a delay line that is a few hundred feet long.

The delay line will be almost 600 feet long.

[tomato]

The delay line will be almost 600 feet long.

Yes, I know.  You might want to do a quick calculation of how much the amplitude of a 10 Hz sideband is attenuated when measured with a 600' delay line.

Here's another quick sanity check:  Add 1 kHz sidebands to a 10MHz oscillator.  Make a direct measurement of the modulation index with your spectrum analyzer. Then set up a delay line measurement and measure the apparent modulation index at various delay line lengths. Repeat the experiment with 10 kHz, 100 kHz, and 1 MHz sidebands and look for a trend.

[dnessett]

Yes, I know.  You might want to do a quick calculation of how much the amplitude of a 10 Hz sideband is attenuated when measured with a 600' delay line.

Here's another quick sanity check:  Add 1 kHz sidebands to a 10MHz oscillator.  Make a direct measurement of the modulation index with your spectrum analyzer. Then set up a delay line measurement and measure the apparent modulation index at various delay line lengths. Repeat the experiment with 10 kHz, 100 kHz, and 1 MHz sidebands and look for a trend.

For the first calculation, do you mean add a 10 Hz sideband in the frequency domain? This isn't what we are talking about and it would be hard to predict, since this coax attenuation chart only goes down to 1 MHz. However, the attenuation per 100 feet decreases with decreasing frequency, so the ratio of sideband to carrier power would be greater in the delayed signal, making it easier to detect.

However, I presume you mean a 10 Hz signal FM modulating a 10 MHz signal (which is what 10 Hz of phase noise represents). FM modulation produces more than one sideband for a modulating pure tone, so to make things simple, focus on the sidebands nearest to the carrier. They manifest themselves at 9,999,990 Hz and 10,000,010 Hz. These are so close to 10 MHz that they should attenuate at effectively the same rate as the carrier (1.4 dB per 100 feet of RG-58), so the dBc value should remain constant.

The real problem is phase noise for a good oscillator is generally much weaker than the carrier. Detecting these modulating signals is difficult, a problem that has nothing to do with delay lines. For example, the Rubidium spec for 10 Hz is -100 dBc, whereas for 100 Hz it is -125 dBc. This suggests that for a typical oscillator with a Christmas tree shaped spectrum around the carrier (where the phase noise resides) it is easier to detect phase noise closer to the carrier than such noise farther away.

In regards to your second sanity check, I again presume you mean modulate a 10 MHz signal with 1 KHz, 10 KHz, 100 KHz and 1 Mhz. It would be an interesting experiment, but you have left off one parameter, the amplitude of the modulating signal.

[pigrew]

What is the observed phase noise of a rubidium oscillator? I can't find any specs online... Does any equipment directly use the 6.835... GHz signal? Is it less noisy than a quartz oscillator (OCXO)?

I should have read a few more minutes before posting. The RF is synthesized from the 10 MHz signal... so the 10 MHz would be better quality than the 6.8 GHz.

[tomato]

For the first calculation, do you mean add a 10 Hz sideband in the frequency domain?

Sorry, my choice of of the term attenuation was unfortunate, as it led to confusion.  I was referring to attenuation of the signal due to the measurement technique, not due to cable losses.

1) Here is the calculation: If you have a 10 MHz carrier phase modulated at 10 Hz, calculate how large the detected (10 Hz) signal will be if you measure phase with a delay line setup and a 600' delay line.  (You can ignore cable losses for the calculation.)  You don't actually have to do an exact calculation; a "back of the envelope" calculation will still be enlightening.

2) The sanity check is to actually measure some sidebands using both the spectrum analyzer and a delay line setup.  For convenience, modulate the 10 MHz carrier at 1 kHz, 10 kHz, 100 kHz, and 1 MHz. The spectrum analyzer will easily resolve these sidebands and give you a confirmation of the modulation amplitude.  Compare these results to those measured with the delay line.

[dnessett]

Sorry, my choice of of the term attenuation was unfortunate, as it led to confusion.  I was referring to attenuation of the signal due to the measurement technique, not due to cable losses.

1) Here is the calculation: If you have a 10 MHz carrier phase modulated at 10 Hz, calculate how large the detected (10 Hz) signal will be if you measure phase with a delay line setup and a 600' delay line.  (You can ignore cable losses for the calculation.)  You don't actually have to do an exact calculation; a "back of the envelope" calculation will still be enlightening.

I spent yesterday evening and this morning thinking about this and for the life of me, I cannot understand what you are getting at. For a while I thought you were referencing possible non-linearities in the coax for large distances, but that would not entail a "back of the envelope" calculation. In addition, the cable TV services run thousands of feet of coax to distribute TV channels, so I don't think 600' of coax will have significant non-linearities.

If the coax is treated as a linear transmission line and we are to ignore attenuation due to cable losses, then I'm not sure what else to consider. The wavelength of 10 MHz in RG-58 coax is 64.9 feet (see this post), so 584.1 feet will provide a delay of 9 wavelengths. That is, the original and delayed signals will be in phase after the signal traverses a coax of that length. The only attenuation I can think of is that caused by cable losses. If there is some other attenuating mechanism, you will have to mention it explicitlly.

2) The sanity check is to actually measure some sidebands using both the spectrum analyzer and a delay line setup.  For convenience, modulate the 10 MHz carrier at 1 kHz, 10 kHz, 100 kHz, and 1 MHz. The spectrum analyzer will easily resolve these sidebands and give you a confirmation of the modulation amplitude.  Compare these results to those measured with the delay line.

My function generator can only FM modulate signals up to 20 KHz, so I set it up to modulate a 1 KHz signal on a 10 MHz carrier. Figure 1 shows the spectrum produced by that experiment. Markers 1 and 3 give the amplitude of the two nearest sidebands for this modulated signal. At the bottom is a marker table that shows the amplitude for the carrier (marker 2) and the two sidebands. The amplitude of markers 1 and 3 are relative to the carrier (i.e., they are in units of dBc).

Figure 1 -

Figure 2 shows the spectrum produced when that signal is delayed by 183 feet of RG-58 (I have ordered, but not yet received the extra 400 feet I need for the complete delay line). This spectrum shows that the carrier power has decreased by about -3dB. However, the two sidebands have maintained their relative power with respect to the carrier (their relative power actually has slightly increased).

Figure 2 -

So, this suggests that the delay line will maintain or even slightly improve the relative power of the sidebands with respect to the carrier.

[tomato]

I spent yesterday evening and this morning thinking about this and for the life of me, I cannot understand what you are getting at.

We're discussing your latest proposal for measuring the phase noise of on oscillator, using the "delay line" approach.  Follow the ball ...

I plan to start out with a one oscillator test set up (using the delay line approach), to get an estimate of phase noise of each oscillator...

The delay line method is a perfectly good way to make measurements, but you will want to buy a giant spool of coax if you want to do it.  Your (relatively) short delay line will only allow you to see higher frequency phase noise. A much longer delay line is needed if you want to measure phase noise near the carrier.

I think you may find that none of the phase noise of the OCXO is "short term", as defined by the delay line.  In other words, all the phase noise is close to the carrier and, therefore, not readily measured by the delay line method.

In the context of delay line measurements, 10 Hz - 10kHz from the carrier is near the carrier.  You will not be able to measure this with a delay line that is a few hundred feet long.

You might want to do a quick calculation of how much the amplitude of a 10 Hz sideband is attenuated when measured with a 600' delay line.

Here is the calculation: If you have a 10 MHz carrier phase modulated at 10 Hz, calculate how large the detected (10 Hz) signal will be if you measure phase with a delay line setup and a 600' delay line.  (You can ignore cable losses for the calculation.)

[dnessett]

Follow the ball ...

I think the ball you have launched bounces all over the place and I am having trouble following it. You write:

1) Here is the calculation: If you have a 10 MHz carrier phase modulated at 10 Hz, calculate how large the detected (10 Hz) signal will be if you measure phase with a delay line setup and a 600' delay line.  (You can ignore cable losses for the calculation.)  You don't actually have to do an exact calculation; a "back of the envelope" calculation will still be enlightening.

You suggest calculating the strength of a 10 Hz signal that modulates a 10 MHz carrier after transiting a 600 foot coax, but I am to ignore cable losses. What property of the coax am I to use to carry out this calculation? What effects the diminution of modulating signal strength over a coax other than attenuation due to its lumped elements (fundamentally, its resistance per unit length)?

I measured the diminution of a 1 KHz modulating signal on a 10 MHz carrier over 183 feet of coax and found that it looses strength at the same rate as the carrier. What makes 10 Hz modulating 10 MHz over 600 feet different?

What are you trying to get at in your proposal:

If you have a 10 MHz carrier phase modulated at 10 Hz, calculate how large the detected (10 Hz) signal will be if you measure phase with a delay line setup and a 600' delay line.

If you mean the delayed signal amplitude will be lower than the non-delayed signal, that is pretty obvious (and is a result of cable losses you suggest I ignore). However, the AD8302 uses logarithmic amplifiers to ensure the two signals are at roughly the same amplitude before presenting them to the phase detector circuit. If you mean something else, just state it. Stop trying to mimic Aristotle Socrates (identified the wrong ancient Greek philosopher).

So far, I am unconvinced that the delay line approach has any problem that the two oscillator approach doesn't have, other than a higher noise floor. In addition, I think digging the noise signal out of the modulated oscillator signal is by far the hardest problem to solve. This is true whether one uses the one or two oscillator setup.

[tomato]

I think the ball you have launched bounces all over the place and I am having trouble following it. You write:

1) Here is the calculation: If you have a 10 MHz carrier phase modulated at 10 Hz, calculate how large the detected (10 Hz) signal will be if you measure phase with a delay line setup and a 600' delay line.  (You can ignore cable losses for the calculation.)  You don't actually have to do an exact calculation; a "back of the envelope" calculation will still be enlightening.

You suggest calculating the strength of a 10 Hz signal that modulates a 10 MHz carrier after transiting a 600 foot coax, but I am to ignore cable losses. What property of the coax am I to use to carry out this calculation? What effects the diminution of modulating signal strength over a coax other than attenuation due to its lumped elements (fundamentally, its resistance per unit length)?

I measured the diminution of a 1 KHz modulating signal on a 10 MHz carrier over 183 feet of coax and found that it looses strength at the same rate as the carrier. What makes 10 Hz modulating 10 MHz over 600 feet different?

What are you trying to get at in your proposal:

If you have a 10 MHz carrier phase modulated at 10 Hz, calculate how large the detected (10 Hz) signal will be if you measure phase with a delay line setup and a 600' delay line.

If you mean the delayed signal amplitude will be lower than the non-delayed signal, that is pretty obvious (and is a result of cable losses you suggest I ignore). However, the AD8302 uses logarithmic amplifiers to ensure the two signals are at roughly the same amplitude before presenting them to the phase detector circuit. If you mean something else, just state it. Stop trying to mimic Aristotle.

So far, I am unconvinced that the delay line approach has any problem that the two oscillator approach doesn't have, other than a higher noise floor. In addition, I think digging the noise signal out of the modulated oscillator signal is by far the hardest problem to solve. This is true whether one uses the one or two oscillator setup.

The delay line method has one serious limitation.  I stated what it was five times in my previous post.  I can't state any more plainly.

The issue is not the properties of the cable.  It is about the measurement method, i.e how does a delay line allow an oscillator to serve as its own phase reference, and what are the consequences?

One more time:
"If you have a 10 MHz carrier phase modulated at 10 Hz, calculate how large the detected (10 Hz) signal will be if you measure phase with a delay line setup and a 600' delay line.  (You can ignore cable losses for the calculation.)" 

You can approach the problem from another angle, by considering these three questions:
1. What do you see with the delay line method if the delay line has zero length?
2. What do you see with the delay line method if the delay line is infinitely long?
3. What do you see with the delay line method if the delay line has a non-zero, finite length?

[rhb]

Not to put too sharp a point on it, but:

 sin(w*t) - sin(w*(t+dt)) = 2*cos(w*(2*t+dt)/2)*sin(w*dt/2)

So the result is a cosine wave at over twice the frequency and the maximum amplitude goes to *zero* at certain delays.

You can use a delay line if one of two conditions is true:

you can vary the frequency of the oscillator over a sufficiently large range
you can vary the delay over a sufficiently large range

The required delay and frequency relationship is controlled by the sin(w*dt) term.

Fundamentally you are trying to apply a technique more suited to UHF and above to HF without bothering to make actual calculations.  Rather like when I handed you the solution from Papoulis for a problem and you complained that the upper limit of integration was not infinity.

Would you *please* do the brain dead obvious experiment of try each oscillator as the reference for the SA and post the spectra for the other oscillators?  That's 12 plots.  You just might learn something in the process.

[dnessett]

Not to put too sharp a point on it, but:

 sin(w*t) - sin(w*(t+dt)) = 2*cos(w*(2*t+dt)/2)*sin(w*dt/2)

So the result is a cosine wave at over twice the frequency and the maximum amplitude goes to *zero* at certain delays.

Your formulation is incorrect:

When you combine the generated and delayed signals at the mixer to get the phase difference, the result is not:

sin(w*t) - sin(w*(t+dt)), it is:

sin(w*t)*sin(w*(t+dt))
= 1/2 [cos((w*t)-w*(t+dt)) - cos((w*t)+w*(t+dt))]
= 1/2 [cos(-w*dt) - cos((w*(2t+dt))].

This will be zero when:

cos(-w*dt) = cos(w*(2t+dt)) or when:

-w*dt = w*(2t+dt) + 2*n*PI or equivalently when:

(-w*dt)-w*(2t+dt) = 2*n*PI, for some integer n.

This occurs when w*(t+dt) = -n*PI. Without loss of generality, we can dispense with the negative sign, since n can be either a positive or negative integer and eliding the minus sign has no effect on the equation.

Solving for dt,

dt = (n*PI/w)-t

The mixed signal will be zero only at those points in time that satisfy this equation. This is checked by substituting the value of dt into the mixer equation:

sin(w*t)*sin(w*(t+dt)) = sin(w*t)*sin(w*(t+[(n*PI/w)-t]))
= sin(w*t)*sin(n*PI) = 0

Note that we could have solved for t:

 t = (n*PI/w)-dt
 
 Substituting this into the mixer equation yields:
 
 sin(w*t)*sin(w*(t+dt)) = sin(w*[(n*PI/w)-dt])*sin(w*([(n*PI/w)-dt]+dt))
 = sin(n*PI-w*dt)*sin(n*PI-w*dt+w*dt) = sin(n*PI-w*dt)*sin(n*PI) = 0
 
Either approach yields the same result. There is no value of dt for which the mixer equation is zero for all values of t.

[dnessett]

In the context of delay line measurements, 10 Hz - 10kHz from the carrier is near the carrier.  You will not be able to measure this with a delay line that is a few hundred feet long.

I am going to go out on a limb and say you are wrong. There is no structural reason why the delay line (aka one oscillator) set up cannot measure phase noise arbitrarily close to the carrier. According to Phase Noise and AM noise measurement in the Frequency Domain, the noise floor of the one oscillator set up is reduced compared to the two oscillator approach. The graph given in support of this shows the noise floor rising as the the Fourier frequency of the phase noise approaches that of the carrier. Unfortunately, the justification for this graph is another paper that I have not been able to acquire. So, there is no way to check the argument that led to that graph. However, the text makes no mention of a "structural problem" that leads to the result.

There are plenty of practical problems with measuring phase noise close to the carrier. However, these are not specific to the one oscillator set up. They apply equally to the two oscillator set up. I will describe them in a separate post.

So, on to the argument that the delay line/one oscillator measurement set up is not structurally deficient as a measurement technique. This argument follows your lead in assuming transmission lines are perfect (not lossy and linear) and it assumes all electronic circuits are perfect (e.g., filters have cutoff frequencies that are exact - they do not drop off over a range of frequencies). In this regard, the argument assumes a bandpass filter that passes only the carrier frequency and the carrier frequency plus 1 Hz. This filter is placed on the oscillator output before the signal enters one side of the mixer and the delay line. So, the signal presented to the double balanced mixer on both sides comprises a 2 Hz band limited to the carrier frequency and the carrier frequency plus 1 Hz. Since the delay line is perfect, the amplitudes of the generated and delayed signal are exactly equal.

To keep the argument simple, it is assumed that the generated signal is either at the carrier frequency or at the carrier frequency plus 1. No frequencies between these two are possible. Also, it is assumed that we are interested in SSB measurements. That is why the filter does not admit a band comprising the carrier frequency plus or minus 1.

Consider the output of the mixer. Represent the carrier frequency by f_c. There are 3 situations to consider:

1) Both the generated and delayed signal are at f_c. The mixer/phase detector will indicate in-phase.

2) Either the generated or delayed signal is at the carrier frequency and the other is at the f_c+1. The mixer/phase detector will indicate out-of-phase.

3) Both the generated and delayed signal are at f_c+1. The mixer/phase detector will indicate in-phase.

The spectral density associated with the 1 Hz phase noise will be proportional to the fraction of time the mixer is (Changed 7-29-28) in situation 2 divided by the fraction of time the mixer is in either situation 1 or 3 (I thought about this later and now think the formula should be:) in either situation 2 or 3 divided by the fraction of time the mixer is in situation 1. (The exact constant of proportionality requires further thought - but I probably won't spend any time on it, since this is a conceptual argument, not a proposal for an actual measurement setup)

I am completely aware that this setup framework is impossible to achieve in practice. However, it demonstrates that the one oscillator set up is structurally capable of measuring phase noise as close to the carrier as one may wish.

If you disagree or find fault with this argument, I welcome you to provide a counter-argument or refutation. However, I am not interested in playing 20 questions with you. So, if you follow your recent habit of patronizating discourse, I probably will not respond.

[dnessett]

There has been a lot of discussion recently on this thread about measuring phase noise close to the carrier. I have thought about this a bit and have concluded some of the implied objectives in those posts are unrealistic for a hobbiest, such as I. This post documents the rationale behind that conclusion.

Some have proposed that the one oscillator (delay line) set up will have difficulty measuring phase noise close to the carrier due to structural reasons. I have provided an argument against this view and await comment. However, in those posts it is suggested that the one oscillator setup would not be able to measure 1 Hz phase noise associated with a 10 MHz oscillator. While I don't believe there are structural reasons why the single oscillator setup could not achieve this, there are plenty of practical reasons why this objective is outside the capabilities of a hobbiest whether the one or two oscillator set up is used.

1 Hz phase noise is that which occurs when an oscillator's instantaneous frequency is at the carrier frequency plus/minus 1 Hz. In the case of a 10 MHz oscillator, this frequency is either 10,000,001 Hz or 9,999,999 Hz. Consider the latter case. The period of a 10 MHz oscillator is 100 ns. The period of an oscillator vibrating at 9,999,999 Hz is 1/9,999,999 = 100.00001 ns. The difference between the 10 MHz and 9,999,999 Hz periods is 10 femto-seconds. Just to get a feel for the realm in which this period resides, visible light has a period roughly in the 2 femto-second range.

What phase difference exists when comparing a 10 MHz signal with a 9,999,999 Hz signal? One degree of phase difference for a 10 MHz signal corresponds to roughly 278 pico-seconds. One degree is about .0088 radians. So, for a 10 MHz signal 1 milli-radian in phase difference corresponds to roughly 31.8 pico-seconds. In order to discriminate between a 10 MHz signal and a 9,999,999 Hz signal would require a phase detector capable of resolving phase differences on the order of 36 micro-degrees (.000036 degrees) or .000036*.0088 = 317 nano-radians.

This is obviously well outside the capabilities of a typical hobbiest. It may be something that a national laboratory would be equipped to handle, but not an amateur.

This raises the question of the limits inherent to the AD8302 in measuring phase noise. The spec gives a figure of 1 degree per 10mV of output voltage by the phase detector on the AD8302. I could find nowhere in the spec where it is indicated that 1 degree is the limit of its phase difference precision. Phase difference precision is not given.

So, I have to assume it cannot provide better precision than 1 degree. Given this, what is the lower bound of phase noise frequency it is capable of measuring for a 10 MHz oscillator. As stated previously, one degree for 10 MHz corresponds to about 278 ps. Since the period of a 10 MHz oscillator is 100 ns, the frequency of a signal with a period one degree less is 1/((100-.278)*10e-9) = 10,027,877 MHz. So, the AD8302 can only discrimiate phase noise at about 28 Khz and above.

Given the oscillators I wish to characterize, this isn't very good. So, my plan is to get some experience measuring phase noise with the AD8302 and then acquire a more precise phase detector, perhaps one attached to a high-precision PLL. To get into the tens of Hz I would need a phase detector able to discriminate differences at least as low as .001 degrees for two signals in the neighborhood of 10 MHz.

Anyone have any suggestions of ICs that might meet those requirements?

[tomato]

I am going to go out on a limb and say you are wrong. There is no structural reason why the delay line (aka one oscillator) set up cannot measure phase noise arbitrarily close to the carrier.

According to Phase Noise and AM noise measurement in the Frequency Domain, the noise floor of the one oscillator set up is reduced compared to the two oscillator approach. The graph given in support of this shows the noise floor rising as the the Fourier frequency of the phase noise approaches that of the carrier. Unfortunately, the justification for this graph is another paper that I have not been able to acquire. So, there is no way to check the argument that led to that graph. However, the text makes no mention of a "structural problem" that leads to the result.

There are plenty of practical problems with measuring phase noise close to the carrier. However, these are not specific to the one oscillator set up. They apply equally to the two oscillator set up. I will describe them in a separate post.

So, on to the argument that the delay line/one oscillator measurement set up is not structurally deficient as a measurement technique. This argument follows your lead in assuming transmission lines are perfect (not lossy and linear) and it assumes all electronic circuits are perfect (e.g., filters have cutoff frequencies that are exact - they do not drop off over a range of frequencies). In this regard, the argument assumes a bandpass filter that passes only the carrier frequency and the carrier frequency plus 1 Hz. This filter is placed on the oscillator output before the signal enters one side of the mixer and the delay line. So, the signal presented to the double balanced mixer on both sides comprises a 2 Hz band limited to the carrier frequency and the carrier frequency plus 1 Hz. Since the delay line is perfect, the amplitudes of the generated and delayed signal are exactly equal.

See equation 84. It tells you why the delay line method has limitations. (But I won't ask you any questions about it.)

If you disagree or find fault with this argument, I welcome you to provide a counter-argument or refutation. However, I am not interested in playing 20 questions with you. So, if you follow your recent habit of patronizating discourse, I probably will not respond.

I apologize if you feel I've been patronizing.  A few posts back you wrote the following:

But, in order to learn, I have to understand what I am doing and why... I don't want to make the same mistakes others have turned into knowledge.

... my point is that just telling someone new to the field to do something is useful, but limited. It is better to explain why they should do it - what is the experience on which the advise is based.

I stated what the limitations of the delay line method are, but you don't seem to want to simply be told the answers.  I have posed questions designed to make you think critically about what you're doing, with the goal of leading you to the answers, but you have now rejected that approach.  I don't know any other way to convey the information to you.

[awallin]

While I don't believe there are structural reasons why the single oscillator setup could not achieve this, there are plenty of practical reasons why this objective is outside the capabilities of a hobbiest whether the one or two oscillator set up is used.

depends on the level of hobbyist...

software defined radio, digitizes two 10MHz signals REF and DUT, downcoversion, low-pass filtering, and decimation on FPGA:
https://arxiv.org/abs/1605.03505
around -140dBc/Hz for 10MHz signals, or 7e-14 @ 1s ADEV in 1 Hz BW.
this is with an Ettus/NI N210 which is about 1800eur new or about 800eur on e-bay.

Andrew Holme has some impressive stuff here:
http://www.aholme.co.uk/PhaseNoise/Main.htm
to me it looks like a xilinx dev-board, then an ADC-dev board on the FMC-connector, and some home-made front-ends on that.
Probably a bit more $$/eur but still within reach of advanced hobbyist.
Looks like he is using the cross-spectrum method (4 ADCs, two for REF, two for DUT) which overcomes the ADC-noise floor - given enough averaging time.

YMMV with cheaper two-channel SDRs (like red-pitaya or similar). Noise floor should scale with bit-depth, so if you are just into frequency comparisons of Rb-clocks/GPSDOs an 8-bit two-channel SDR might be enough. If H-masers is more of a thing for you then look at 14-bit or 16-bit SDRs. It would be good to come up with common gnu-radio and UI software for this, so that time-nuts worldwide could evaluate and compare the bang-for-buck of different SDR setups.

AW

[dnessett]

YMMV with cheaper two-channel SDRs (like red-pitaya or similar). Noise floor should scale with bit-depth, so if you are just into frequency comparisons of Rb-clocks/GPSDOs an 8-bit two-channel SDR might be enough. If H-masers is more of a thing for you then look at 14-bit or 16-bit SDRs. It would be good to come up with common gnu-radio and UI software for this, so that time-nuts worldwide could evaluate and compare the bang-for-buck of different SDR setups.

The red-pitaya looks intriguing. From what I have read so far, it appears that it is not open hardware, so when you say "similar", I presume you do not mean a clone. Can you point me anywhere that might reveal what systems are considered "similar" or mention them yourself?

Added later: One thing the red-pitaya doesn't have is a high precision phase difference detector, which was what my original query sought. Anyone have information on such a device (preferably an IC with ~ .001 degree precision).

[dnessett]

YMMV with cheaper two-channel SDRs (like red-pitaya or similar). Noise floor should scale with bit-depth, so if you are just into frequency comparisons of Rb-clocks/GPSDOs an 8-bit two-channel SDR might be enough. If H-masers is more of a thing for you then look at 14-bit or 16-bit SDRs. It would be good to come up with common gnu-radio and UI software for this, so that time-nuts worldwide could evaluate and compare the bang-for-buck of different SDR setups.

An alternative to measuring phase differences between a reference and DUT using hardware would be to utilize the two inputs on the red-pitaya and attempt to do this in software after the signals are captured. The red-pitaya supports 125 Msa/s so each sample is 8 ns apart. So, one approach would be to observe when a signal transitions from negative to positive and extrapolate from the two voltages (the first at the negative sample and the second at the positive sample) to obtain the time when the signal crossed zero. Doing so for both the reference and DUT signals would allow the computation of an estimate of their phase difference. However, in thinking about this, there seems to be at least one problem.

At 10 MHz, phase noise of 100 Hz represents a difference in zero crossing time between the ref and DUT of ~ 1 ps (after subtracting any constant phase differences due to things like the signal propagation through the test setup). But, an ADC doesn't provide an instantaneous quantization of its input. In particular there is settling time involved. This indicates two issues. First, the variance of the settling time of one ADC is going to be non-zero, the voltage value for the negative sample and positive sample will have errors. Note, this is not due to quantization error, it is due to variance in the settling time.

More importantly, the two ADCs will not be perfectly synchronized, so the difference between the time one produces a negative/positive sample pair and the time the other produces such a pair would have some uncertainty. If the two were not controled by the same sampling clock, this uncertainty could be as much as almost 8 ns. Even if they are controlled by the same sampling clock, the uncertainty is unlikely to be on the order of 1 ps. (Added later to clarify: It is likely to be greater)

I could find nowhere in the specs where sampling synchronization between the two ADCs is described or where time bounds on the sampling time between them is given. If this information exists somewhere and someone knows where it is, would they provide a pointer to it?

[tautech]

Stumbled on this thread about a Fluke counter that just might give to the info you need for oscillator analysis:
https://www.eevblog.com/forum/testgear/fluke-pm6690-12-digits-frequency-counter/

Lots of examples of what it can do later in the thread.

[dnessett]

Stumbled on this thread about a Fluke counter that just might give to the info you need for oscillator analysis:
https://www.eevblog.com/forum/testgear/fluke-pm6690-12-digits-frequency-counter/

Lots of examples of what it can do later in the thread.

Thanks. I'll give the thread a look-over.

[dnessett]

Stumbled on this thread about a Fluke counter that just might give to the info you need for oscillator analysis:
https://www.eevblog.com/forum/testgear/fluke-pm6690-12-digits-frequency-counter/

Lots of examples of what it can do later in the thread.

I didn't find the discussion in the thread over-exciting, but I downloaded the PM6690 operator's manual and read sections. The material I found most interesting was the phase function, which measures phase differences between input signals A and B. I then went to the back of the manual, which gives the instrument's specifications.

The material on the phase function is a bit disappointing. First, in regards to phase measurement uncertainties, the spec states the following: "NOTE. Phase is an auxiliary measurement function, intended to give an indication, with no guaranteed specification." So, it seems phase measurements are not reliable.

Second, when I read the specification on phase resolution, it is 0.1 degree between 1 MHz and 10 MHz. This is somewhat better than the AD8302 (<1 degree), but given that a used PM6690 will set me back at least $300 (probably more), I am reluctant to invest that much for only a small increase in precision. I am thinking of experiments that would provide measurements of the AD8302's phase measurement precision, since the data sheet doesn't really give a figure.

Anyway, thanks for thinking of this project and forwarding the information you did. I am happy to look at material that might provide a solution to the problems I face. In the future if you run into something else you think might help, please don't hesitate to mention it.

[Vgkid]

The HP 5335a has 0.1deg phase resolution. It is 30Hz - 1MHz , though.

[dnessett]

The HP 5335a has 0.1deg phase resolution. It is 30Hz - 1MHz , though.

Thanks. However, I need something that will measure phase differences for a 10 MHz signal. I am looking for anything (instrument, IC) that has a precision of .001 degree, although given the lack of success I have experienced, I am now willing to consider something that provides .01 degree precision.